Rs Aggarwal 2017 Solutions for Class 8 Math Chapter 1 Rational Numbers are provided here with simple step-by-step explanations. These solutions for Rational Numbers are extremely popular among Class 8 students for Math Rational Numbers Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Rs Aggarwal 2017 Book of Class 8 Math Chapter 1 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Rs Aggarwal 2017 Solutions. All Rs Aggarwal 2017 Solutions for class Class 8 Math are prepared by experts and are 100% accurate.
Page No 3:
Question 1:
Express as a rational number with denominator
(i) 20
(ii) −30
(iii) 35
(iv) −40
Answer:
If is a fraction and is a non-zero integer, then .
Now,
(i)
(ii)
(iii)
(iv)
Page No 3:
Question 2:
Express as a rational number with denominator 7.
Answer:
If is a rational number and is a common divisor of , then .
∴
Page No 3:
Question 3:
Express as a rational number with denominator 5.
Answer:
If is a rational integer and is a common divisor of , then .
∴
Page No 3:
Question 4:
Express each of the following rational numbers in standard form:
(i)
(ii)
(iii)
(iv)
Answer:
A rational number is said to be in the standard form if and have no common divisor other than unity and .
Thus,
(i) The greatest common divisor of 12 and 30 is 6.
∴ (In the standard form)
(ii)The greatest common divisor of 14 and 49 is 7.
∴ (In the standard form)
(iii)
The greatest common divisor of 24 and 64 is 8.
∴ (In the standard form)
(iv)
The greatest common divisor of 36 and 63 is 9.
∴ (In the standard form)
Page No 3:
Question 5:
Which of the two rational numbers is greater in the given pair?
(i)
(ii)
(iii)
(iv)
(v)
(vi)
Answer:
We know:
(i) Every positive rational number is greater than 0.
(ii) Every negative rational number is less than 0.
Thus, we have:
(i) is a positive rational number.
∴
(ii) is a negative rational number.
∴
(iii) is a negative rational number.
∴
Also,
is a positive rational number.
∴
Combining the two inequalities, we get:
(iv)Both and have the same denominator, that is, 7.
So, we can directly compare the numerators.
∴
(v)The two rational numbers are and .
The LCM of the denominators 3 and 4 is 12.
Now,
Also,
Further
∴
(vi)The two rational numbers are and .
We can write .
The LCM of the denominators 2 and 1 is 2.
Now,
Also,
∵
∴
Page No 3:
Question 6:
Which of the two rational numbers is greater in the given pair?
(i)
(ii)
(iii)
(iv)
(v)
(vi)
Answer:
1. The two rational numbers are .
The LCM of the denominators 3 and 7 is 21.
Now,
Also,
Further,
∴
2. The two rational numbers are .
The first fraction can be expressed as .
The LCM of the denominators 9 and 8 is 72.
Now,
Also,
Further,
∴
3. The two rational numbers are .
The LCM of the denominators 3 and 5 is 15.
Now,
Also,
Further,
∴
4. The two rational numbers are .
The LCM of the denominators 13 and 12 is 156.
Now,
Also,
Further,
∴
5. The two rational numbers are .
∴
The LCM of the denominators 5 and 10 is 10.
Now,
Also,
Further,
∴
6. The two rational numbers are
.
The LCM of the denominators is 5.
Now,
Because , we can conclude that .
Page No 3:
Question 7:
Fill in the blanks with the correct symbol out of >, = and <:
(i)
(ii)
(iii)
(iv)
(v)
(vi)
Answer:
(i)We will write each of the given numbers with positive denominators.
One number =
Other number =
LCM of 7 and 13 = 91
∴
And,
Clearly,
∴
Thus,
(ii) We will write each of the given numbers with positive denominators.
One number =
Other number =
LCM of 13 and 91 = 91
∴ and
Clearly,
∴
Thus,
(iii) We will write each of the given numbers with positive denominators.
One number =
We can write -2 as.
Other number =
LCM of 1 and 5 = 5
∴ and
Clearly,
∴
Thus,
(iv) We will write each of the given numbers with positive denominators.
One number =
Other number =
LCM of 3 and 8 = 24
∴ and
Clearly,
∴
Thus,
(v)
is a positive number.
Because every positive rational number is greater than 0, .
(vi) We will write each of the given numbers with positive denominators.
One number =
Other number =
LCM of 9 and 10 = 90
∴ and
Clearly,
∴
Thus,
Page No 3:
Question 8:
Arrange the following rational numbers in ascending order:
(i)
(ii)
(iii)
(iv)
Answer:
(i) We will write each of the given numbers with positive denominators.
We have:
and
Thus, the given numbers are
LCM of 9, 12, 18 and 3 is 36.
Now,
Clearly,
∴
That is
(ii) We will write each of the given numbers with positive denominators.
We have:
and
Thus, the given numbers are
LCM of 4, 12, 16 and 24 is 48.
Now,
Clearly,
∴
That is
(iii) We will write each of the given numbers with positive denominators.
We have:
Thus, the given numbers are
LCM of 5, 10, 15 and 20 is 60.
Now,
Clearly,
∴ .
That is
(iv) We will write each of the given numbers with positive denominators.
We have:
Thus, the given numbers are
LCM of 7, 14, 28 and 42 is 84.
Now,
Clearly,
∴ .
That is
Page No 3:
Question 9:
Arrange the following rational numbers in descending order:
(i)
(ii)
(iii)
(iv)
Answer:
(i) We will first write each of the given numbers with positive denominators. We have:
Thus, the given numbers are
LCM of 1, 6, 3 and 3 is 6
Now,
and
Clearly,Thus,
∴ . i.e
(ii) We will first write each of the given numbers with positive denominators. We have:
and
Thus, the given numbers are
LCM of 10, 15, 20 and 30 is 60
Now,
and
Clearly,
∴ . i.e
(iii) We will first write each of the given numbers with positive denominators. We have:
Thus, the given numbers are
LCM of 6, 12, 18 and 24 is 72
Now,
and
Clearly,
∴ . i.e
(iv) The given numbers are
LCM of 11, 22, 33 and 44 is 132
Now,
and
Clearly,
∴
Page No 3:
Question 10:
Which of the following statements are true and which are false?
(i) Every whole number is a rational number.
(ii) Every integer is a rational number.
(iii) 0 is a whole number but it is not a rational number.
Answer:
1. True
A whole number can be expressed as . Thus, every whole number is rational.
2. True
Every integer is a rational number because any integer can be expressed as . Thus, every integer is a rational number.
3. False
Thus, 0 is a rational and whole number.
Page No 5:
Question 1:
Represent each of the following numbers on the number line:
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
(viii) 8
Answer:
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
(viii)
Page No 5:
Question 2:
Represent each of the following numbers on the number line:
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii) −3
(viii)
Answer:
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
(viii)
Page No 5:
Question 3:
Which of the following statements are true and which are false?
(i) lies to the left of 0 on the number line.
(ii) lies to the right of 0 on the number line.
(iii) The rational numbers and are on opposite sides of 0 on the number line.
(iv) The rational number lies to the left of 0 on the number line.
Answer:
(i) True
A negative number always lies to the left of 0 on the number line.
(ii) False
A negative number always lies to the left of 0 on the number line.
(iii) True
Negative and positive numbers always lie on the opposite sides of 0 on the number line.
(iv) False
The negative sign cancels off and the number becomes ; it lies to the right of 0 on the number line.
Page No 10:
Question 1:
Add the following rational numbers:
(i)
(ii)
(iii)
(iv)
(v)
(vi)
Answer:
1.
2.
3.
4.
5.
6.
Page No 10:
Question 2:
Add the following rational numbers:
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
(viii)
(ix)
Answer:
1. The denominators of the given rational numbers are 4 and 5.
LCM of 4 and 5 is 20.
Now,
and
∴
2. The denominators of the given rational numbers are 8 and 12.
LCM of 8 and 12 is 24.
Now,
and
∴
3. The denominators of the given rational numbers are 9 and 6.
LCM of 9 and 6 is 18.
Now,
and
∴
4. The denominators of the given rational numbers are 16 and 24.
LCM of 16 and 24 is 48.
Now,
and
∴
5. We will first write each of the given numbers with positive denominators.
The denominators of the given rational numbers are 18 and 27.
LCM of 18 and 27 is 54.
Now,
and
∴
6. We will first write each of the given numbers with positive denominators.
and
The denominators of the given rational numbers are 12 and 15.
LCM of 12 and 15 is 60.
Now,
and
∴
7. We can write -1 as.
The denominators of the given rational numbers are 1 and 4.
LCM of 1 and 4 is 4.
Now,
and
∴
8. We can write 2 as.
The denominators of the given rational numbers are 1 and 4.
LCM of 1 and 4 is 4.
Now,
and
∴
9. We can write 0 as.
The denominators of the given rational numbers are 1 and 5.
LCM of 1 and 5 is 5, that is, (1 5).
Now,
and
∴
Page No 10:
Question 3:
Verify the following:
(i)
(ii)
(iii)
(iv)
Answer:
1. LHS =
LCM of 5 and 7 is 35.
RHS =
LCM of 5 and 7 is 35.
∴
2. LHS =
LCM of 8 and 13 is 104.
RHS =
LCM of 13 and 8 is 104.
∴
3. LHS =
LCM of 1 and 12 is 12.
RHS =
LCM of 12 and 1 is 12.
∴
4. LHS =
We will write the given numbers with positive denominators.
and
LCM of 7 and 35 is 35.
RHS =
We will write the given numbers with positive denominators.
and
LCM of 35 and 7 is 35.
∴
Page No 10:
Question 4:
Verify the following:
(i)
(ii)
(iii)
Answer:
1.
LHS =
RHS =
∴
2.
LHS =
We will first make the denominator positive.
RHS =
We will first make the denominator positive.
∴
3.
LHS =
RHS =
∴
Page No 10:
Question 5:
Fill in the blanks.
(i)
(ii)
(iii)
(iv)
(v)
(vi)
Answer:
(i) Addition is commutative, that is, .
Hence, the required solution is .
(ii) Addition is commutative, that is, .
Hence, the required solution is .
(iii) Addition is associative, that is, .
Hence, the required solution is .
(iv) Addition is associative, that is, .
Hence, the required solution is .
(v) Addition is associative, that is, .
Hence, the required solution is.
(vi) 0 is the additive identity, that is, .
Hence, the required solution is .
Page No 11:
Question 6:
Find the additive inverse of each of the following:
(i)
(ii)
(iii) −18
(iv)
(v)
(vi)
(vii)
(viii) 0
(ix)
(x)
Answer:
The additive inverse of is . Therefore,
(i) Additive inverse of
(ii) Additive inverse of
(iii) Additive inverse of -18 is 18.
(iv) Additive inverse of
(v) In the standard form, we write
Hence, its additive inverse is .
(vi) We can write:
Hence, its additive inverse is .
(vii) Additive inverse of
(viii) Additive inverse of 0 is 0.
(ix) In the standard form, we write
Hence, its additive inverse is .
(x) We can write:
Hence, its additive inverse is .
Page No 11:
Question 7:
Subtract:
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
(viii)
Answer:
(i)
=
(ii)
= (Because the additive inverse of )
=
(iii)
= (Because the additive inverse of )
=
(iv)
= (Because the additive inverse of )
=
(v)
= (Because the additive inverse of )
=
(vi)
= (Because the additive inverse of )
=
(vii)
= (Because the additive inverse of )
=
(viii)
= (Because the additive inverse of )
=
Page No 11:
Question 8:
Using the rearrangement property find the sum:
(i)
(ii)
(iii)
(iv)
Answer:
(i)
=
.
(ii)
=
=
=
(iii)
=
=
.
(iv)
=
=
Page No 11:
Question 9:
The sum of two rational numbers is −2. If one of the numbers is , find the other.
Answer:
Page No 11:
Question 10:
The sum of two rational numbers is . If one of the numbers is , find the other.
Answer:
Page No 11:
Question 11:
What number should be added to so as to get ?
Answer:
Let the required number be x.
Now,
(Adding to both the sides)
Hence, the required number is .
Page No 11:
Question 12:
What number should be added to −1 so as to get ?
Answer:
Let the required number be x.
Now,
(Adding 1 to both the sides)
Hence, the required number is .
Page No 11:
Question 13:
What number should be subtracted from to get ?
Answer:
Let the required number be x.
Now,
(Adding to both the sides)
(Adding to both the sides)
Hence, the required number is.
Page No 11:
Question 14:
(i) Which rational number is its own additive inverse?
(ii) Is the difference of two rational numbers a rational number?
(iii) Is addition commutative on rational numbers?
(iv) Is addition associative on rational numbers?
(v) Is subtraction commutative on rational numbers?
(vi) Is subtraction associative on rational numbers?
(vii) What is the negative of a negative rational number?
Answer:
1. Zero is a rational number that is its own additive inverse.
2. Yes
Consider
Since are integers since integers are closed under the operation of multiplication and is an integer since integers are closed under the operation of subtraction, then
since it is in the form of one integer divided by another and the denominator is not equal to 0
Since, b and d were not equal to 0
Thus, is a rational number.
3. Yes, rational numbers are commutative under addition. If a and b are rational numbers, then the commutative law under addition is .
4. Yes, rational numbers are associative under addition. If a, b and c are rational numbers, then the associative law under addition is .
5. No, subtraction is not commutative on rational numbers. In general, for any two rational numbers, .
6. Rational numbers are not associative under subtraction. Therefore, .
7. Negative of a negative rational number is a positive rational number.
Page No 16:
Question 1:
Find each of the following products:
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
(viii)
(ix)
(x)
(xi)
(xii)
Answer:
(i)
(ii)
(iii)
Simplifying the above rational number, we get:
(iv)
Simplifying the above rational number, we get:
(v)
Simplifying the above rational number, we get:
(vi)
Simplifying the above rational number, we get:
(vii)
Simplifying the above rational number, we get:
(viii)
Simplifying the above rational number, we get:
(ix)
Simplifying the above rational number, we get:
(x)
Simplifying the above rational number, we get:
(xi)
Simplifying the above rational number, we get:
(xii)
Simplifying the above rational number, we get:
Page No 16:
Question 2:
Verify each of the following:
(i)
(ii)
(iii)
(iv)
Answer:
(i)
LHS = RHS
(ii)
(iii)
LHS = RHS
(iv)
LHS = RHS
Page No 16:
Question 3:
Verify each of the following:
(i)
(ii)
(iii)
Answer:
(i)
∴
(ii)
∴
(iii)
∴
Page No 16:
Question 4:
Fill in the blanks:
(i)
(ii)
(iii)
(iv)
Answer:
(i)
(ii)
(iii)
(iv)
Page No 16:
Question 5:
Find the multiplicative inverse (i.e., reciprocal) of:
(i)
(ii)
(iii)
(iv) 18
(v) −16
(vi)
(vii) −1
(viii)
(ix)
(x)
Answer:
Page No 17:
Question 6:
Find the value of:
(i)
(ii)
(iii)
(iv)
Answer:
We know that or
Page No 17:
Question 7:
Verify the following:
(i)
(ii)
(iii)
(iv)
Answer:
∴
(iii)
(iv)
Page No 17:
Question 8:
Name the property of multiplication illustrated by each of the following statements:
(i)
(ii)
(iii)
(iv)
(v)
(vi)
Answer:
- Commutative property
- Associative property
- Distributive property
- Property of multiplicative identity
- Property of multiplicative inverse
- Multiplicative property of 0
Page No 17:
Question 9:
Fill in the blanks:
(i) The product of a rational number and its reciprocal is .......
(ii) Zero has ....... reciprocal.
(iii) The numbers ....... and ....... are their own reciprocals.
(iv) zero is ....... the reciprocal of any number.
(v) The reciprocal of a, where a ≠ 0, is .......
(vi) The reciprocal of , where a ≠ 0, is .......
(vii) The reciprocal of a positive rational rational number is .......
(viii) The reciprocal of a negative rational number is .......
Answer:
(i) 1
(ii) no
(iii) 1; -1
(iv) not
(v)
(vi) a
(vii) positive
(viii) negative
Page No 19:
Question 1:
Simplify:
(i)
(ii)
(iii)
(iv)
(v)
(vi)
Answer:
Page No 19:
Question 2:
Verify whether the given statement is true or false:
(i)
(ii)
(iii)
(iv)
Answer:
Page No 19:
Question 3:
Verify whether the given statement is true or false:
(i)
(ii)
(iii)
Answer:
(ii)
(iii)
Page No 19:
Question 4:
The product of two rational numbers is −9. If one of the numbers is −12, find the other.
Answer:
Page No 19:
Question 5:
The product of two rational numbers is . If one of the numbers is , find the other.
Answer:
.
Page No 19:
Question 6:
By what rational number should we multiply to get ?
Answer:
Page No 19:
Question 7:
By what rational number should be multiplied to obtain ?
Answer:
Page No 19:
Question 8:
By what number should be divided to get ?
Answer:
Page No 19:
Question 9:
Divide the sum of and by the product of and
Answer:
Page No 19:
Question 10:
Divide the sum of and by their difference.
Answer:
Page No 19:
Question 11:
Fill in the blanks:
(i)
(ii)
(iii)
(iv)
Answer:
Page No 19:
Question 12:
(i) Are rational numbers always closed under division?
(ii) Are rational numbers always commutative under division?
(iii) Are rational numbers always associative under division?
(iv) Can we divide 1 by 0?
Answer:
(i) No, rational numbers are not closed under division in general.
; it is not a rational number.
(ii) No
Therefore, division is not commutative.
(iii) No, rational numbers are not associative under division.
(iv) No, we cannot divide 1 by 0. The answer will be, which is not defined.
Page No 21:
Question 1:
Find a rational number between
Answer:
Page No 21:
Question 2:
Find a rational number between 2 and 3.
Answer:
Page No 21:
Question 3:
Find a rational number between
Answer:
Page No 21:
Question 4:
Find two rational numbers between −3 and −2.
Answer:
Page No 21:
Question 5:
Find three rational numbers between 4 and 5.
Answer:
Page No 21:
Question 6:
Find three rational numbers between
Answer:
Page No 21:
Question 7:
Find 10 rational numbers between
Answer:
We can take any 10 out of these.
Page No 21:
Question 8:
Find 12 rational numbers between −1 and 2.
Answer:
Page No 21:
Question 1:
From a rope 11 m long, two pieces of lengths are cut off. What is the length of the remaining rope?
Answer:
Length of the rope when two pieces of lengths and are cut off = Total length of the rope - Length of the two cut off pieces
Now,
LCM of 5 and 10 is 10, i.e., .
∴
Length of the remaining rope
Therefore, the length of the remaining rope is .
Page No 21:
Question 2:
A drum full of rice weighs kg. If the empty drum weighs kg, find the weight of rice in the drum.
Answer:
Weight of rice in the drum = Weight of the drum full of rice - Weight of the empty drum
Therefore, the weight of rice in the drum is .
Page No 21:
Question 3:
A basket contains three types of fruits weighing in all. If of these be apples, be oranges and the rest pears, what is the weight of the pears in the basket?
Answer:
Weight of pears in the basket = Weight of the basket containing three types of fruits - (Weight of apples + Weight of oranges)
=
Now,
LCM of 9 and 6 is 18, that is, .
∴
Now,
Weight of pears in the basket =
Therefore, the weight of the pears in the basket is .
Page No 22:
Question 4:
On one day a rickshaw puller earned Rs 160. Out of his earnings he spent Rs on tea and snacks, Rs on food and Rs on repairs of the rickshaw. How much did he save on that day?
Answer:
Total earning = ₹160
Money spent on tea and snacks = ₹
Money spent on food = ₹
Money spent on repairs = ₹
Let the savings be ₹x.
Money spent on tea and snacks + Money spent on food + Money spent on repairs + Savings = Total earning
So, + + + x = 160
So, the savings are ₹.
Page No 22:
Question 5:
Find the cost of metres of cloth at Rs per metre.
Answer:
Cost of 1 m of cloth = ₹
So, cost of m of cloth
= ×
So, the cost of m of cloth is ₹.
Page No 22:
Question 6:
A car is moving at an average speed of km/hr. How much distance will it cover in hours?
Answer:
Speed =
Time = h
We know that
Hence, the distance covered in h is .
Page No 22:
Question 7:
Find the area of a rectangular park which is m long and m broad.
Answer:
Area of the rectangular park = Length of the park Breadth of the park (∵ Area of rectangle = Length Breadth)
Therefore, the area of the rectangular park is .
Page No 22:
Question 8:
Find the area of a square plot of land whose each side measures metres.
Answer:
Area of the square plot = Side Side = = a2 (Because the area of the square is , where a is the side of the square)
Therefore, the area of the square plot is .
Page No 22:
Question 9:
One litre of petrol costs ₹ . What is the cost of 34 litres of petrol?
Answer:
Cost of 1 litre of petrol = ₹
Cost of 34 litres of petrol = × 34 =
So, the cost of 34 litres of petrol is ₹.
Page No 22:
Question 10:
An aeroplane covers 1020 km in an hour. How much distance will it cover in hours?
Answer:
Distance covered by the aeroplane in hours =
Therefore, the distance covered by the aeroplane is .
Page No 22:
Question 11:
The cost of metres of cloth is ₹ . what is the cost of one metre of cloth?
Answer:
Cost of m of cloth = ₹
So, the cost of 1 m of cloth =
Hence, the cost of 1 m of cloth is ₹ .
Page No 22:
Question 12:
A cord of length m has been cut into 26 pieces of equal length. What is the length of each piece?
Answer:
Length of each piece of the cord =
Hence, the length of each piece of the cord is .
Page No 22:
Question 13:
The area of a room is If its breadth is metres, what is its length?
Answer:
Area of a room = Length Breadth
Thus, we have:
Hence, the length of the room is 12 metres.
Page No 22:
Question 14:
The product of two fractions is If one of the fractions is find the other.
Answer:
Let the other fraction be x.
Now, we have:
Hence, the other fraction is .
Page No 22:
Question 15:
In a school, of the students are boys. If there are 240 girls, find the number of boys in the school.
Answer:
If of the students are boys, then the ratio of girls is , that is, .
Now, let x be the total number of students.
Thus, we have:
Hence, the total number of students is 640.
Now,
Number of boys = Total number of students - Number of girls
Hence, the number of boys is 400.
Page No 22:
Question 16:
After reading of a book, 40 pages are left. How many pages are there in the book?
Answer:
Ratio of the read book =
Ratio of the unread book =
Let x be the total number of pages in the book.
Thus, we have:
Hence, the total number of pages in the book is 180.
Page No 22:
Question 17:
Rita had Rs 300. She spent of her money on notebooks and of the remainder on stationery items. How much money is left with her?
Answer:
Amount of money spent on notebooks =
∴ Money left after spending on notebooks =
Amount of money spent on stationery items from the remainder =
∴ Amount of money left with Rita =
Page No 22:
Question 18:
Amit earns ₹ 32000 per month. He spends of his income of food; of the remainder on house rent and of the remainder on the education of children. How much money is still left with him?
Answer:
Amit's income per month = ₹32,000
Money spent on food =
Remaining amount = ₹32,000 − ₹8,000 = ₹24,000
Money spent on house rent =
Money left = ₹24,000 − ₹7,200 = ₹16,800
Money spent on education of children =
Amount of money still left with him = ₹16,800 − ₹4,000 = ₹12,800
Page No 22:
Question 19:
If of a number exceeds its by 44, find the number.
Answer:
Let x be the required number.
We know that of the number exceeds its by 44.
That is,
Hence, the number is 140.
Page No 22:
Question 20:
At a cricket test match of the spectators were in a covered place while 15000 were in open. Find the total number of spectators.
Answer:
Ratio of spectators in the open
Total number of spectators in the open = x
Then,
Hence, the total number of spectators is 21,000
Page No 22:
Question 1:
Tick (✓) the correct answer
(a)
(b)
(c)
(d)
Answer:
(c)
The denominators of the given rational numbers are 16 and 12, respectively.
LCM of 16 and 12 is
Now, we have:
Page No 23:
Question 2:
Tick (✓) the correct answer
(a)
(b)
(c)
(d)
Answer:
(b)
and
Now, we have:
LCM of 15 and 3 is
Page No 23:
Question 3:
Tick (✓) the correct answer
(a)
(b)
(c)
(d)
Answer:
Now, we have:
LCM of 26 and 39 is 1014, that is,
(a)
Page No 23:
Question 4:
Tick (✓) the correct answer
(a)
(b)
(c)
(d)
Answer:
(b)
and
Now, we have:
LCM of 1 and 7 is 7
Page No 23:
Question 5:
Tick (✓) the correct answer
(a)
(b)
(c)
(d)
Answer:
(d)
We have:
LCM of 4 and 8 is 8, that is,
Page No 23:
Question 6:
Tick (✓) the correct answer
What should be added to
(a)
(b)
(c)
(d)
Answer:
(b)
Let the required number be x.
Now,
Page No 23:
Question 7:
Tick (✓) the correct answer
(a)
(b)
(c)
(d)
Answer:
(c)
Using the commutative and associative laws, we can arrange the terms in any suitable manner. Using this rearrangement property, we have:
Page No 23:
Question 8:
Tick (✓) the correct answer
The sum of two numbers is If one of the numbers is −5, what is the other?
(a)
(b)
(c)
(d)
Answer:
(b)
Let the other number be x.
Now,
Page No 23:
Question 9:
Tick (✓) the correct answer
What should be added to
(a)
(b)
(c)
(d)
Answer:
(c)
Let the required number be x.
Now,
Page No 23:
Question 10:
Tick (✓) the correct answer
What should be subtracted from
(a)
(b)
(c)
(d)
Answer:
(d)
Let the required number be x.
Now,
Thus, the required number is
Page No 23:
Question 11:
Tick (✓) the correct answer
(a)
(b)
(c)
(d) none of these
Answer:
(b)
The reciprocal of is
Page No 23:
Question 12:
Tick (✓) the correct answer
The product of two rational numbers is . If one of the numbers is then the other one is
(a)
(b)
(c)
(d)
Answer:
(a)
Let the other number be x.
Now,
Thus, the other number is
Page No 23:
Question 13:
Tick (✓) the correct answer
The product of two numbers is If one of the numbers is , the other is
(a)
(b)
(c)
(d)
Answer:
(c)
Let the other number be x.
Now,
Thus, the other number is
Page No 24:
Question 14:
Tick (✓) the correct answer
What should be subtracted from to get −2?
(a)
(b)
(c)
(d)
Answer:
(d)
Let the required number be x.
Now,
Thus, the required number is
Page No 24:
Question 15:
Tick (✓) the correct answer
The sum of two rational numbers is −3. If one of them is then the other one is
(a)
(b)
(c)
(d)
Answer:
(c)
Let the other number be x.
Now,
Thus, the other number is
Page No 24:
Question 16:
Tick (✓) the correct answer
Which of the following numbers is in standard form?
(a)
(b)
(c)
(d)
Answer:
(b) and (c)
The numbers and are in the standard form because they have no common divisor other than 1 and their denominators are positive.
Page No 24:
Question 17:
Tick (✓) the correct answer
(a)
(b)
(c)
(d)
Answer:
(a)
Page No 24:
Question 18:
Tick (✓) the correct answer
(a)
(b)
(c)
(d)
Answer:
(d)
Page No 24:
Question 19:
Tick (✓) the correct answer
(a)
(b)
(c)
(d)
Answer:
(d)
Let
Now,
Hence, the missing number is .
Page No 24:
Question 20:
Tick (✓) the correct answer
Additive inverse of is
(a)
(b) 0
(c)
(d)
Answer:
(c)
Additive inverse of is .
Page No 24:
Question 21:
Tick (✓) the correct answer
Reciprocal of is
(a)
(b)
(c)
(d) 0
Answer:
(c)
Reciprocal of is
Page No 24:
Question 22:
Tick (✓) the correct answer
A rational number between
(a)
(b)
(c)
(d)
Answer:
(d)
Rational number between and =
Page No 24:
Question 23:
Tick (✓) the correct answer
The reciprocal of a negative rational number
(a) is a positive rational number
(b) is a negative rational number
(c) can be either a positive or a negative rational number
(d) does not exist
Answer:
(b) is a negative rational number
The reciprocal of a negative rational number is a negative rational number.
Page No 27:
Question 1:
Find the additive inverse of:
(i)
(ii)
Answer:
(i)
Additive inverse of .
(ii) Additive inverse of .
Page No 27:
Question 2:
The sum of two rational numbers is −4. If one of them is , find the other.
Answer:
Page No 27:
Question 3:
What number should be added to
Answer:
Page No 27:
Question 4:
What number should be subtracted from to get ?
Answer:
Page No 27:
Question 5:
Find the multiplicative inverse of:
(i)
(ii)
Answer:
Page No 27:
Question 6:
The product of two numbers is −8. If one of them is −12, find the other.
Answer:
Page No 27:
Question 7:
Evaluate:
(i)
(ii)
(iii)
Answer:
Page No 27:
Question 8:
Name the property of multiplication shown by each of the following statements:
(i)
(ii)
(iii)
(iv)
(v)
Answer:
(i) Commutative law of multiplication
(ii) Existence of multiplicative identity
(iii) Associative law of multiplication
(iv) Multiplicative property of 0
(v) Distributive law of multiplication over addition
Page No 27:
Question 9:
Find two rational numbers lying between
Answer:
Page No 27:
Question 10:
Mark (✓) against the correct answer
What should be added to
(a)
(b)
(c)
(d)
Answer:
(c)
Let the number be .
Now,
Page No 27:
Question 11:
Mark (✓) against the correct answer
What should be subtracted from to get
(a)
(b)
(c)
(d)
Answer:
(d)
Let the number be .
Now,
Page No 27:
Question 12:
Mark (✓) against the correct answer
(a)
(b)
(c)
(d)
Answer:
(b)
We have:
Page No 27:
Question 13:
Mark (✓) against the correct answer
The product of two numbers is . If one of them is then the other is
(a)
(b)
(c)
(d)
Answer:
(a)
Let the required number be .
Now,
Page No 28:
Question 14:
Mark (✓) against the correct answer
(a)
(b)
(c)
(d)
Answer:
(b)
We have:
Page No 28:
Question 15:
Mark (✓) against the correct answer
(a)
(b)
(c)
(d)
Answer:
(c)
Page No 28:
Question 16:
Mark (✓) against the correct answer
Reciprocal of is
(a)
(b)
(c)
(d) none of these
Answer:
(b)
Page No 28:
Question 17:
A rational number between and is
(a)
(b)
(c)
(d)
Answer:
(b)
Page No 28:
Question 18:
Fill in the blanks.
(i)
(ii)
(iii)
(iv)
Answer:
(ii)
(iii)
(iv)
Page No 28:
Question 19:
Write 'T' for true and 'F' for false for each of the following:
(i) Rational numbers are always closed under subtraction.
(ii) Rational numbers are aways closed under division.
(iii) 1 ÷ 0 = 0.
(iv) Subtraction is commutative on rational numbers.
(v)
Answer:
(i) T
If are rational numbers, then is also a rational number because are all rational numbers.
(ii) F
Rational numbers are not always closed under division. They are closed under division only if the denominator is non-zero.
(iii) F
cannot be defined.
(iv) F
Let represent rational numbers.
Now, we have:
∴
(v) T
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