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Question 1:

Divide:
(i) 142.45 by 10
(ii) 54.25 by 10
(iii) 3.45 by 10
(iv) 0.57 by 10
(v) 0.043 by 10
(vi) 0.004 by 10

(i)

(ii)

(iii)

(iv)
$\frac{0.57}{10}=\frac{57}{1000}\phantom{\rule{0ex}{0ex}}=0.057$

(v)
$\frac{0.043}{10}=\frac{43}{10×1000}\phantom{\rule{0ex}{0ex}}=0.0043$

(vi)
$\frac{0.004}{10}=\frac{4}{10×1000}\phantom{\rule{0ex}{0ex}}=0.0004$

Question 2:

Divide:
(i) 459.5 by 100
(ii) 74.3 by 100
(iii) 5.8 by 100
(iv) 0.7 by 100
(v) 0.48 by 100
(vi) 0.03 by 100

(i)  $\frac{459.5}{100}=\frac{4595}{1000}\phantom{\rule{0ex}{0ex}}=4.595$

(ii) $\frac{74.3}{100}=\frac{743}{1000}\phantom{\rule{0ex}{0ex}}=0.743$

(iii)   $\frac{5.8}{100}=\frac{58}{1000}\phantom{\rule{0ex}{0ex}}=0.058$

(iv)  $\frac{0.7}{100}=\frac{7}{1000}\phantom{\rule{0ex}{0ex}}=0.007$

(v)  $\frac{0.48}{100}=\frac{48}{100×100}\phantom{\rule{0ex}{0ex}}=0.0048$

(vi)  $\frac{0.03}{100}=\frac{3}{100×100}\phantom{\rule{0ex}{0ex}}=0.0003$

Question 3:

Divide:
(i) 235.41 by 1000
(ii) 29.5 by 1000
(iii) 3.8 by 1000
(iv) 0.7 by 1000

(i)  $\frac{235.41}{1000}=\frac{23541}{1000×100}\phantom{\rule{0ex}{0ex}}=0.23451$

(ii) $\frac{29.5}{1000}=\frac{295}{1000×10}\phantom{\rule{0ex}{0ex}}=0.0295$

(iii)   $\frac{3.8}{1000}=\frac{38}{1000×10}\phantom{\rule{0ex}{0ex}}=0.0038$

(iv)  $\frac{0.7}{1000}=\frac{7}{1000×10}\phantom{\rule{0ex}{0ex}}=0.0007$

Question 4:

Divide:
(i) 0.45 by 9
(ii) 217.44 by 18
(iii) 319.2 by 2.28
(iv) 40.32 by 9.6
(v) 0.765 by 0.9
(vi) 0.768 by 1.6

(i)
$\frac{0.45}{9}=\frac{45}{9×100}\phantom{\rule{0ex}{0ex}}=\frac{5}{100}\phantom{\rule{0ex}{0ex}}=0.05$

(ii)
$\frac{217.44}{18}=\frac{21744}{18×100}\phantom{\rule{0ex}{0ex}}=12.08$

(iii)
$\frac{319.2}{2.28}=\frac{3192×100}{228×10}\phantom{\rule{0ex}{0ex}}=140$

(iv)
$\frac{40.32}{9.6}=\frac{4032×10}{96×100}\phantom{\rule{0ex}{0ex}}=4.2\phantom{\rule{0ex}{0ex}}$

(v)
$\frac{0.765}{0.9}=\frac{765×10}{9×1000}\phantom{\rule{0ex}{0ex}}=\frac{7650}{9000}\phantom{\rule{0ex}{0ex}}=0.85$

(vi)
$\frac{0.768}{1.6}=\frac{768×10}{16×1000}\phantom{\rule{0ex}{0ex}}=\frac{7680}{16000}\phantom{\rule{0ex}{0ex}}=0.48$

Question 5:

Divide:
(i) 16.64 by 20
(ii) 0.192 by 12
(iii) 163.44 by 24
(iv) 403.2 by 96
(v) 16.344 by 12
(vi) 31.92 by 228

(i)
$\frac{16.64}{20}=\frac{1664}{20×100}\phantom{\rule{0ex}{0ex}}=0.832$

(ii)
$\frac{0.192}{12}=\frac{192}{12×1000}\phantom{\rule{0ex}{0ex}}=0.016$

(iii)
$\frac{163.44}{24}=\frac{16344}{24×100}\phantom{\rule{0ex}{0ex}}=6.81$

(iv)
$\frac{403.2}{96}=\frac{4032}{960}\phantom{\rule{0ex}{0ex}}=4.2$

(v)
$\frac{16.344}{12}=\frac{16344}{12×1000}\phantom{\rule{0ex}{0ex}}=\frac{1362}{1000}\phantom{\rule{0ex}{0ex}}=1.362$

(vi)
$\frac{31.92}{228}=\frac{3192}{228×100}\phantom{\rule{0ex}{0ex}}=\frac{14}{100}\phantom{\rule{0ex}{0ex}}=0.14$

Question 6:

Divide:
(i) 15.68 by 20
(ii) 164.6 by 200
(iii) 403.80 by 30

(i)

$\frac{15.68}{20}$
$=\frac{1568}{20×100}\phantom{\rule{0ex}{0ex}}=0.784$

(ii)

$\frac{164.6}{200}$
$\frac{1646}{200×10}\phantom{\rule{0ex}{0ex}}=\frac{1646}{2000}\phantom{\rule{0ex}{0ex}}=0.823$

(iii)

$\frac{403.8}{30}$
$=\frac{4038}{30×10}\phantom{\rule{0ex}{0ex}}=\frac{4038}{300}\phantom{\rule{0ex}{0ex}}=13.46$

Question 7:

Divide:
(i) 76 by 0.019
(ii) 88 by 0.08
(iii) 148 by 0.074
(iv) 7 by 0.014

(i)
$\frac{76}{0.019}=\frac{76×1000}{19}\phantom{\rule{0ex}{0ex}}=4000\phantom{\rule{0ex}{0ex}}$

(ii)
$\frac{88}{0.08}=\frac{88×100}{8}\phantom{\rule{0ex}{0ex}}=1100$

(iii)
$\frac{148}{0.074}=\frac{148×1000}{74}\phantom{\rule{0ex}{0ex}}=2000$

(iv)
$\frac{7}{0.014}=\frac{7×1000}{14}\phantom{\rule{0ex}{0ex}}=500$

Question 8:

Divide:
(i) 20 by 50
(ii) 8 by 100
(iii) 72 by 576
(iv) 144 by 15

(i)

$\frac{20}{50}\phantom{\rule{0ex}{0ex}}=\frac{2}{5}\phantom{\rule{0ex}{0ex}}=0.4$

(ii)

$\frac{8}{100}\phantom{\rule{0ex}{0ex}}=0.08$

(iii)

$\frac{72}{576}\phantom{\rule{0ex}{0ex}}=\frac{18}{144}\phantom{\rule{0ex}{0ex}}=\frac{3}{24}\phantom{\rule{0ex}{0ex}}=0.125$

(iv)

$\frac{144}{15}\phantom{\rule{0ex}{0ex}}=\frac{48}{5}\phantom{\rule{0ex}{0ex}}=9.6$

Question 9:

A vehicle covers a distance of 43.2 km in 2.4 litres of petrol. How much distance will it travel in 1 litre of petrol?

Distance travelled by the vehicle in 2.4 litres of petrol = 43.2 km

$\therefore$ Distance travelled in 1 litre of petrol will be:

Thus, the vehicle will travel 18 km in 1 litre of petrol.

Question 10:

The total weight of some bags of wheat is 1743 kg. If each bag weights 49.8 kg, how many bags are there?

Let the number of bags of wheat be x.

Given:

Weight of x bags = 1,743 kg

Weight of one bag = 49.8 kg

Therefore, 49.8 $×$ x = 1,743
x =
= 35

Thus, there are 35 bags of wheat.

Question 11:

Shikha cuts 50 m of cloth into pieces of 1.25 m each. How many pieces does she get?

Length of cloth = 50 m

Length of one piece of cloth = 1.25 m

Let the number of pieces be x.

$\therefore$ Number of piecesâ€‹ of cloth $×$ Length of each piece of cloth = Total length of cloth

x $×$1.25 = 50
x = $\frac{50}{1.25}$
=

Thus, she gets 40 pieces of 1.25 m cloth from a total of 50 m.

Question 12:

Each side of a rectangular polygon is 2.5 cm in length. The perimeter of the polygon is 12.5 cm. How many sides does the polygon have?

Length of each side of the polygon  = 2.5 cm

Perimeter of the polygon = 12.5 cm

Let the number of sides of the polygon be z.

$\therefore$ 2.5 $×$ z = 12.5 ( Perimeter = Length of one side multiplied by the number of sides)
or, z = $\frac{12.5}{2.5}\phantom{\rule{0ex}{0ex}}=5$

Thus, the polygon has 5 sides.

Question 13:

The product of two decimals is 42.987. If one of them is 12.46, find the other.

One decimal is 12.46.

Let the other decimal be x.

According to the question:

12.46 $×$ x = 42.987

Thus, the other decimal is 3.45.

Question 14:

The weight of 34 bags of sugar is 3483.3 kg. If all bags weigh equally, find the weight of each bag.

Number of bags = 34

Weight of 34 bags = 3483.3 kg

$\therefore$ Weight of one bag =
$\frac{3483.3}{34}\phantom{\rule{0ex}{0ex}}=\frac{34833}{340}\phantom{\rule{0ex}{0ex}}=102.45$

Thus, weight of each bag = 102.45 kg

Question 15:

How many buckets of equal capacity can be filled from 586.5 litres of water, if each bucket has capacity of 8.5 litres?

Capacity of one bucket = 8.5 litres

Total water in all buckets = 586.5 litres

Let the number of buckets with equal capacity be x.

According to the question:

8.5 $×$ x = 586.5

Thus, there are 69 buckets.

Question 1:

Write each of the following as decimals:
(i) $\frac{8}{100}$
(ii) $20+\frac{9}{10}+\frac{4}{100}$
(iii) $23+\frac{2}{10}+\frac{6}{1000}$

(i)  We have 8 hundredths.
∴ $\frac{8}{100}$ = 0.08

(ii) We have 2 tens, 9 tenths and 4 hundredths.
∴
= 20.94

(iii) We have 2 tens, 3 ones , 2 tenths and 6 thousandths.

= 23.2006

Question 2:

Convert each of the following into fractions in the lowest form:
(i) 0.04
(ii) 2.34
(iii) 0.342
(iv) 17.38

i) Multiplying and Dividing 0.04 by 100, we get:

Thus, fraction in the lowest form is $\frac{1}{25}$.

ii) Multiplying and Dividing 2.34 by 100, we get:

$\frac{2.34×100}{100}=\frac{234}{100}=\frac{117}{50}$
Thus, fraction in the lowest form is $\frac{117}{50}$.

iii) Multiplying and Dividing 0.342 by 1000, we get:

$\frac{0.342×1000}{1000}=\frac{342}{1000}=\frac{171}{500}$
Therefore, fraction in the lowest form is $\frac{171}{500}$.

iv) Multiplying and Dividing 17.38 by 100, we get:

$\frac{17.38×100}{100}=\frac{1738}{100}=\frac{869}{50}$
Thus, fraction in the lowest form is $\frac{869}{50}$.

Question 3:

Express the following fractions as decimals:
(i) $\frac{23}{10}$
(ii) $25\frac{1}{8}$
(iii) $39\frac{7}{35}$
(iv) $15\frac{1}{25}$

i)  In the given fraction, we have 2 tenths and 3 ones.

$\therefore$
ii) Let us first convert the given fraction to a proper fraction. We get:

$25\frac{1}{8}$$\frac{201}{8}$
To convert $\frac{201}{8}$ into decimals, let us multiply the numerator and denominator separately by 125. We get:

$\frac{201×125}{8×125}=\frac{25125}{1000}=25.125$

iii)By simplifying $39\frac{7}{35}$ we get

Now let us first convert the fraction to a proper fraction. We get:

Now to convert $\frac{196}{5}$ into decimals, let us multiply the numerator and denominator separately by 2. We get:

iv) Let us first convert the given fraction to a proper fraction. We get:

$15\frac{1}{25}$ = $\frac{376}{25}$
To convert $\frac{376}{25}$ into decimals, let us multiply the numerator and denominator separately by 4. We get:

Question 4:

(i) 41.8, 39.24, 5.01 and 62.6
(ii) 18.03, 146.3, 0.829 and 5.324

i) Let us first convert the given decimals to like decimals.

We get the decimals as: 41.80, 39.24, 05.01, 62.60

ii) Let us first convert the given decimals to like decimals.

We get the decimals as: 018.030, 146.300, 000.829, 005.324.

018.030
146.300
000.829
+ 005.324
= 170.483

Question 5:

Find the value of:
(i) 9.756 − 6.28
(ii) 48.1 − 0.37
(iii) 108.032 − 86.8
(iv) 100 − 26.32

i) On converting the given decimals to like decimals, we get the new decimals as 9.756 and 6.280.

Let us now subtract them.

9.756
$-$ 6.280
=  3.476

ii) On converting the given decimals to like decimals, we get the new decimals as 48.10 and 00.37.

Let us now subtract them.

48.10
$-$  00.37
=   47.73

iii) On converting the given decimals to like decimals, we get the new decimals as 108.032 and 086.800.

Let us now subtract them.

108.032
$-$   086.800
=      21.232

iv)  On converting the given decimals to like decimals, we get the new decimals as 100.00 and 026.32.

Let us now subtract them.

100.00
$-$     026.32
=      73.68

Question 6:

Take out 3.547 from 7.2

According to the question, we need to subtract 3.547 from 7.2.

On converting the given decimals to like decimals, we get the new decimals as 3.547 and 7.200.

Let us now subtract them.

7.200
$-$ 3.547
=  3.653

Question 7:

What is to be added to 36.85 to get 59.41?

Let x be added to 36.85 to get 59.41.

$\therefore$ 36.85 + x = 59.41

or, x = 59.41 $-$ 36.85
= 22.56

Thus, we need to add 22.56 to 36.85 to get 59.41.

Question 8:

What is to be subtracted from 17.1 to get 2.051?

Let x be subtracted from 17.1 to get 2.051.

$\therefore$ 17.1 $-$ x = 2.051

or, x = 17.1 $-$ 2.051
=  15.049

Thus, we need to subtract 15.049 from 17.1 to get 2.051.

Question 9:

By how much should 34.79 be increased to get 70.15?

Let 34.79 be increased by x to get 70.15.

$\therefore$ 34.79 + x = 70.15

or, x = 70.15 $-$ 34.79
= 35.36

Thus, 34.79 should be increased by 35.36 to get 70.15.

Question 10:

By how much should 59.71 be decreased to get 34.58?

Let 59.71 be decreased by x to get 34.58.

$\therefore$ 59.71 $-$ x = 34.58

or, x = 59.71 $-$ 34.58
= 25.13

Thus, 59.71 should be decreased by 25.13 to get 34.58.

Question 1:

Find the product:
(i) 4.74 × 10
(ii) 0.45 × 10
(iii) 0.0215 × 10
(iv) 0.0054 × 10

i) On dividing by 100, we get:

4.74 $×$10 =

ii) On dividing by 100, we get:

iii) Because the decimal is after 4 places from the right, we will divide by 10,000. We get:

iv) Because the decimal is after 4 places from the right, we will divide by 10,000. We get:

Question 2:

Find the product:
(i) 35.853 × 100
(ii) 42.5 × 100
(iii) 12.075 × 100
(iv) 100 × 0.005

i) On dividing by 1,000, we get:

ii) On dividing by 10, we get:

iii) On dividing by 1,000, we get:

iv) On dividing by 1,000, we get:

Question 3:

Find the product:
(i) 2.506 × 1000
(ii) 20.708 × 1000
(iii) 0.0529 × 1000
(iv) 1000 × 0.1

i) On dividing by 1000, we get:

ii) On dividing by 1000, we get:

iii) On dividing by 10,000, we get:

iv) On dividing by 10, we get:

Question 4:

Find the product:
(i) 3.4 × 17
(ii) 0.745 × 12
(iii) 28.73 × 47
(iv) 0.0415 × 59

i) On dividing the decimal by 10 and multiplying the numbers, we get:

ii) On dividing the decimal by 1000 and multiplying the numbers, we get:

iii) On dividing the decimal by 100 and multiplying the numbers, we get:

iv) On dividing the decimal by 10000 and multiplying the numbers, we get:

Question 5:

Find:
(i) 1.07 × 0.02
(ii) 211.9 × 1.13
(iii) 10.05 × 1.05
(iv) 13.01 × 5.01

i)
$\frac{107}{100}×\frac{2}{100}\phantom{\rule{0ex}{0ex}}=\frac{107×2}{10000}\phantom{\rule{0ex}{0ex}}$
= 0.0214

ii)
$\frac{2119}{10}×\frac{113}{100}\phantom{\rule{0ex}{0ex}}=\frac{239447}{1000}\phantom{\rule{0ex}{0ex}}=239.447$

iii)
$\frac{1005}{100}×\frac{105}{100}\phantom{\rule{0ex}{0ex}}=\frac{105525}{10000}\phantom{\rule{0ex}{0ex}}=10.5525$

iv)

$\frac{1301}{100}×\frac{501}{100}\phantom{\rule{0ex}{0ex}}=\frac{651801}{10000}\phantom{\rule{0ex}{0ex}}=65.1801\phantom{\rule{0ex}{0ex}}$

Question 6:

Find the area of a rectangle whose length is 5.5 m and breadth is 3.4 m.

Length of the rectangle = 5.5 m

Breadth of the rectangle = 3.4 m

We know:

Area of rectangle = Length $×$ Breadth
=

Thus, area of the rectangle = 18.7 m2

Question 7:

If the cost of a book is Rs 25.75, find the cost of 24 such books.

Cost of one book = Rs. 25.75

∴ Cost of 24 books = Rs. 25.75 $×$ 24

=

Hence, the cost of 24 books is Rs. 618.

Question 8:

A car covers a distance of 14.75 km in one litre of petrol. How much distance will it cover in 15.5 litres of petrol?

Distance travelled by the car in 1 litre of petrol = 14.75 km

∴ Distance travelled by the car in 15.5 litres of petrol =

$\frac{1475}{100}×\frac{155}{10}$
$\frac{228625}{1000}$
= 228.625 km

Thus, the car travelled 228.625 km in 15.5 litres of petrol.

Question 9:

One kg of rice costs Rs 42.65. What will be the cost of 18.25 kg of rice?

Price of 1 kg of rice = Rs. 42.65

Price of 18.25 kg of rice = Rs. 42.65 $×$ 18.25
= $\frac{4265}{100}×\frac{1825}{100}\phantom{\rule{0ex}{0ex}}=\frac{7783625}{10000}$

= 778.3625

Thus, 18.25 kg of rice will cost Rs. 778.36.

Question 10:

One metre of cloth costs Rs 152.50. What is the cost of 10.75 metres of cloth?

$\therefore$ Cost of 10.75 m of cloth = Rs. 152.50 $×$ 10.75
$\frac{1525}{10}×\frac{1075}{100}\phantom{\rule{0ex}{0ex}}=\frac{1639375}{1000}\phantom{\rule{0ex}{0ex}}$