Given, 5 - 18 + 8 27 . Rational Numbers can be added by converting them into equivalent rational numbers. Therefore, 5 - 18 + 8 27 = ( - 5 × 3 ) ( 18 × 3 ) + ( 8 × 2 ) ( 27 × 2 ) (Take LCM of 18 and 27 as 54 ) = - 15 54 + 16 54 = - 15 + 16 54 = 1 54 Hence, the required answer is 1 54 .

Simplify: ( 3 4 + 5 18 ) × 21 74

Given, the expression is ( 3 4 + 5 18 ) × 21 74 , we need to simplify the given expression. Therefore, 3 4 + 5 18 × 21 74 = 3 × 9 36 + 5 × 2 36 × 21 74 (Taking the LCM of 4 and 18 as 36 ) = 27 36 + 10 36 × 21 74 = 37 36 × 21 74 = 37 × 3 × 7 3 × 3 × 2 × 2 × 37 × 2 (Expand 21 = 3 × 7 , 36 = 3 × 3 × 2 × 2 , 74 = 37 × 2 ) = 7 24 (cancel out the same terms which are in numerator and denominator) Hence, the required answer is 7 24 .

Subtract the sum of - 4 5 and 7 9 from - 1 2 .

Given, - 4 5 and 7 9 to be subtracted from - 1 2 . So, the addition of first two rational numbers is: - 4 5 + 7 9 = ( - 4 × 9 ) + 7 × 5 45 (Taking LCM of 5 and 9 is 45 ) = - 36 + 35 45 = - 1 45 Now, the subtraction of this sum from given addition is: - 1 2 - - 1 45 = - 1 × 45 90 + 2 × 1 90 (Taking LCM of 45 and 2 is 90 ) = - 45 90 + 2 90 = - 45 + 2 90 = - 43 90 Hence, the required answer is - 43 90 .

Divide: 32 50 ÷ 24 30 ÷ 12 20

Given, 32 50 ÷ 24 30 ÷ 12 20 , we need to divide the given expression. Division by a rational number is same as multiplication with its reciprocal. 32 50 ÷ 24 30 ÷ 12 20 = 32 50 × 30 24 × 20 12 ( 30 24 and 20 12 are multiplicative inverse of 24 30 and 12 20 respectively.) = 16 25 × 15 12 × 10 6 = 2 × 2 × 2 × 2 × 3 × 5 × 2 × 5 5 × 5 × 2 × 2 × 3 × 2 × 3 = 4 3 Hence, the required answer is = 4 3 = 1 1 3 .

Simplify: ( 13 21 ÷ 26 35 ) × - 4 7

Given, 13 21 ÷ 26 35 × - 4 7 , we need to simplify the given expression. Use simplification after converting division into multiplication with reciprocals . Therefore, ( 13 21 ÷ 26 35 ) × - 4 7 = 13 21 × 35 26 × - 4 7 (Multiplicative inverse of 26 35 = 35 26 ) = 13 3 × 5 26 × - 4 7 = 1 3 × 5 2 × - 4 7 = 1 3 × 5 1 × - 2 7 = - 10 21 Hence, the required value is - 10 21 .

Find two rational numbers between 2 3 and 4 5 .

Given, Two rational numbers are 2 3 and 4 5 , we need to find two rational numbers between the given rational numbers. The equivalent rational numbers to above can be found with an equal denominator to both. So, the LCM of 3 and 5 is 15 . ∴ 2 3 = 2 × 5 3 × 5 = 10 15 and 4 5 = 4 × 3 5 × 3 = 12 15 It is clearly seen that only integer 11 lies between 10 and 12 . Therefore, the rational number lies between them is 11 15 . Similarly, taking LCM of 3 and 5 is 30 . ∴ 2 3 = 10 × 2 3 × 10 = 20 30 and 4 5 = 4 × 6 5 × 6 = 24 30 So, the another rational number between them is 22 30 . Hence, the two rational numbers between 2 3 and 4 5 are 11 15 and 22 30 .

Rachna has two packets of rice weighing 2 7 8 kg and 3 1 4 kg respectively. She gave 2 1 4 kg of rice to her friend. What is the total weight of rice left with Rachna?

Given, Rachna has two packets of rice weighing 2 7 8 kg and 3 1 4 kg . She gave 2 1 4 kg to her friend. Total weight of rice: 2 7 8 + 3 1 4 = 23 8 + 13 4 = 23 + 26 8 = 49 8 She gave 2 1 4 kg to her friend. So, the total weight of rice left with Rachna is: 49 8 - 9 4 = 49 - 18 8 = 31 8 = 3 7 8 kg Hence, the total weight of rice left with Rachna is 3 7 8 kg .

E M B I B E

Math Sight>Chapter 3 - Rational Numbers>Test Paper 2

Jharne De and Ranjana Kumar Solutions for Chapter: Rational Numbers, Exercise 9: Test Paper 2

Author:Jharne De & Ranjana Kumar

Jharne De Mathematics Solutions for Exercise - Jharne De and Ranjana Kumar Solutions for Chapter: Rational Numbers, Exercise 9: Test Paper 2

Attempt the free practice questions on Chapter 3: Rational Numbers, Exercise 9: Test Paper 2 with hints and solutions to strengthen your understanding. Math Sight solutions are prepared by Experienced Embibe Experts.

Questions from Jharne De and Ranjana Kumar Solutions for Chapter: Rational Numbers, Exercise 9: Test Paper 2 with Hints & Solutions

MEDIUM

7th CBSE

IMPORTANT

Math Sight>Chapter 3 - Rational Numbers>Test Paper 2>Q 5

Add: $\frac{5}{- 18} + \frac{8}{27}$

MEDIUM

7th CBSE

IMPORTANT

Math Sight>Chapter 3 - Rational Numbers>Test Paper 2>Q 6

Simplify: $(\frac{3}{4} + \frac{5}{18}) \times \frac{21}{74}$

MEDIUM

7th CBSE

IMPORTANT

Math Sight>Chapter 3 - Rational Numbers>Test Paper 2>Q 7

Subtract the sum of $(\frac{- 4}{5} and \frac{7}{9})$ from $\frac{- 1}{2}$ .

MEDIUM

7th CBSE

IMPORTANT

Math Sight>Chapter 3 - Rational Numbers>Test Paper 2>Q 8

Divide: $\frac{32}{50} \div \frac{24}{30} \div \frac{12}{20}$

MEDIUM

7th CBSE

IMPORTANT

Math Sight>Chapter 3 - Rational Numbers>Test Paper 2>Q 9

Convert $0.441$ into a rational number.

MEDIUM

7th CBSE

IMPORTANT

Math Sight>Chapter 3 - Rational Numbers>Test Paper 2>Q 10

Simplify: $(\frac{13}{21} \div \frac{26}{35}) \times \frac{- 4}{7}$

MEDIUM

7th CBSE

IMPORTANT

Math Sight>Chapter 3 - Rational Numbers>Test Paper 2>Q 11

Find two rational numbers between $\frac{2}{3}$ and $\frac{4}{5}$ .

MEDIUM

7th CBSE

IMPORTANT

Math Sight>Chapter 3 - Rational Numbers>Test Paper 2>Q 12

Rachna has two packets of rice weighing $2 \frac{7}{8} kg$ and $3 \frac{1}{4} kg$ respectively. She gave $2 \frac{1}{4} kg$ of rice to her friend. What is the total weight of rice left with Rachna?

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