In this section each question has two matching lists. Choices for the correct combination of elements from List-I and List-II are given as options (a), (b), (c) and (d) out of which one is correct. List-I List-II (P) Divide the sum of 12 5 and 13 7 by the product of - 4 7 and - 1 2 . (1) 7 10 (Q) Cheena spent 3 4 of her pocket money. She spent 1 2 of it on a book, 1 6 on a movie and rest for a dress. What part of her pocket money did she spend on the dress? (2) 3 19 28 (R) If 35 shirts of equal size can be stitches from 49 2 metres of cloth, calculate the length (in m) of cloth required for each shirt. (3) 14 9 10 (S) Two packets of chocolates weigh 9 4 kg and 10 7 kg respectively. What is the total weigh (in kg) of the chocolates? (4) 1 4

P ‐ 3 , Q ‐ 4 , R ‐ 1 , S ‐ 2

P ‐ 2 , Q ‐ 4 , R ‐ 1 , S ‐ 3

P ‐ 1 , Q ‐ 2 , R ‐ 3 , S ‐ 4

P ‐ 4 , Q ‐ 3 , R ‐ 2 , S ‐ 1

Simplify and express the result as a rational number in standard form. 15 28 × - 119 9 + - 19 20 × - 30 - 57 + - 39 3 × 14 5 × - 12 56

Given, 15 28 × - 119 9 + - 19 20 × - 30 - 57 + - 39 3 × 14 5 × - 12 56 , To simplify this, = 15 28 × - 119 9 + - 19 20 × - 30 - 57 + - 39 3 × 14 5 × - 12 56 Simplify the rational numbers in each expression, = 5 4 × - 119 9 + - 19 20 × - 30 - 57 + - 39 3 × 14 5 × - 12 56 = 5 4 × - 17 3 + - 1 2 + - 13 × - 3 5 = - 85 12 - 1 2 + 39 5 = - 425 - 30 + 468 60 = 13 60 Hence, 13 60 is the standard form.

Simplify: - 3 2 × 4 5 + 9 5 × - 10 3 - 1 2 × 3 4 ÷ 21 9 × 3 7 + 7 8 × 16 14

Given, To simplify, - 3 2 × 4 5 + 9 5 × - 10 3 - 1 2 × 3 4 ÷ 21 9 × 3 7 + 7 8 × 16 14 First multiply the rational numbers in each of the expression, = - 3 2 × 4 5 + 9 5 × - 10 3 - 1 2 × 3 4 ÷ 21 9 × 3 7 + 7 8 × 16 14 = - 12 10 + - 90 15 - 3 8 ÷ 63 63 + 112 112 = - 6 5 - 6 - 3 8 ÷ 1 + 1 = - 48 - 240 - 15 40 ÷ 2 = - 303 40 ÷ 2 = - 303 40 × 1 2 = - 303 80 Therefore, the solution is - 303 80 .

Simplify: 1 12 + - 3 4 + 7 8 × 3 2 5 - 7 10 + - 2 15 - 10 1 30

Given, To simplify 1 12 + - 3 4 + 7 8 × 3 2 5 - 7 10 + - 2 15 - 10 1 30 , First find L.C.M of the given rational numbers, = 1 12 - 3 4 + 7 8 × 17 5 - 7 10 - 2 5 - 301 30 = 2 - 18 + 21 24 × 102 - 21 - 4 - 301 30 = 5 24 × - 244 30 = - 5 24 × 224 30 = - 1 3 × 28 6 = - 28 18 = - 14 9 = - 1 5 9 Therefore, the solution is - 1 5 9 .

The product of two rational numbers is - 759 189 . If one of the numbers is 7 13 , find the other number.

Given, Product of two rational numbers = - 759 189 One number = 7 13 Let the other number be x . ∴ x × 7 13 = - 759 189 ⇒ x = - 759 189 ÷ 7 13 = - 759 189 × 13 7 = - 9867 1323 = - 3289 441 Therefore, the solution is - 3289 441 .

EXERCISE

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7th CBSE

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Foundation Course Mathematics>Chapter 9 - Rational Numbers>EXERCISE>Q 12

From his home, Rahul walks $\frac{6}{7}$ km towards school and then returns $\frac{5}{6}$ km on the same way towards his home to reach a landmark. At what distance will he be now from his home?

MEDIUM

7th CBSE

IMPORTANT

Foundation Course Mathematics>Chapter 9 - Rational Numbers>EXERCISE>Q 1

In this section each question has two matching lists. Choices for the correct combination of elements from List-I and List-II are given as options (a), (b), (c) and (d) out of which one is correct.

List-I	List-II
(P) Equivalent rational number of $\frac{- 16}{128}$ is	(1) $\frac{1}{2}$
(Q) $\frac{- 3}{4} + \frac{5}{6} =$	(2) $\frac{- 1}{8}$
(R) $(\frac{5}{3} \times \frac{4}{6}) + (\frac{- 2}{3} + \frac{5}{- 3}) =$	(3) $\frac{1}{12}$
(S) $\frac{1}{3}$ is smaller than	(4) $- \frac{11}{9}$

HARD

7th CBSE

IMPORTANT

Foundation Course Mathematics>Chapter 9 - Rational Numbers>EXERCISE>Q 2

In this section each question has two matching lists. Choices for the correct combination of elements from List-I and List-II are given as options (a), (b), (c) and (d) out of which one is correct.

List-I	List-II
(P) Divide the sum of $\frac{12}{5}$ and $\frac{13}{7}$ by the product of $\frac{- 4}{7}$ and $\frac{- 1}{2}$ .	(1) $\frac{7}{10}$
(Q) Cheena spent $\frac{3}{4}$ of her pocket money. She spent $\frac{1}{2}$ of it on a book, $\frac{1}{6}$ on a movie and rest for a dress. What part of her pocket money did she spend on the dress?	(2) $3 \frac{19}{28}$
(R) If $35$ shirts of equal size can be stitches from $\frac{49}{2}$ metres of cloth, calculate the length (in m) of cloth required for each shirt.	(3) $14 \frac{9}{10}$
(S) Two packets of chocolates weigh $\frac{9}{4}$ kg and $\frac{10}{7}$ kg respectively. What is the total weigh (in kg) of the chocolates?	(4) $\frac{1}{4}$

EASY

7th CBSE

IMPORTANT

Foundation Course Mathematics>Chapter 9 - Rational Numbers>EXERCISE>Q 1

Simplify and express the result as a rational number in standard form.

$(\frac{15}{28} \times \frac{- 119}{9}) + (\frac{- 19}{20} \times \frac{- 30}{- 57}) + (\frac{- 39}{3} \times \frac{14}{5} \times \frac{- 12}{56})$

MEDIUM

7th CBSE

IMPORTANT

Foundation Course Mathematics>Chapter 9 - Rational Numbers>EXERCISE>Q 2

Simplify and express the result as a rational number in standard form.

$(Multiply \frac{- 7}{15} by \frac{5}{28}) + (Multiply \frac{- 55}{12} by \frac{- 96}{33})$ .

MEDIUM

7th CBSE

IMPORTANT

Foundation Course Mathematics>Chapter 9 - Rational Numbers>EXERCISE>Q 3

Simplify:

$[(\frac{- 3}{2} \times \frac{4}{5}) + (\frac{9}{5} \times \frac{- 10}{3}) - (\frac{1}{2} \times \frac{3}{4})] \div [(\frac{21}{9} \times \frac{3}{7}) + (\frac{7}{8} \times \frac{16}{14})]$

MEDIUM

7th CBSE

IMPORTANT

Foundation Course Mathematics>Chapter 9 - Rational Numbers>EXERCISE>Q 4

Simplify:

$(\frac{1}{12} + (\frac{- 3}{4}) + \frac{7}{8}) \times (3 \frac{2}{5} - \frac{7}{10} + (\frac{- 2}{15}) - 10 \frac{1}{30})$

MEDIUM

7th CBSE

IMPORTANT

Foundation Course Mathematics>Chapter 9 - Rational Numbers>EXERCISE>Q 5

The product of two rational numbers is $\frac{- 759}{189}$ . If one of the numbers is $\frac{7}{13}$ , find the other number.

EXERCISE

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