M l aggarwal understanding icse mathematics class 8 Solutions for Chapter 1 rational numbers

Add the following:

(i) 4 / 7 and 5 / 7

(ii) 7 / – 13 and 4 / – 13

Simplify:

Verify commutative property of addition for the following pairs of rational

numbers.

(i) – 4 / 3 and 3 / 7

(ii) – 2 / – 5 and 1 / 3

(iii) 9 / 11 and 2 / 13

Find the additive inverse of the following rational numbers:

(i) 2 / – 3

(ii) – 7 / – 12

Verify that – (- x) = x for

(i) x = 10 / 13

(ii) x = – 15 / 17

Fill in the blanks:

(i) (- 4 / 9) + (2 / 7) is a ……….. number

(ii) (43 / 89) + (- 51 / 47) = …….. + (43 / 89)

(iii) 2 / 7 + …… = 2 / 7 = 0 + ………

(iv) 4 / 11 + {(- 7 / 12) + 9 / 10} = {(4 / 11) + (- 7 / 12)} + …..

(v) 5 / 9 + …… = 0 = (- 5 / 9) + ………

If a = – 11 / 27, b = 4 / 9 and c = – 5 / 18, then verify that a + (b + c) = (a + b) + c

Multiply and express the result in the lowest form:(i) 6 /-7 \times 14 / 30 (ii) 6 \frac{2}{3} \times 1 \frac{2}{7} (iii) 25 /-9 \times-3 / 10

The Sum of two rational numbers is 3 / 5. If one of them is – 2 / 7, find the other.

Verify commutative property of multiplication for the following pairs of rational

numbers:

(i) 4 / 5 and – 7 / 8

(ii)13 \frac{1}{3} \text { and } 1 \frac{1}{8}

(iii) – 7 / – 20 and 5 / – 14

Verify the following and name the property also:

(i) 3 / 5 × (- 4 / 7 × – 8 / 9) = (3 / 5 × – 4 / 7) × – 8 / 9

(ii) 5 / 9 × (- 3 / 2 + 7 / 5) = 5 / 9 × – 3 / 2 + 5 / 9 × 7 / 5

What rational number should be added to – 5 / 11 to get – 7 / 8?

What rational number should be subtracted from to get-4 \frac{3}{5} \text { to get }^{-3 \frac{1}{2}} ?

Find the multiplication inverse of the following:

(i) 12

(ii) 2 / 3

(iii) – 4 / 7

(iv) – 3 / 8 × (- 7 / 13)

Using the appropriate properties of operations of rational numbers, evaluate the

following:

(i) 2 / 5 × – 3 / 7 – 1 / 14 – 3 / 7 × 3 / 5

(ii) 8 / 9 × 4 / 5 + 5 / 6 – 9 / 5 × 8 / 9

(iii) – 3 / 7 × 14 / 15 × 7 / 12 × (- 30 / 35)

Subtract the sum of – 5 / 7 and – 8 / 3 from the sum of 5 / 2 and – 11 / 12

If x = – 4 / 7 and y = 2 / 5, then verify that x – y ≠ y – x

If p = – 8 / 27, q = 3 / 4 and r = – 12 / 15, then verify that

(i) p × (q × r) = (p × q) × r

(ii) p × (q – r) = p × q – p × r

Fill in the following blanks:

(i) 2 / 3 × – 4 / 5 is a …… number.

(ii) 54 / 81 × – 63 / 108 = ………. × 54 / 81

(iii) 4 / 5 × 1 = …… = 1 × ……

(iv) 5 / – 12 × …… = 1 = – 12 / 5 × ……

(v) 3 / 7 × (- 2 / 8 × …..) = (3 / 7 × – 2 / 8) × 5 / 9

(vi) – 8 / 9 × {4 / 13 + 5 / 17} = – 8 / 9 × 4 / 13 + ………

(vii) – 6 / 13 × {8 / 9 – 4 / 7} = – 6 / 13 × ……. – (- 6 / 13) × (4 / 7)

(viii) 16 / 23 × ……… = 0

(ix) The reciprocal of 0 is ………..

(x) The numbers …… and …… are their own reciprocals.

(xi) If y be the reciprocal of x, then the reciprocal of y2 in terms of x will be ……

(xii) The product of a non-zero rational number and its reciprocal is ……….

(xiii) The reciprocal of a negative rational number is ……….

If x = 4 / 9, y = – 7 / 12 and z = – 2 / 3, then verify that x – (y – z) ≠ (x – y) – z

Which of the following statement is true/false?

(i) 2 / 3 – 4 / 5 is not a rational number.

(ii) – 5 / 7 is the additive inverse of 5 / 7.

(iii) 0 is the additive inverse of its own.

(iv) The commutative property holds for the subtraction of rational numbers.

(v) The associative property does not hold for the subtraction of rational numbers.

(vi) 0 is the identity element for the subtraction of rational numbers.

If 4 / 5 the multiplicative inverse of ? Why or why not?-1 \frac{1}{4}

Using distributivity, find

(i) {7 / 5 × (- 3 / 12)} + {7 / 5 + 5 / 12}

(ii) {9 / 16 × 4 / 12} + {9 / 16 × (- 3 / 9)}

Find the sum of additive inverse and multiplication inverse of 9

Find the product of additive inverse and multiplicative inverse of – 3 / 7

Find the value of the following:

(i) – 3 / 7 ÷ 4

(ii)4 \frac{5}{8}÷ (- 4 / 9)

(iii) – 8 / 9 ÷ – 3 / 5

State whether the following statements are true or false:

(i) – 9 / 13 ÷ 2 / 7 is a rational number.

(ii) 4 / 13 ÷ 11 / 12 = 11 / 12 ÷ 4 / 13

(iii) – 3 / 4 ÷ (5 / 9 ÷ – 4 / 11) = (- 3 / 4 ÷ 5 / 9) ÷ – 4 / 11

(iv) 13 / 14 ÷ – 5 / 7 ≠ – 5 / 7 ÷ 13 / 14

(v) (- 7 ÷ 4 / 5) ÷ – 9 / 10 ≠ – 7 ÷ (4 / 5 ÷ – 9 / 10)

(vi) – 7 / 24 ÷ 6 / 11 is not a rational number.

The product of two rational numbers is – 11 / 12. If one of them is2 \frac{4}{9} find the

other.

By what rational number should – 7 / 12 be multiplied to get the product as 5 /

14?

By what rational number should – 3 is divided to get – 9 / 13?

Divide the sum of – 13 / 8 and 5 / 12 by their difference.

Divide the sum of 8 / 3 and 4 / 7 by the product of – 3 / 7 and 14 / 9.

If p = – 3 / 2, q = 4 / 5 and r = – 7 / 12, then verify that (p ÷ q) ÷ r ≠ p ÷ (q ÷ r)

Represent the following rational numbers on the number line.

(i) 11 /4

(ii) 4 \frac{3}{5}

(iii) – 9 / 7

(iv) – 2 / – 5

Write the rational numbers for each point labeled with a letter:

Find twenty rational numbers between – 3 / 7 and 2 / 3

Find six rational numbers between – 1 / 2 and 5 / 4

Find three rational numbers between – 2 and – 1

Write ten rational numbers which are greater than 0.

Write five rational numbers which are smaller than – 4

Identify the rational number which is different from the other three. Explain your

reasoning

(- 5 / 11), (- 1 / 2), (- 4 / 9), (- 7 / 3)

In a bag, there is 20 kg of fruits. If 7 \frac{1}{6} kg of these fruits be oranges and 8 \frac{2}{3} kg of

these are apples and rest are grapes. Find the mass of the grapes in the bag.

The population of a city is 6, 63,432. If 1 / 2 of the population are adult males and

1 / 3 of the population are adult females, then find the number of children in the

city.

In an election of a housing society, there are 30 voters. Each of them gives the vote.

Three-person X, Y, and Z are standing for the post of Secretary. If Mr. X got 2 / 5 of

the total votes and Mr. Z got 1 / 3 of the total votes, then find the number of votes

which Mr. Y got.

A person earns Rs 100 in a day. If he spent Rs 14 \frac{2}{7} on food and Rs 30 \frac{2}{3} on petrol.

How much did he save on that day?

In an examination, 400 students appeared. If 2 / 3 of the boys and all 130 girls

passed in the examination, then find how many boys failed in an examination?

A car is moving at the speed of 40 \frac{2}{3} km / h. Find how much distance will it cover

in 9 / 10 hrs?

Find the area of a square lawn whose one side is5 \frac{7}{9} m long.

Perimeter of a rectangle is 15 \frac{3}{7} \mathrm{m} If the length is 4 \frac{2}{7} find its breadth

Rahul had a rope of 325 \frac{4}{5}m long. He cut off a150 \frac{3}{5} m long piece, then he divided

the rest of the rope into 3 parts of equal length. Find the length of each part.

If 3 \frac{1}{2} litre of petrol costs Rs 270 \frac{3}{8} then find the cost of 4 litre of petrol.

Ramesh earns Rs 40,000 per month. He spends 3 / 8 of the income on food, 1 / 5

of the remaining on LIC premium and then 1 / 2 of the remaining on other expenses.

Find how much money is left with him?

A, B, C, D, and E went to a restaurant for dinner. A paid 1 / 2 of the bill, B paid 1

/ 5 of the bill and rest of the bill was shared equally by C, D and E. What fractions

of the bill was paid by each?

2 / 5 of the total number of students of a school come by a car while 1 / 4 of students

come by bus to school. All the other students walk to school of which 1 / 3 walk on

their own and the rest are escorted by their parents. If 224 students come to school

walking on their own, how many students study in the school?

A mother and her two sons got a room constructed for Rs 60,000. The elder son

contributes 3 / 8 of his mother’s contribution while the younger son contributes 1 / 2

of his mother’s share. How much do the three contribute individually?

In a class of 56 students, the number of boys is 2 / 5 th of the number of girls.

Find the number of boys and girls.

A man donated 1 / 10 of his money to a school, 1 / 6 th of the remaining to a

church, and the remaining money he distributed equally among his three children. If

each child gets Rs 50000, how much money did the man originally have?

If 1 / 4 of a number is added to 1 / 3 of that number, the result is 15 greater than

half of that number. Find the number.

A student was asked to multiply a given number by 4 / 5. By mistake, he divided

the given number by 4 / 5. His answer was 36 more than the correct answer. What

was the given number?