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Page No 82:

Question 1:

Write the fraction representing the shaded portion:
(i) Figure
(ii) Figure
(iii) Figure
(iv) Figure
(v) Figure
(vi) Figure

Answer:

(i) The shaded portion is 3 parts of the whole figure.
     34            
(ii) The shaded portion is 1 parts of the whole figure.
      14      
(iii) The shaded portion is 2 parts of the whole figure.
     23        
(iv) The shaded portion is 3 parts of the whole figure.
     310              
(v)The shaded portion is 4 parts of the whole figure.
     49          
(vi) The shaded portion is 3 parts of the whole figure.
     38

Page No 82:

Question 2:

Shade 49 of the given figure.
Figure

Answer:

Page No 82:

Question 3:

In the given figure, if we say that the shaded region is 14, then identify the error in it.
Figure

Answer:

The given rectangle is not divided into four equal parts.

Thus, the shaded region is not equal to 14 of the whole.

Page No 82:

Question 4:

Write a fraction for each of the following:
(i) three-fourths
(ii) four-sevenths
(iii) two-fifths
(iv) three-tenths
(v) one-eighth
(vi) five-sixths
(vii) eight-ninths
(viii) seven-twelfths

Answer:

(i) 34        (ii) 47             (iii) 25           (iv) 310           (v) 18
(vi) 56             (vii)89              (viii) 712



Page No 83:

Question 5:

Write down the numerator and the denominator of each of the fractions given below:
(i) 49
(ii) 611
(iii) 815
(iv) 1217
(v) 51

Answer:

     Numerator        Denominator
(i) 4                         9
(ii) 6                       11
(iii) 8                      15
(iv) 12                     17
(v) 5                        1

Page No 83:

Question 6:

Write down the fraction in which
(i) numerator = 3, denominator = 8
(ii) numerator = 5, denominator = 12
(iii) numerator = 7, denominator = 16
(iv) numerator = 8, denominator = 15

Answer:

(i)38        (ii) 512          (iii)716             (iv) 815

Page No 83:

Question 7:

Write down the fractional number for each of the following:
(i) 23
(ii) 49
(iii) 25
(iv) 710
(v) 13
(vi) 34
(vii) 38
(viii) 914
(ix) 511
(x) 615

Answer:

(i) two-thirds
(ii) four-ninths
(iii) two-fifths
(iv) seven-tenths
(v) one-thirds
(vi) three-fourths
(vii) three-eighths
(viii) nine-fourteenths 
(ix) five-elevenths
(x) six-fifteenths

Page No 83:

Question 8:

What fraction of an hour is 24 minutes?

Answer:

We know: 1 hour = 60 minutes
∴ The required fraction = 2460=25  

 

Page No 83:

Question 9:

How many natural numbers are there from 2 to 10? What fraction of them are prime numbers?

Answer:

There are total 9 natural numbers from 2 to 10. They are 2, 3, 4, 5, 6, 7, 8, 9, 10.
Out of these natural numbers, 2, 3, 5, 7 are the prime numbers.
∴ The required fraction = 49.

Page No 83:

Question 10:

Determine:
(i) 23 of 15 pens
(ii) 23 of 27 balls
(iii) 23 of 36 balloons

Answer:

(i) 23 of 15 pens = 231×1551 = 10 pens
(ii) 23 of 27 balls = 231×2791 = 18 balls
(iii) 23 of 36 balloons = ​231×36121 = 24 balloons

Page No 83:

Question 11:

Determine:
(i) 34 of 16 cups
(ii) 34 of 28 rackets
(iii) 34 of 32 books

Answer:

(i) 34 of 16 cups = 341 × 1641 = 12 cups
(ii) 34 of 28 rackets = 341 × 2871 = 21 rackets
(iii) 34 of 32 books = 341 × 3281 = 24 books

Page No 83:

Question 12:

Neelam has 25 pencils. She gives 45 of them to Meena. How many pencils does Meena get? How many pencils are left with Neelam?

Answer:

Neelam gives 45 of 25 pencils to Meena.
 451 × 2551 = 20 Pencils
Thus, Meena gets 20 pencils.
∴ Number of pencils left with Neelam = 25 - 20 = 5 pencils
Thus, 5 pencils are left with Neelam.

Page No 83:

Question 13:

Represent each of the following fractions on the number line:
(i) 38
(ii) 59
(iii) 47
(iv) 25
(v) 14

Answer:

Draw a 0 to 1 on a number line. Label point 1 as A and mark the starting point as 0.

(i) Divide the number line from 0 to 1 into 8 equal parts and take out 3 parts from it to reach point P.



(ii) Divide the number line from 0 to 1 into 9 equal parts and take out 5 parts from it to reach point P

.

(iii) Divide the number line from 0 to 1 into 7 equal parts and take out 4 parts from it to reach point P.



(Iv) Divide the number line from 0 to 1 into 5 equal parts and take out 2 parts from it to reach point P.



(v) Divide the number line from 0 to 1 into 4 equal parts and take out 1 part from it to reach point P.



Page No 85:

Question 1:

Which of the following are proper fractions?
12,35,10774, 2, 158,1616,1011,2310

Answer:

12, 35, 1011

Page No 85:

Question 2:

Which of the following are improper fractions?
32,56,94,88, 3, 2716,2331,1918,1013,2626

Answer:

A fraction whose numerator is greater than or equal to its denominator is called an improper fraction. Hence, 32, 94, 88, 2716, 1918 and 2626 are improper fractions.

Page No 85:

Question 3:

Write six improper fractions with denominator 5.

Answer:

Clearly, 65, 75, 85, 95, 115and 125 are improper fractions, each with 5 as the denominator.

Page No 85:

Question 4:

Write six improper fractions with numerator 13.

Answer:

Clearly, 132, 133, 134, 135, 136, 137 are improper fractions, each with 13 as the numerator.

Page No 85:

Question 5:

Convert each of the following into an improper fraction:
(i) 557
(ii) 938
(iii) 6310
(iv) 3511
(v) 10914
(vi) 12715
(vii) 8813
(viii) 5123

Answer:

We have:
(i) 557 = (5 × 7) + 57 = 407

(ii) 938 = (9 × 8) + 38 = 758

(iii) 6310 = (6 × 10) + 310 = 6310

(iv) 3511 = (3 × 11) + 511 = 3811

(v) 10914 = (10 × 14) + 914 = 14914

(vi) 12715 = (12 × 15) + 715 = 18715

(vii) 8813 = (8 × 13) + 813 = 11213

(viii) 5123 = (51 × 3) + 23 = 1553

Page No 85:

Question 6:

Convert each of the following into a mixed fraction:
(i) 175
(ii) 627
(iii) 1018
(iv) 9513
(v) 8111
(vi) 8716
(vii) 10312
(viii) 11720

Answer:

(i) On dividing 17 by 5, we get:
    Quotient = 3
    Remainder = 2
   ∴ 175 =  3 +25 = 325  

(ii) On dividing 62 by 7, we get:
    Quotient = 8
    Remainder = 6
   ∴ 627 =  8 +67 = 867  

(iii) On dividing 101 by 8, we get:
    Quotient = 12
    Remainder = 5
   ∴ 1018 =  12 +58 = 1258  

(iv) On dividing 95 by 13, we get:
    Quotient = 7
    Remainder = 4
   ∴ 9513 =  7 +413 = 7413  

(v) On dividing 81 by 11, we get:
    Quotient = 7
    Remainder = 4
   ∴ 8111 =  7 +411 = 7411  

(vi) On dividing 87 by 16, we get:
    Quotient = 5
    Remainder = 7
   ∴ 8716 =  5 +716 = 5716  

(vii) On dividing 103 by 12, we get:
    Quotient = 8
    Remainder = 7
   ∴ 10312 =  8 +712 = 8712  

(viii) On dividing 117 by 20, we get:
    Quotient = 5
    Remainder = 17
   ∴ 11720 =  5 +1720 = 51720  

Page No 85:

Question 7:

Fill up the blanks with '>', '<' or '=':
(i) 12      1
(ii) 34      1
(iii) 1      67
(iv) 66      1
(v) 30163016      1
(vi) 115      1

Answer:

An improper fraction is greater than 1. Hence, it is always greater than a proper fraction, which is less than 1.
(i) 12  <  1

(ii) 34  <  1

(iii) 1  >  67

(iv) 66  =  1

(v) 30163016  =  1

(vi) 115  >  1



Page No 86:

Question 8:

Draw number lines and locate the following points:
(i) 14, 12, 34, 44
(ii) 18, 28, 38, 58, 78
(iii) 25, 35, 45, 85

Answer:

(i) Draw a number line. Mark 0 as the starting point and 1 as the ending point.
Then, divide 0 to 1 in four equal parts, where each part is equal to 1/4.
Show the consecutive parts as 1/4, 1/2, 3/4 and at 1 show 4/4 = 1.



(ii) Draw 0 to 1 on a number line. Divide the segment into 8 equal parts, each part corresponds to 1/8. Show the consecutive parts as 1/8, 2/8, 3/8, 4/8, 5/8, 6/8, 7/8 and 8/8. Highlight the required ones only.



(iii) Draw 0 to 2 on a number line. Divide the segment between 0 and 1 into 5 equal parts, where each part is equal to 1/5.
Show 2/5, 3/5, 4/5 and 8/5 3 parts away from 1 towards 2. (1 < 8/5 < 2)



Page No 89:

Question 1:

Write five fractions equivalent to each of the following:
(i) 23
(ii) 45
(iii) 58
(iv) 710
(v) 37
(vi) 611
(vii) 79
(viii) 512

Answer:

(i) 23 =2×23×2 =  2×33×3=  2×43×4= 2×53×5 = 2×63×6

   ∴ 23 = 46 = 69 = 812 = 1015 = 1218

Hence, the five fractions equivalent to 23 are  46, 69, 812, 1015 and 1218.


(ii) ​ 45 =4×25×2 =  4×35×3=  4×45×4= 4×55×5 = 4×65×6

   ∴ 45 = 810 = 1215 = 1620 = 2025 = 2430

Hence, the five fractions equivalent to 45 are  810, 1215, 1620, 2025 and 2430.


(iii) ​ 58 =5×28×2 =  5×38×3=  5×48×4= 5×58×5 = 5×68×6

   ∴ 58 = 1016 = 1524 = 2032 = 2540 = 3048

Hence, the five fractions equivalent to 58 are   1016, 1524, 2032, 2540 and 3048.



(iv) ​ 710 =7×210×2 =  7×310×3=  7×410×4= 7×510×5 = 7×610×6

   ∴ 710 = 1420 = 2130 = 2840 =  3550= 4260

Hence, the five fractions equivalent to 710 are  1420, 2130, 2840, 3550 and 4260.


(v) ​​ 37 =3×27×2 =  3×37×3=  3×47×4= 3×57×5 = 3×67×6

   ∴ 37 = 614 = 921 = 1228 =  1535= 1842

Hence, the five fractions equivalent to 37 are 614, 921, 1228,1535 and 1842.


(vi)  ​ 611 =6×211×2 =  6×311×3=  6×411×4= 6×511×5 = 6×611×6

   ∴ 611 = 1222 = 1833 = 2444 =  3055= 3666

Hence, the five fractions equivalent to 611 are  1222, 1833, 2444, 3055 and 3666.


(vii)  79 =7×29×2 =  7×39×3=  7×49×4= 7×59×5 = 7×69×6

   ∴ 79 = 1418 = 2127 = 2836 =  3545= 4254

Hence, the five fractions equivalent to 79 are  1418, 2127, 2836, 3545 and 4254.


(viii)  512 =5×212×2 =  5×312×3=  5×412×4= 5×512×5 = 5×612×6

   ∴ 512 = 1024 = 1536 = 2048 =  2560= 3072

Hence, the five fractions equivalent to 512 are 1024, 1536, 2048,2560 and 3072.

Page No 89:

Question 2:

Which of the following are the pairs of equivalent fractions?
(i) 56 and 2024
(ii) 38 and 1540
(iii) 47 and 1621
(iv) 29 and 1463
(v) 13 and 924
(vi) 23 and 3322

Answer:

The pairs of equivalent fractions are as follows:
(i) 56 and 2024                         2024 = 5×46×4
(ii) 38 and 1540                         1540 = 3×58×5
(iv) 29 and 1463                         1463 = 2×79×7

Page No 89:

Question 3:

Find the equivalent fraction of 35 having
(i) denominator 30
(ii) numerator 24

Answer:

(i) Let 35 = 30
Clearly, 30 = 5 × 6
So, we multiply the numerator by 6.

∴ ​35 = 3×65×6= 1830
Hence, the required fraction is 1830.
(ii)  ​Let 35 = 24
   Clearly, 24 = 3 × 8
   So, we multiply the denominator by 8.

∴ ​35 = 3×85×8= 2440
Hence, the required fraction is 2440.

Page No 89:

Question 4:

Find the equivalent fraction of 59 having
(i) denominator 54
(ii) numerator 35

Answer:

(i) Let 59 = 54
Clearly, 54 = 9 × 6
So, we multiply the numerator by 6.
∴ ​59 = 5×69×6= 3054
Hence, the required fraction is 3054.
(ii)  ​Let 59 = 35
   Clearly, 35 = 5 × 7
   So, we multiply the denominator by 7.
∴ ​59 = 5×79×7= 3563
Hence, the required fraction is 3563.

Page No 89:

Question 5:

Find the equivalent fraction of 611 having
(i) denominator 77
(ii) numerator 60

Answer:

(i) Let 611 = 77
   Clearly, 77 = 11 × 7
   So, we multiply the numerator by 7.

∴ ​611 = 6×711×7= 4277
Hence, the required fraction is 4277.
(ii)  ​Let 611 = 60
   Clearly, 60 = 6 × 10
   So, we multiply the denominator by 10.

∴ ​611 = 6×1011×10= 60110
Hence, the required fraction is 60110.

Page No 89:

Question 6:

Find the equivalent fraction of 2430 having numerator 4.

Answer:

   Let 2430 = 4
   Clearly, 4 = 24 ÷ 6
   So, we divide the denominator by 6.
 ∴ ​2430 = 24÷630÷6= 45
  Hence, the required fraction is 45.

Page No 89:

Question 7:

Find the equivalent fraction of 3648 with
(i) numerator 9
(ii) denominator 4

Answer:

(i) Let 3648 = 9
   Clearly, 9 = 36 ÷ 4
   So, we divide the denominator by 4.
∴ ​3648 = 36÷448÷4= 912
Hence, the required fraction is 912.
(ii)  ​Let 3648 = 4
   Clearly, 4 = 48 ÷ 12
   So, we divide the numerator by 12.
∴ ​3648 = 36÷1248÷12= 34
Hence, the required fraction is 34.

Page No 89:

Question 8:

Find the equivalent fraction of 5670 with
(i) numerator 4
(ii) denominator 10

Answer:

(i) Let 5670 = 4
   Clearly, 4 = 56 ÷ 14
   So, we divide the denominator by 14.
  ∴ ​5670 = 56÷1470÷14= 45
  Hence, the required fraction is 45.
(ii)  ​Let 5670 = 10
     Clearly, 10 = 70 ÷ 7
     So, we divide the numerator by 7.
   ∴ ​5670 = 56×770×7= 810
   Hence, the required fraction is 810.

Page No 89:

Question 9:

Reduce each of the following fractions into its simplest form:
(i) 915
(ii) 4860
(iii) 8498
(iv) 15060
(v) 7290

Answer:

(i) Here, numerator = 9 and denominator = 15
Factors of 9 are 1, 3 and 9.
Factors of 15 are 1, 3, 5 and 15.
Common factors of 9 and 15 are 1 and 3.
H.C.F. of 9 and 15 is 3.
∴ 915 =9÷315÷3 = 35
Hence, the simplest form of 915 is 35.

(ii) Here, numerator = 48 and denominator = 60
Factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.
Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60.
Common factors of 48 and 60 are 1, 2, 3, 4, 6 and 12.
H.C.F. of 48 and 60 is 12.
∴ 4860 =48÷1260÷12 = 45
Hence, the simplest form of 4860 is 45.

(iii) Here, numerator = 84 and denominator = 98
Factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 42 and 84.
Factors of 98 are 1, 2, 7, 14, 49 and 98.
Common factors of 84 and 98 are 1, 2, 7 and 14.
H.C.F. of 84 and 98 is 14.
∴ 8498 =84÷1498÷14 = 67
Hence, the simplest form of 8498 is 67.

(iv) Here, numerator = 150 and denominator = 60
Factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 75 and 150.
Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60.
Common factors of 150 and 60 are 1, 2, 3, 5, 6, 10, 15 and 30.
H.C.F. of 150 and 60 is 30.
∴ 15060 =150÷3060÷30 = 52
Hence, the simplest form of 15060 is 52.

(v) ​Here, numerator = 72 and denominator = 90
Factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72.
Factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45 and 90.
Common factors of 72 and 90 are 1, 2, 3, 6, 9 and 18.
H.C.F. of 72 and 90 is 18.
∴ 7290 =72÷1890÷18 = 45
Hence, the simplest form of 7290 is 45.

Page No 89:

Question 10:

Show that each of the following fractions is in the simplest form:
(i) 811
(ii) 914
(iii) 2536
(iv) 815
(v) 2110

Answer:

(i) Here, numerator = 8 and denominator = 11
    Factors of 8 are 1, 2, 4 and 8.
    Factors of 11 are 1 and 11.

    Common factor of 8 and 11 is 1.
   Thus, H.C.F. of 8 and 11 is 1.
   Hence, 811 is the simplest form.

(ii) Here, numerator = 9 and denominator = 14
    Factors of 9 are 1, 3 and 9.
    Factors of 14 are 1, 2, 7 and 14.
   Common factor of 9 and 14 is 1.
   Thus, H.C.F. of 9 and 14 is 1.
   Hence, 914 is the simplest form.

(iii) Here, numerator = 25 and denominator = 36
     Factors of 25 are 1, 5 and 25.
     Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36.
    Common factor of 25 and 36 is 1.
    Thus, H.C.F. of 25 and 36 is 1.
   Hence, 2536 is the simplest form.

(iv) Here, numerator = 8 and denominator = 15
      Factors of 8 are 1, 2, 4 and 8.
      Factors of 15 are 1, 3, 5 and 15.
      Common factor of 8 and 15 is 1.
     Thus, H.C.F. of 8 and 15 is 1.
     Hence, 815 is the simplest form.
(v) Here, numerator = 21 and denominator = 10
     Factors of 21 are 1, 3, 7 and 21.
     Factors of 10 are 1, 2, 5 and 10.
     Common factor of 21 and 10 is 1.
    Thus, H.C.F. of 21 and 10 is 1.
    Hence, 2110 is the simplest form.



Page No 90:

Question 11:

Replace      by the correct number in each of the following:
(i) 27=8    
(ii) 35=    35
(iii) 58=20    
(iv) 4560=9    
(v) 4056=    7
(vi) 4254=7    

Answer:

(i) 28            27 = 2×47×4 = 828
(ii) 21           35 = 3×75×7 = 2135
(iii) 32          58 = 5×48×4 = 2032
(iv) 12          4560 = 45÷560÷5 = 912
(v) 5             4056 = 40÷856÷8 = 57 
(vi) 9              4254 = 42÷654÷6 = 79



Page No 93:

Question 1:

Define like and unlike fractions and give five examples of each.

Answer:

Like fractions:
Fractions having the same denominator are called like fractions.
Examples: 311, 511, 711, 911, 1011

Unlike fractions:
Fractions having different denominators are called unlike fractions.
Examples: 34, 45, 67, 911, 213

Page No 93:

Question 2:

Convert 35, 710, 815 and 1130 into like fractions.

Answer:

The given fractions are 35, 710, 815 and 1130.


L.C.M. of 5, 10, 15 and 30 = (5 × 2 × 3) = 30
So, we convert the given fractions into equivalent fractions with 30 as the denominator.
(But, one of the fractions already has 30 as its denominator. So, there is no need to convert it into an equivalent fraction.)
Thus, we have:
35 = 3×65×6 = 1830; 710 = 7×310×3 = 2130 ; 815 = 8×215×2 = 1630

Hence, the required like fractions are 1830, 2130, 1630 and 1130.

Page No 93:

Question 3:

Convert 14, 58, 712 and 1324 into like fractions.

Answer:

The given fractions are 14, 58, 712 and 1324 .
L.C.M. of 4, 8, 12 and 24 = (4 × 2 × 3) = 24
So, we convert the given fractions into equivalent fractions with 24 as the denominator.
(But one of the fractions already has 24 as the denominator. So, there is no need to convert it into an equivalent fraction.)
Thus, we have:
14 = 1×64×6 = 624; 58 = 5×38×3 = 1524 ; 712 = 7×212×2 = 1424

Hence, the required like fractions are 624, 1524, 1424 and 1324.

Page No 93:

Question 4:

Fill in the place holders with the correct symbol > or <:
(i) 89      59
(ii) 910      710
(iii) 37      67
(iv) 1115      815
(v) 611      511
(vi) 1120      1720

Answer:

Between two fractions with the same denominator, the one with the greater numerator is the greater of the two.

(i) >
(ii) >
(iii) <
(iv) >
(v) >
(vi) <

Page No 93:

Question 5:

Fill in the place holders with the correct symbol > or <:
(i) 34      35
(ii) 78      710
(iii) 411      49
(iv) 811      813
(v) 512      58
(vi) 1114      1115

Answer:

Between two fractions with the same numerator, the one with the smaller denominator is the greater of the two.

(i) >
(ii) >
(iii)<
(iv) >
(v) <
(vi) >

Page No 93:

Question 6:

Compare the fractions given below:
45, 57

Answer:

45,  57
By cross multiplying:
5 × 5 = 25 and 4 × 7 = 28     
Clearly, 28 > 25
 45 > 57

Page No 93:

Question 7:

Compare the fractions given below:
38, 56

Answer:

38,  56
By cross multiplying:
3 × 6 = 18 and 5 × 8 = 40        
Clearly, 18 < 40
 38  <   56

Page No 93:

Question 8:

Compare the fractions given below:
711, 67

Answer:

711 , 67

By cross multiplying:
7 × 7 = 49 and 11 × 6 = 66        
Clearly, 49 < 66
711 <  67

Page No 93:

Question 9:

Compare the fractions given below:
56, 911

Answer:

711 , 67
By cross multiplying:
5 × 11 = 55 and 9 × 6 = 54         
Clearly, 55 > 54
 56  >  911

Page No 93:

Question 10:

Compare the fractions given below:
23, 49

Answer:

711 , 67
By cross multiplying:
2 × 9 = 18 and 4 × 3 = 12     
Clearly, 18 > 12
 23 > 49

Page No 93:

Question 11:

Compare the fractions given below:
613, 34

Answer:

613 , 34
By cross multiplying:
6 × 4 = 24 and 13 × 3 = 39      
Clearly, 24 < 39
 613 < 34

Page No 93:

Question 12:

Compare the fractions given below:
34, 56

Answer:

613, 34
By cross multiplying:
3 × 6 = 18 and 4 × 5 = 20     
Clearly, 18 < 20
 34 < 56

Page No 93:

Question 13:

Compare the fractions given below:
58, 712

Answer:

58 ,712
By cross multiplying:
5 × 12 = 60 and 8 × 7 = 56     
Clearly, 60 > 56
 58  > 712

Page No 93:

Question 14:

Compare the fractions given below:
49, 56

Answer:

L.C.M. of 9 and 6 = (3 × 3 × 2) = 18
Now, we convert 49 and 56 into equivalent fractions having 18 as the denominator. 
∴​ 49  = 4×29×2  = 818 and   56 = 5×36×3 = 15184949
         
Clearly, 818 < 1518
 49 < 56

Page No 93:

Question 15:

Compare the fractions given below:
45, 710

Answer:

L.C.M. of 5 and 10 = (5 × 2) = 10
Now, we convert 45  into an equivalent fraction having 10 as the denominator as the other fraction has already 10 as its denominator.
∴​ 45  = 4×25×2  = 810 4949
         
Clearly, 810 > 710
 45 > 710

Page No 93:

Question 16:

Compare the fractions given below:
78, 910

Answer:

L.C.M. of 8 and 10 = (2 × 5 × 2 × 2) = 40
Now, we convert 78 and 910 into equivalent fractions having 40 as the denominator.
∴​ 78  = 7×58×5  = 3540 and 910  = 9×410×4  = 3640 4949
         
Clearly, 3540 < 3640
 78 < 910

Page No 93:

Question 17:

Compare the fractions given below:
1112, 1315

Answer:

L.C.M. of 12 and 15 = (2 × 2 × 3 × 5) = 60
Now, we convert 1112 and 1315 into equivalent fractions having 60 as the denominator.
∴​ 1112  = 11×512×5  = 5560 and 1315  = 13×415×4  = 5260 4949
         
Clearly, 5560 > 5260
 1112 > 1315

Page No 93:

Question 18:

Arrange the following fractions in ascending order:
12, 34, 56 and 78

Answer:



The given fractions are 12, 34, 56 and 78.
L.C.M. of 2, 4, 6 and 8 = (2 × 2 × 2 × 3) = 24
We convert each of the given fractions into an equivalent fraction with denominator 24.
Now, we have:
 12 = 1×122×12 = 1224; 34 = 3×64×6 = 182456 = 5×46×4 = 2024; 78 = 7×38×3 = 2124

Clearly, 1224 <1824 <2024 <2124

∴ ​12 <34 <56 <78
Hence, the given fractions can be arranged in the ascending order as follows:
12, 34, 56, 78

Page No 93:

Question 19:

Arrange the following fractions in ascending order:
23, 56, 79 and 1118

Answer:

The given fractions are 23, 56, 79 and 1118.


L.C.M. of 3, 6, 9 and 18 = (3 × 2  × 3) = 18
So, we convert each of the fractions whose denominator is not equal to 18 into an equivalent fraction with denominator 18.
Now, we have:
23 = 2×63×6 = 1218; 56 = 5×36×3 = 1518; 79 = 7×29×2 = 1418
Clearly, 1118 <1218 <1418 <1518
∴ ​1118 <23 <79 <56

Hence, the given fractions can be arranged in the ascending order as follows:
1118 ,23 ,79 ,56

Page No 93:

Question 20:

Arrange the following fractions in ascending order:
25, 710, 1115 and 1730

Answer:

The given fractions are 25,710, 1115 and 1730.
L.C.M. of 5, 10, 15 and 30 = (2 × 5 × 3) = 30  

                                        
So, we convert each of the fractions whose denominator is not equal to 30 into an equivalent fraction with denominator 30.
Now, we have:
25 = 2×65×6 = 1230; 710 = 7×310×3 = 2130; 1115 = 11×215×2 = 2230
Clearly, 1230 <1730 <2130 <2230
∴ ​25 <1730 <710 <1115

Hence, the given fractions can be arranged in the ascending order as follows:
25, 1730, 710, 1115 

Page No 93:

Question 21:

Arrange the following fractions in ascending order:
34, 78, 1116 and 2332

Answer:

The given fractions are 34, 78, 1116 and 2332.
L.C.M. of 4, 8, 16 and 32 = (2 ⨯ 2 ⨯ 2 ⨯ 2 ⨯ 2) = 32    

                                      
So, we convert each of the fractions whose denominator is not equal to 32 into an equivalent fraction with denominator 32.
Now, we have:
34 = 3×84×8 = 2432; 78 = 7×48×4 = 2832; 1116 = 11×216×2 = 2232
Clearly, 2232 <2332 <2432 <2832
∴ ​1116 <2332 <34 <78

Hence, the given fractions can be arranged in the ascending order as follows:
1116, 2332, 34, 78

Page No 93:

Question 22:

Arrange the following fractions in descending order:
34, 58, 1112 and 1724

Answer:

The given fractions are 34, 58, 1112 and 1724.
L.C.M. of 4, 8, 12 and 24 = (2 ⨯ 2 ⨯ 2 ⨯ 3) = 24            

                             
So, we convert each of the fractions whose denominator is not equal to 24 into an equivalent fraction with denominator 24.
Thus, we have;
34 = 3×64×6 = 1824; 58 = 5×38×3 = 1524; 1112 = 11×212×2 = 2224
Clearly, 2224 >1824 >1724 >1524

∴ ​1112 >34 >1724 >58

Hence, the given fractions can be arranged in the descending order as follows:
1112, 34, 1724, 58

Page No 93:

Question 23:

Arrange the following fractions in descending order:
79, 512, 1118 and 1736

Answer:

The given fractions are 79, 512, 1118 and 1736.
L.C.M. of 9, 12, 18 and 36 = (3 ⨯ 3 ⨯ 2 ⨯ 2) = 36      

                                   
We convert each of the fractions whose denominator is not equal to 36 into an equivalent fraction with denominator 36.
Thus, we have:
79 = 7×49×4 = 2836; 512 = 5×312×3 = 1536; 1118 = 11×218×2 = 2236
Clearly, 2836 >2236 >1736 >1536

∴ ​79 >1118 >1736 >512

Hence, the given fractions can be arranged in the descending order as follows:
79 ,1118,1736,512

Page No 93:

Question 24:

Arrange the following fractions in descending order:
23, 35, 710 and 815

Answer:

The given fractions are 23, 35, 710 and 815.
L.C.M. of 3, 5,10 and 15 = (2 ⨯ 3 ⨯ 5) = 30  

                                       
So, we convert each of the fractions into an equivalent fraction with denominator 30.
Thus, we have:
23 = 2×103×10 = 2030; 35 = 3×65×6 = 1830; 710 = 7×310×3 = 2130; 815 = 8×215×2 = 1630
Clearly, 2130 >2030 >1830 >1630
∴ ​710 >23 >35 >815

Hence, the given fractions can be arranged in the descending order as follows:
710 ,23 ,35 ,815

Page No 93:

Question 25:

Arrange the following fractions in descending order:
57, 914, 1721 and 3142

Answer:

The given fractions are 57, 914, 1721 and 3142.
L.C.M. of 7, 14, 21 and 42 = (2 ⨯ 3 ⨯ 7) = 42                                          


We convert each one of the fractions whose denominator is not equal to 42 into an equivalent fraction with denominator 42.
Thus, we have:
57 = 5×67×6 = 3042; 914 = 9×314×3 = 2742; 1721 = 17×221×2 = 3442
Clearly, 3442 >3142 >3042 >2742
∴ ​1721 >3142 >57 >914
Hence, the given fractions can be arranged in the descending order as follows:
1721,3142,57, 914

Page No 93:

Question 26:

Arrange the following fractions in descending order:
112, 123, 17, 19, 117, 150

Answer:

The given fractions are 112,123, 17, 19 , 117 and 150.
As the fractions have the same numerator, we can follow the rule for the comparison of such fractions.
This rule states that when two fractions have the same numerator, the fraction having the smaller denominator is the greater one.
Clearly, 17 >19 >112 >117>123>150
Hence, the given fractions can be arranged in the descending order as follows:
17, 19, 112, 117, 123, 150

Page No 93:

Question 27:

Arrange the following fractions in descending order:
37, 311, 35, 313, 34, 317

Answer:

The given fractions are 37, 311, 35, 313, 34 and 317.
As the fractions have the same numerator, so we can follow the rule for the comparison of such fractions.
This rule states that when two fractions have the same numerator, the fraction having the smaller denominator is the greater one.

Clearly, 34 >35 >37 >311>313>317
Hence, the given fractions can be arranged in the descending order as follows:
34, 35, 37, 311, 313, 317 



Page No 94:

Question 28:

Lalita read 30 pages of a book containing 100 pages while Sarita read 25 of the book. Who read more?

Answer:

Lalita read 30 pages of a book having 100 pages.
Sarita read 25 of the same book.
 25 of 100 pages = ​25 × 100 = 2005 = 40 pages
Hence, Sarita read more pages than Lalita as 40 is greater than 30.

Page No 94:

Question 29:

Rafiq exercised for 23 hour, while Rohit exercise for 34 hour. Who exercised for a longer time?

Answer:

To know who exercised for a longer time, we have to compare 23 hour with 34 hour .
On cross multiplying:
4 × 2 = 8 and 3 × 3 = 9
Clearly, 8 < 9
 23 hour < 34 hour
Hence, Rohit exercised for a longer time.

Page No 94:

Question 30:

In a school 20 students out of 25 passed in VI A, while 24 out of 30 passed in VI B. Which section gave better result?

Answer:

Fraction of students who passed in VI A = 2025 = 20÷525÷5 = 45

Fraction of students who passed in VI B = 2430 = 24÷630÷6 = 45
In both the sections, the fraction of students who passed is the same, so both the sections have the same result.



Page No 96:

Question 1:

Find the sum:
58+18

Answer:

The given fractions are like fractions.
We know:
Sum of like fractions  = Sum of the numeratorsCommon denominator
Thus, we have:
58 + 18 = 5+1 8 = 6 384 = 34

Page No 96:

Question 2:

Find the sum:
49+89

Answer:

The given fractions are like fractions.
We know:
Sum of like fractions  = Sum of the numeratosCommon denominator
Thus, we have:
49 + 89 = 4+8 9 = 12493 = 43 = 113

Page No 96:

Question 3:

Find the sum:
135+245

Answer:

The given fractions are like fractions.
We know:
Sum of like fractions  = Sum of the numeratorsCommon denominator
Thus, we have:
135 + 245 = 85 + 145 = 8+14 5 = 225 = 425 

Page No 96:

Question 4:

Find the sum:
29+56

Answer:

L.C.M. of 9 and 6 = (2 × 3 × 3) = 18                                   


Now, we have:

     29 = 2 × 29 × 2 = 418; 56 = 5 × 36 × 3 = 1518 29 + 56 = 418 + 1518 = 4 + 1518 = 1918 = 1118                                                                                                                                                                                       

Page No 96:

Question 5:

Find the sum:
712+916

Answer:

L.C.M. of 12 and 16 = (2 × 2 × 2 × 2 × 3) = 48                                   


Now, we have:

     712 = 7 × 412 × 4 = 2848; 916 = 9 × 316 × 3 = 2748 712 + 916 = 2848 + 2748 = 28 + 2748 = 5548 = 1748                                                                                                                                                                                       

Page No 96:

Question 6:

Find the sum:
415+1720

Answer:

L.C.M. of 15 and 20 = (3 × 5 × 2 × 2) = 60                                   


      415 + 1720 = 16 + 5160     60 ÷ 15 = 4, 4 × 4 = 16 and 60 ÷ 20 = 3, 17 × 3 = 51                       = 6760 = 1760                                                                                                                                                                                       

Page No 96:

Question 7:

Find the sum:
234+556

Answer:

We have:                                              

                                                                                     
     234 + 556 = 114 + 356                                L.C.M. of 4 and 6 = (2 × 2 × 3) = 12  = 66 + 14024                                   24 ÷ 4 = 6, 6 × 11 = 66 and 24 ÷ 6 = 4, 4 × 35 = 140    = 2061032412 = 10312 = 8712
234+556

Page No 96:

Question 8:

Find the sum:
318+1512

Answer:

We have:
                                                                                                                                                       

     318 + 1512 = 258 + 1712                                L.C.M. of 8 and 12 = (2 × 2 × 2 × 3) = 24  = 75 + 3424                                   24 ÷ 8 = 3, 3 × 25 = 75 and 24 ÷ 12 = 2, 2 × 17 = 34    = 10924  = 41324
234+556

Page No 96:

Question 9:

Find the sum:
2710+3815

Answer:

We have:

                                                                                                                                                 
     2710 + 3815 = 2710 + 5315                                L.C.M. of 10 and 15 = (2 × 3 × 5) = 30  = 81 + 10630                                   30 ÷10 = 3, 3 × 27 = 81 and 30 ÷ 15 = 2, 2 × 53 = 106    = 18730  = 6730
234+556

Page No 96:

Question 10:

Find the sum:
323+156+2

Answer:

We have:


                                                                                                                                                       
     323 + 156 + 2 = 113 + 116 + 21                             L.C.M. of 3 and 6 = (2 × 3) = 6  = 22 + 11 + 126                                   6 ÷ 3 = 2, 2 × 11 = 22, 6 ÷ 6 =1, 1 × 11 = 11 and 6 ÷ 1 = 6, 6 × 2 = 12    = 451562  = 152 = 712
234+556

Page No 96:

Question 11:

Find the sum:
3+1415+1320

Answer:

We have:

                                                                                                                                                       
     3 + 1415 + 1320  = 31 + 1915 + 2320                              L.C.M. of 15 and 20 = (2 × 2 × 3 × 5) = 60  = 180 + 76 + 6960                                   60 ÷ 1 = 60, 60 × 3 = 180, 60 ÷ 15 = 4, 4 × 19 = 76 and 60 ÷ 20 =3, 3 × 23 = 69    =  325656012  = 6512 = 5512
234+556

Page No 96:

Question 12:

Find the sum:
313+414+616

Answer:

We have:


                                                                                                                                                       
     313 + 414 + 616  = 103 + 174 + 376                              L.C.M. of 3, 4 and 6 = (2 × 2 × 3) = 12  = 40 + 51 + 7412                                   12 ÷ 3 = 4, 4 × 10 = 40, 12 ÷ 4 = 3, 3 × 17 = 51 and 12 ÷ 6 =2, 2 × 37 = 74    =  16555124  = 554 = 1334
234+556

Page No 96:

Question 13:

Find the sum:
23+316+429+2518

Answer:

We have:

                                                                                                                                                       
    23 + 316 + 429 + 2518  = 23 + 196 + 389 + 4118                              L.C.M. of 3, 6 and 9 = (2 × 3 × 3) = 18  = 12 + 57 + 76 + 4118                                   18 ÷ 3 = 6, 6 × 2 = 12, 18 ÷ 6 = 3, 3 × 19 = 57, 18 ÷ 9 =2, 2 × 38 = 76 and 18 ÷ 18 = 1, 1 × 41= 41    =  18631183  = 313 = 1013
234+556

Page No 96:

Question 14:

Find the sum:
213+114+256+3712

Answer:

We have:
                                                                                                                                                       

    213 + 114 + 256 + 3712  = 73 + 54 + 176 + 4312                              L.C.M. of 3, 4, 6 and 12 = (2 × 2 × 3) = 12  = 28 + 15 + 34 + 4312                                   12 ÷ 3 = 4, 4 × 7 = 28, 12 ÷ 4 = 3, 3 × 5 = 15, 12 ÷ 6 =2, 2 × 17 = 34 and 12 ÷ 12 = 1, 1 × 43 = 43     =  12010121  =  10
234+556

Page No 96:

Question 15:

Find the sum:
2+34+158+3716

Answer:

We have:
                                                                                                                                     

    2  + 34 + 158 + 3716  = 21 + 34 + 138 + 5516                              L.C.M. of 4, 8, and 16  =  (2 × 2 × 2 × 2) = 16  = 32 + 12 + 26 + 5516                                   16 ÷ 1 = 16, 16 × 2 = 32, 16 ÷ 4 = 4, 4 × 3 = 12, 16 ÷ 8 =2, 2 × 13 = 26 and 16 ÷ 16 = 1, 1 × 55= 55    =  12516 =  71316
234+556

Page No 96:

Question 16:

Rohit bought a pencil for Rs 325 and an eraser for Rs 2710. What is the total cost of both the articles?

Answer:

Total cost of both articles = Cost of pencil + Cost of eraser 
Thus, we have:
   Rs 325 + Rs 2710 = 175 + 2710                               =  34 + 2710           (L.C.M. of 5 and 10 = (5 × 2) = 10)                                 = 6110 = Rs 6110
Hence, the total cost of both the articles is Rs 6110.

Page No 96:

Question 17:

Sohini bought 412m of cloth for her kurta and 223m of cloth for her pyjamas. Ho much cloth did she purchase in all?

Answer:

Total cloth purchased by Sohini = Cloth for kurta + Cloth for pyjamas
Thus, we have:
                                         412 +  223  m = 92 + 83 m                (L.C.M. of 2 and 3 = (2 × 3) = 6)= 27 + 166  m                                 6 ÷ 2 = 3, 3 × 9 = 27 and 6 ÷ 3 = 2, 2 × 8 = 16 = 436 m =  716 m
Total length of cloth purchased =  716 m

Page No 96:

Question 18:

While coming back home from his school, Kishan covered 434 km by rickshaw and 112 km on foot. What is the distance of his house from the school?

Answer:

Distance from Kishan's house to school = Distance covered by him by rickshaw + Distance covered by him on foot
Thus, we have:
    434 +  112  km =  194 + 32 km                 = 19  + 64  km            (L.C.M .of 2 and 4 = (2 ×2) = 4)= 254 km =  614km


Hence, the distance from Kishan's house to school is  614 km.

Page No 96:

Question 19:

The weight of an empty gas cylinder is 1645 kg and it contains 1423 kg of gas. What is the weight of the cylinder filled with gas?

Answer:

Weight of the cylinder filled with gas = Weight of the empty cylinder + Weight of the gas inside the cylinder
Thus, we have:
   1645 +  1423  kg =  845 + 443 kg                (L.C.M. of 5 and 3 = (3 × 5) = 15)= 252 + 22015  kg                                       = 47215 kg = 31715 kg
Hence, the weight of the cylinder filled with gas is 31715 kg.



Page No 99:

Question 1:

Find the difference:
58-18

Answer:

Difference of like fractions = Difference of numerator ÷ Common denominator
58 - 18 = 5 - 18 = 4182 = 12

Page No 99:

Question 2:

Find the difference:
712-512

Answer:

Difference of like fractions = Difference of numerator ÷ Common denominator
712 - 512 = 7 - 512 = 21126 = 16

Page No 99:

Question 3:

Find the difference:
437-247

Answer:

Difference of like fractions = Difference of numerator ÷ Common denominator
437 - 247 = 317 - 187                    = 31 - 187                      = 137  

Page No 99:

Question 4:

Find the difference:
56-49

Answer:


56 - 49

 3  6, 9 2  2, 3 3  1, 3     1, 1
L.C.M. of 6 and 9 = (3 × 2 × 3) = 18
Now, we have:
56 = 5 × 36 × 3 = 1518; 49 = 4 × 29 × 2 = 818 56 - 49 = 1518 - 818 = 15 - 818 = 718

Page No 99:

Question 5:

Find the difference:
12-38

Answer:

12 - 38

L.C.M. of 2 and 8 = (2 × 2 × 2) = 8
Now, we have:
12 = 1 × 42 × 4 = 48  12 - 38 = 48 - 38 = 4 - 38 = 18

Page No 99:

Question 6:

Find the difference:
58-712

Answer:

58 - 712

  2 8, 12  2 4, 6  2 2, 3   3 1, 3     1, 1
L.C.M. of 8 and 12 = (2 × 2× 2×3) = 24
Now, we have:
58 = 5 × 38 × 3 = 1524; 712 = 7 × 212 × 2 = 1424 58 - 712 = 1524 - 1424 = 15 - 1424 = 124

Page No 99:

Question 7:

Find the difference:
279-1815

Answer:

279 - 1815 = 259 - 2315 3  9, 15  3 3, 5  51, 5     1, 1L.C.M. of 9 and 15 =(3 × 3 × 5) = 45  259 - 2315 =  125 - 6945 = 56 45  = 11145                                          45 ÷ 9 = 5, 5 × 25 = 125 and 45 ÷ 15 = 3, 3 × 23 = 69

Page No 99:

Question 8:

Find the difference:
358-2512

Answer:

358 - 2512 = 298 - 2912    2   8, 12    2  4, 6   2  2, 3    3  1, 3        1, 1  L.C.M. of 8 and 12 =(2 × 2 × 2 × 3) = 24  298 - 2912 =  87 - 5824 = 29 24   = 1524                                          24 ÷ 8 = 3, 3 × 29 = 87 and  24 ÷ 12 = 2, 2 × 29 = 58

Page No 99:

Question 9:

Find the difference:
2310-1715

Answer:

2310 - 1715 = 2310 - 2215      5 10, 15  2 2, 3  3 1, 3                                    1, 1  L.C.M. of 10 and 15 = (2 × 3 × 5) = 30= 69 - 4430                               30 ÷ 10 = 3, 3 × 23 = 69 and 30 ÷ 15 = 2, 2 × 22 = 44 = 255306  = 56

Page No 99:

Question 10:

Find the difference:
623-334

Answer:

623 - 334  = 203 - 154                                   L.C.M. of 3 and 4 = (2 × 2 × 3) = 12                            = 80 - 4512                               12 ÷ 3 = 4, 4 × 20 = 80 and 12 ÷ 4 = 3, 3 × 15 = 45= 3512 = 21112 

Page No 99:

Question 11:

Find the difference:
7 - 523

Answer:

7 - 523  = 71 - 173                                   L.C.M. of 1 and 3 = 3                       = 21 - 173                               3 ÷ 1 = 3, 3 × 7 = 21 and 3 ÷ 3 = 1, 1 × 17 = 17= 43 = 113

Page No 99:

Question 12:

Find the difference:
10 - 638

Answer:

10 - 638  = 101 - 518                                   L.C.M. of 1 and 8 = 8                       = 80 - 518                               8 ÷ 1 = 8, 8 × 10 = 80 and 8 ÷ 8 = 1, 1 × 51 = 51= 298 = 358

Page No 99:

Question 13:

Simplify:
56-49+23

Answer:

We have:

  56 - 49  + 23                                L.C.M. of 3, 6 and 9 =2 × 3 × 3  = 18                       = 15 - 8 + 1218             18 ÷ 6 = 3, 3 × 5 = 15, 18 ÷ 9 = 2, 2 × 4 = 8 and 18 ÷ 3 = 6, 6 × 2 = 12 = 27 - 818 =1918 =  1118
3 3, 6, 93 1, 2, 32 1, 2, 1   1, 1, 1

Page No 99:

Question 14:

Simplify:
58+34-712

Answer:

We have:                                                                                                                                       
  58 + 34 - 712        2 4, 8, 12  2 2, 4, 6  2 1, 2, 3   3 1, 1, 3        1,1, 1                                L.C.M. of 4, 8 and 12  =  (2 × 2 × 2 × 3) = 24= 15 + 18 -1424                                   24 ÷ 8 = 3, 3 × 5 = 15, 24 ÷ 4 = 6, 6 × 3 = 18 and 24 ÷ 12 =2, 2 × 7 = 14  =  33 - 1424 = 1924             
234+556

Page No 99:

Question 15:

Simplify:
2+1115-59

Answer:

We have:                                                                                                                                            21 + 1115 - 59            3  1, 15, 9   3  1, 5, 3   5  1, 5, 1       1, 1, 1                           L.C.M. of 15  and 9 = (3 × 3 × 5) = 45  = 90 + 33 -2545                                   45 ÷ 1 = 45, 45 × 2 = 90, 45 ÷ 15 = 3, 3 × 11 = 33 and 45 ÷ 9 =5, 5 × 5 = 25    =  90 + 845 = 9845  = 2845
234+556

Page No 99:

Question 16:

Simplify:
534-4512+316

Answer:

We have:                                                                                                                                     
  534 - 4512 + 3 16   =  234 - 5312 + 196                     L.C.M. of 4, 12  and 6 = (2 × 2 × 3) = 12 2 4, 12, 6 2 2, 6, 3  3 1, 2, 3   2 1, 2, 1      1, 1, 1   = 69 - 53 + 3812                                                                   12 ÷ 4 =3, 3 × 23 = 69, 12 ÷ 12 =1, 1 × 53 = 53 and 12 ÷ 6 =2, 2 × 19 = 38    =  107 - 5312 = 5412  =92 = 412
234+556

 

Page No 99:

Question 17:

Simplify:
2+5710-31415

Answer:

We have:                                                                                                                                           2 + 5710 -3 1415   =  21 + 5710 - 5915    5 1, 10, 15  2 1, 2, 3 3  1, 1, 3        1, 1, 1             L.C.M. of 10  and 15 = (2 × 5 × 3) = 30  = 60 + 171 -11830                                                         30 ÷ 1 =30, 30 × 2 = 60, 30 ÷ 10 =3, 3 × 57 = 171 and 30 ÷ 15 =2, 2 × 59 = 118    =  231 -11830 = 11330 = 32330

Page No 99:

Question 18:

Simplify:
8-312-214

Answer:

We have:                                                                                                                                    
  8 - 312 -214   =  81 - 72 - 94   2 1, 2, 4  2 1, 1, 2     1, 1, 1                     L.C.M. of 1, 2 and 4 = (2 × 2) = 4  = 32 - 14 - 94                                                         4 ÷ 1 =4, 4 × 8 = 32, 4 ÷ 2 =2, 2 × 7 = 14 and 4 ÷ 4 =1, 1 × 9 = 9    =  32 - 234 = 94 = 214

Page No 99:

Question 19:

Simplify:
856-338+2712

Answer:

We have:                                                                                                                                    
  856 - 338 + 2712   =  536 - 278 + 3112      2  6, 8, 12 2 3, 4, 6 3 3, 2, 3  2 1, 2, 1        1, 1, 1           L.C.M. of 6, 8 and 12 = (2 × 2 × 2 × 3 ) = 24  = 212 - 81 + 6224                                                         24 ÷ 6 =4, 4 × 53 = 212, 24 ÷ 8 =3, 3 × 27 = 81 and 24 ÷ 12 =2, 2 × 31 = 62    =  274 - 8124 = 19324 = 8124

Page No 99:

Question 20:

Simplify:
616-515+313

Answer:

We have:                                                                                                                                     
  616 - 515 + 313      =  376 - 265 + 103        2  6, 5, 33  3, 5, 3   5 1, 5, 1       1, 1, 1      L.C.M. of 6, 5 and 3 = (2 × 5 × 3) = 30  = 185 - 156 + 10030                         30 ÷ 6 =5, 5 × 37 = 185, 30 ÷ 5 =6, 6 × 26 = 156, and 30 ÷ 3 =10, 10 × 10 = 100  =  285 - 15630 = 129433010   =  4310

Page No 99:

Question 21:

Simplify:
3+115+23-715

Answer:

We have:                                                                                                                                        
  3 + 115 + 23 -715      =  31 + 65 + 23 - 715          5  5, 3, 15  3 1, 3, 3     1, 1, 1              L.C.M. of 1, 5, 3 and 15 = (5 × 3 ) =15  = 45 + 18 + 10 - 715                         15 ÷ 1 =15, 15 × 3 = 45, 15 ÷ 5 =3, 3 × 6 = 18, 15 ÷ 3 = 5, 5 × 2 = 10 and 15 ÷ 15 = 1, 1 × 7 = 7  =  73 - 715 = 6622155   =225   = 425

Page No 99:

Question 22:

What should be added to 923 to get 19?

Answer:

Let x be added to 923 to get 19.

  923 + x = 19Thus, we have:  x = 19 - 923      = 191 - 293                           L.C.M. of 1 and 3 is 3.       =57 - 293                                 3 ÷ 1 = 3, 3 × 19 = 57 and 3 ÷ 3 = 1, 1 × 29 = 29       = 283 = 913923

Page No 99:

Question 23:

What should be added to 6715 to get 815?

Answer:

Let x be added to 6715 to get 815.
  6715 + x = 815Therefore, we have: x  =  815 - 6715      = 415 - 9715                           L.C.M. of 5 and 15 = 5 × 3 = 15      =123 - 9715                                 15 ÷ 5 = 3, 3 × 41 = 123 and 15 ÷ 15 = 1, 1 × 97 = 97      = 2615 = 11115

Page No 99:

Question 24:

Subtract the sum of 359 and 313 from the sum of 556 and 419.

Answer:

    556 + 419 - 359 + 313 =356 + 379  -329 + 103      2 6, 9, 3  3 3, 9, 3  3 1, 3, 1       1, 1, 1                    L.C.M. of 3, 6, 9 = 2 × 3 × 3 = 18 = 105 + 74 - 64 + 6018                        18 ÷ 6 = 3, 3 × 35 = 105 and 18 ÷ 9 = 2, 2 × 37 = 74                                                                               18 ÷ 9 = 2, 2 × 32 = 64 and 18 ÷ 3 = 6, 6 × 10 = 60 = 179 - 12418 = 5518 = 3118

Page No 99:

Question 25:

Of 34 and 57, which is greater and by how much?

Answer:

Let us compare 34 and 57.
3 × 7 = 21 and 4 × 5 = 20
Clearly, 21 > 20
34 > 57
Required difference:
 = 34 - 57                              L.C.M. of 4 and 7 = 2 × 2 × 7 = 28= 21 - 2028                              28 ÷ 4 = 7, 7 × 3 = 21 and 28 ÷ 7 = 4, 4 × 5 = 20= 128
Hence, 34 is greater than 57 by 128.

Page No 99:

Question 26:

Mrs Soni bought 712 litres of milk. Out of this milk, 534 litres was consumed. How much milk is left with her?

Answer:

Amount of milk left with Mrs. Soni = Total amount of milk bought by her - Amount of milk consumed
Amount of milk left with Mrs. Soni =  712 - 534 = 152 - 234                           L.C.M. of 2 and 4 = 2 × 2 = 4= 30 - 234                               4 ÷ 2 = 2, 2 × 15 = 30 and 4 ÷ 4 = 1, 1 × 23 = 23 = 74 = 134 litres

Milk left with Mrs. Soni = 134 litres

Page No 99:

Question 27:

A film show lasted for 313 hours. Out of his time, 134 hours was spent on advertisements. What was the actual duration of the film?

Answer:

Actual duration of the film = Total duration of the show - Time spent on advertisements
                                          =313 - 134 hours  =103 - 74 hours                         L.C.M. of 3 and 4 = 2 × 2 × 3 = 12  =40 - 2112 hours                               12 ÷ 3 = 4, 4 × 10 = 40 and 12 ÷ 4 = 3, 3 × 7 = 21 = 1912 hours = 1712 hours
Thus, the actual duration of the film was 1712 hours.

Page No 99:

Question 28:

In one day, a rickshaw puller earned Rs 13712. Out of this money, he spent Rs 5634 on food. How much money is left with him?

Answer:

Money left with the rickshaw puller = Money earned by him in a day - Money spent by him on food
  = Rs 13712 - 5634                     L.C.M. of 2 and 4=2 × 2 = 4 = Rs 2752 - 2274                          4 ÷ 2 = 2, 2 × 275 = 550 and 4 ÷ 4 = 1, 1 × 227 = 227= Rs 550 - 2274 = Rs 3234 = Rs 8034 
Hence, Rs 8034 is left with the rickshaw puller.

Page No 99:

Question 29:

A piece of wire, 234 metres long, broke into two pieces. One piece is 58 metre long. How long is the other piece?

Answer:

The length of the other piece = (Length of the wire - Length of one piece)
   = 234 - 58 m =114 - 58 m                        L.C.M. of 4 and 8 =2 × 2 × 2 = 8 = 22 - 58 m                  8 ÷ 4 = 2, 2 × 11= 22 and 8 ÷ 8 = 1, 1 × 5 = 5=178 m = 218 m
Hence, the other piece is 218 m long.

Page No 99:

Question 1:

A fraction equivalent to 35 is
(a) 3+25+2
(b) 3-25-2
(c) 3×25×2
(d) none of these

Answer:

(c) 3 × 25 × 2

Page No 99:

Question 2:

A fraction equivalent to 812 is
(a) 8+412+4
(b) 8-412-4
(c) 8÷412÷4
(d) none of these

Answer:

(c) 8 ÷ 412 ÷ 4



Page No 100:

Question 3:

A fraction equivalent to 2436 is
(a) 34
(b) 23
(c) 89
(d) none of these

Answer:

 (b) 23    Factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24.Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36.Common factors of 24 and 36 are 1, 2, 3, 4, 6, 12.H.C.F. =12Dividing both the numerator and the denominator by 12:                                       2436 = 24 ÷ 1236 ÷ 12 = 23

Page No 100:

Question 4:

If 34 is equivalent to x20 then the value of x is
(a) 15
(b) 18
(c)12
(d) none of these

Answer:

(a) 15                              

  Explanation: 
34 = x20                                    We have: 20 = 4 × 5So, we have to multiply the numerator by 5.  x = 3 × 5 = 15

Page No 100:

Question 5:

If 4560 is equivalent to 3x then the value of x is
(a) 4
(b) 5
(c) 6
(d) none of these

Answer:

(a) 4

  Explanation: 
4560 = 3x                                  Now, 3 = 45 ÷15So, we have to divide the denominator by 15.  x = 60 ÷ 15 = 4

Page No 100:

Question 6:

Which of the following are like fractions?
(a) 25, 27, 29, 211
(b) 23, 34, 45, 56
(c) 18, 38, 58, 78
(d) none of these

Answer:

(c) 18, 38, 58, 78       
     

(Fractions having the same denominator are called like fractions.)

Page No 100:

Question 7:

Which of the following is a proper fraction?
(a) 53
(b) 5
(c) 125
(d) none of these

Answer:

(d) none of these


In a proper fraction, the numerator is less than the denominator.

Page No 100:

Question 8:

Which of the following is a proper fractions?
(a) 78
(b) 178
(c) 87
(d) none of these

Answer:

(a) 78
In a proper fraction, the numerator is less than the denominator.

Page No 100:

Question 9:

Which of the following statements is correct?
(a) 34<35
(b) 34>35
(c) 34 and 35 cannot be compared

Answer:

(b) 34 > 35
Between the two fractions with the same numerator, the one with the smaller denominator is the greater.

Page No 100:

Question 10:

The smallest of the fractions 35, 23, 56, 710 is
(a) 23
(b) 710
(c) 35
(d) 56

Answer:

(c) 35

    2  5, 3, 6, 10    5 5, 3, 3, 5    3 1, 3, 3, 1        1, 1, 1, 1 

L.C.M. of 5, 3, 6 and 10 = (2 × 3 × 5) = 30
Thus, we have:
35 = 3 × 65 × 6 = 1830 23 =2 × 103 × 10 = 2030 56 =5 × 56 × 5  = 2530  710 =7 × 310 × 3 = 2130 The smallest fraction = 1830  = 35

Page No 100:

Question 11:

The largest of the fractions 45, 47, 49, 411 is
(a) 411
(b) 45
(c) 47
(d) 49

Answer:

( b ) 45
Among the given fractions with the same numerator, the one with the smallest denominator is the greatest. 

Page No 100:

Question 12:

The smallest of the fractions 611, 711, 811, 911 is
(a) 611
(b) 711
(c) 811
(d) 911

Answer:

(a) 611
 Among like fractions, the fraction with the smallest numerator is the smallest.

Page No 100:

Question 13:

The smallest of the fractions 34, 56, 712, 23 is
(a) 23
(b) 34
(c) 56
(d) 712

Answer:

(d) 712

Explanation: 
    2  4, 6, 12, 3     2 2, 3, 6, 3     3 1, 3, 3, 3        1, 1, 1, 1 

​​L.C.M. of 4, 6, 12 and 3 = (2 × 2 × 3) = 12
Thus, we have:
34 = 3 × 34 × 3 = 912 56 =5 × 26 × 2 = 1012  23 =2 × 43 × 4 = 812 712Clearly, 712   is the smallest fraction.

Page No 100:

Question 14:

435=?
(a) 175
(b) 235
(c) 173
(d) none of these

Answer:

(b) 235

Page No 100:

Question 15:

347=?
(a) 347
(b) 734
(c) 467
(d) none of these

Answer:

(c) 467
On dividing 34 by 7:
Quotient = 4
Remainder = 6
347 = 4 +67 = 467



Page No 101:

Question 16:

58+18=?
(a) 38
(b) 34
(c) 6
(d) none of these

Answer:

(b) 34

Explanation:

Addition of like fractions = Sum of the numerators / Common denominator
58 + 18 = (5 + 1)8 = 6384 = 34

Page No 101:

Question 17:

58-18=?
(a) 14
(b) 12
(c) 116
(d) none of these

Answer:

(b) 12
Explanation: 
58 - 18 = 5 - 18 = 4182 = 12

Page No 101:

Question 18:

334-214=?
(a) 112
(b) 114
(c) 14
(d) none of these

Answer:

(a) 112Explanation:334 - 214154 - 94(15 - 9)464 = 32 = 112

Page No 101:

Question 19:

56+23-49=?
(a) 113
(b) 116
(c) 119
(d) 1118

Answer:

(d) 1118

Explanation: 
    3  3, 6, 9    2 1, 2, 3    3 1, 1, 3        1, 1, 1 

    56 + 23 - 49                        ( L.C.M. of 3, 6 and 9 = 2 × 3 × 3 = 18) = 15 + 12 -818                          18 ÷ 6 = 3,  3 × 5 = 15, 18 ÷ 3 = 6, 6 × 2 = 12 and 18 ÷ 9 = 2, 2 × 4 = 8 = 27 - 818 = 1918 = 1118

Page No 101:

Question 20:

Which is greater: 313 or 3310?
(a) 313
(b) 3310
(c) both are equal

Answer:

(a) 313

Explanation:
Let us compare  313 and 3310 or 103 and 3310 .
10 ⨯ 10 = 100 and 3 ​⨯ 33 = 99
Clearly, 100 > 99
∴ 103>3310 or 313 >3310



Page No 103:

Question 1:

Define a fraction. Give five examples of fractions.

Answer:

A fraction is defined as a number representing a part of a whole, where the whole may be a single object or a group of objects.

Examples: 57 , 85 , 23 , 43 , 49

Page No 103:

Question 2:

What fraction of an hour is 35 minutes?

Answer:

An hour has 60 minutes.
Fraction for 35 minutes = 3576012  = 712
Hence, 712 part of an hour is equal to 35 minutes.

Page No 103:

Question 3:

Find the equivalent fraction of 5/8 with denominator 56.

Answer:

56 = 8 ⨯ 7
So, we need to multiply the numerator by 7.


58 = 5 × 78 × 7 = 3556
Hence, the required fraction is 3556.

Page No 103:

Question 4:

Represent 235 on the number line.

Answer:

Let OA = AB = BC = 1 unit
OB = 2 units and OC = 3 units
Divide BC into 5 equal parts and take 3 parts out to reach point P.
Clearly, point P represents the number 235.

Page No 103:

Question 5:

Find the sum 245+1310+3115.

Answer:

We have:
   245 + 1310 + 3115 = 145 + 1310 + 4615         5  5, 10, 15  2 1, 2, 3  3 1, 1, 3      1, 1, 1                   L.C.M. of 5, 10 and 15 = 5 × 2 × 3 = 30 = 84 + 39 + 9230                   30 ÷ 5 = 6, 6 × 14 = 84, 30 ÷ 10 = 3, 3 × 13 = 39 and 30 ÷ 15 = 2, 2 × 46 = 92 = 21543306 = 436 = 716

Page No 103:

Question 6:

The cost of a pen is Rs 1623 and that of a pencil is Rs 416.
Which costs more and by how much?

Answer:

Cost of a pen = Rs 1623 = Rs 503 = Rs 50 × 23 × 2 = Rs 1006

Cost of a pencil = Rs 416 = Rs 256 
 1006 > 256  Rs 1623 >Rs  416
So, the cost of a pen is more than the cost of a pencil.
Difference between their costs:
  = Rs 503 - 256 = Rs 100 - 256 = Rs 752562 = Rs 252 = Rs 1212
Hence, the cost of a pen is Rs 1212 more than the cost of a pencil.

Page No 103:

Question 7:

Of 34 and 57, which is greater and by how much?

Answer:

Let us compare 34 and 57.
By cross multiplying:
3 ⨯ 7 = 21 and ​4 ⨯ 5 = 20
Clearly, 21 > 20
∴​34>57
 Their difference:
   34 - 57                 L.C.M. of 4 and 7 = 2 × 2 × 7 = 28= 21 - 2028                28 ÷ 4 = 7, 7 × 3 = 21 and  28 ÷ 7 = 4,  4 × 5 = 20= 128 
Hence, 34 is greater than 57 by 128.

Page No 103:

Question 8:

Convert the fractions 12, 23, 49 and 56 into like fractions.

Answer:

 The given fractions are 12, 23, 49, 56.
L.C.M. of 2, 3, 9 and 6 = (2 ⨯ 3 ​⨯ 3) = 18
Now, we have:
12 = 1 × 92 × 9 = 918 23 = 2 × 63 × 6 = 121849 = 4 × 29 × 2 = 818 56 = 5 × 36 × 3 = 1518Hence, 918, 1218, 818 and 1518 are like fractions.

Page No 103:

Question 9:

Find the equivalent fraction of 35 having denominator 30.

Answer:

Let 35 = 30

30 = 5 ​⨯ 6 
So, we have to multiply the numerator by 6 to get the equivalent fraction having denominator 30.

35 = 3 × 65 × 6 = 1830

Thus, 1830 is the equivalent fraction of 35.

Page No 103:

Question 10:

Reduce 8498 to the simplest form.

Answer:

The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84.
The factors of 98 are 1, 2, 7, 14, 49, 98.
The common factors of 84 and 98 are 1, 2, 7, 14.
The H.C.F. of 84 and 98 is 14.
Dividing both the numerator and the denominator by the H.C.F.:
8498 = 84 ÷ 1498 ÷ 14 = 67

Page No 103:

Question 11:

2411 is an example of
(a) a proper fraction
(b) an improper fraction
(c) a mixed fraction
(d) none of these

Answer:

(b) an improper fraction

In an improper fraction, the numerator is greater than the denominator.

Page No 103:

Question 12:

38 is an example of
(a) a proper fraction
(b) an improper fraction
(c) a mixed fraction
(d) none of these

Answer:

(a) proper fraction

In a proper fraction, the numerator is less than the denominator.

Page No 103:

Question 13:

38 and 512 on comparison give
(a) 38>512
(b) 38<512
(c) 38=512
(d) none of these

Answer:

(b) 38<512

Considering 38 and 512:

On cross multiplying, we get:3 × 12 = 36 and 8 × 5 = 40Clearly, 36 < 40 38 < 512

Page No 103:

Question 14:

The largest of the fractions 23, 59, 12 and 712 is
(a) 23
(b) 59
(c) 712
(d) 12

Answer:

(a) 23

Explanation:
L.C.M. of 3, 9, 2 and 12 = ( 2 ⨯ 2 ⨯ 3 ​⨯ 3) = 36
Now, we have:
23 = 2 × 123 × 12  = 2436 59 = 5 × 49 × 4 = 203612 = 1 × 182 × 18 = 1836 712 = 7 × 312 × 3 = 2136Hence, 2436 = 23 is the largest fraction.

Page No 103:

Question 15:

334-112=?
(a) 212
(b) 214
(c) 112
(d) 114

Answer:

(b) 214
Explanation:

334 - 112 = 154 - 32             (L.C.M. of 2 and 4 = 2 × 2 = 4)                       = 15 - 64                        = 94 = 214

Page No 103:

Question 16:

Which of the following are like fractions?
(a) 23, 34, 45, 56
(b) 25, 27, 29, 211
(c) 18, 38, 58, 78
(d) none of these

Answer:

(c) 18, 38, 58, 78
Like fractions have same the denominator.



Page No 104:

Question 17:

?-821=821
(a) 0
(b) 1
(c) 218
(d) 1621

Answer:

(d) 1621

?  - 821 = 821? = 821 + 821 = 1621 

Page No 104:

Question 18:

Fill in the blanks:
(i) 923+......=19
(ii) 616-?=2930
(iii) 7 - 523=......
(iv) 7290 reduced to simples form is ......
(v) 4254=7    

Answer:

(i) 923 +......=19......=19 - 923 ......= 191 - 293  ......=57 - 293 ......= 283 .....= 913                       


(ii)                    
616- ? =2930 ? = 616 - 2930 ? = 376  - 2930 ? = 185 - 2930 ? = 15626305 ? = 515
 

(iii)                   
  7 - 523 = 71 - 173 = 21 -173 = 43 = 113

(iv)
 
The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90.The common factors of 72 and 90 are 1, 2, 3, 6, 9, 18.H.C.F. of 72 and 90 is 18. 72 ÷ 1890 ÷ 18 = 45

 (v) 

4254 =7942 ÷ 654 ÷ 6 = 79

Page No 104:

Question 19:

Write 'T' for true and 'F' for false for each of the statements given below:
(a) 313>3310.
(b) 8-156=716.
(c) 12, 13and 14 are like fractions.
(d) 35 lies between 3 and 5.
(e) Among 12, 13, 34, 43 the largest fractions is 43.

Answer:

(a) T                     
(b) F                   81 - 116 = 48 -116 = 376 = 616
(c) F                    (Because like fractions have the same denominator.)
​(d) F                    (It lies between 0 and 1 as all proper fractions are less than 1.)
(e) T                    (Because it is an improper fraction, while the others are proper fractions.)



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