Simplify the following: - 19 7 × - 15 14 ÷ 95 196

We need to find the value of - 19 7 × - 15 14 ÷ 95 196 First let us multiply the rational numbers and then divide. ⇒ - 19 7 × - 15 14 ÷ 95 196 ⇒ 285 98 ÷ 95 196 ⇒ 285 98 × 196 95 ⇒ 285 1 × 2 95 ⇒ 3 1 × 2 1 = 6 1 Hence, 6 is the required answer.

Simplify the following: - 39 5 + 7 10 - 11 3

We need to find the value of - 39 5 + 7 10 - 11 3 We know that, to add or subtract fractions first convert them into like fractions and then add or subtract the numerators by keeping the denominator same. ⇒ - 39 5 + 7 10 - 11 3 LCM of 5 , 10 , 3 = 30 ⇒ - 39 × 6 5 × 6 + 7 × 3 10 × 3 - 11 × 10 3 × 10 ⇒ - 234 30 + 21 30 - 110 30 ⇒ - 234 + 21 - 110 30 ⇒ - 323 30 Hence, - 323 30 is the required answer.

Simplify the following: - 1 2 + 1 3 ÷ 1 4 - - 1 5

We need to find the value of - 1 2 + 1 3 ÷ 1 4 - - 1 5 First, we will solve the brackets We know that, to add or subtract fractions first convert them into like fractions and then add or subtract the numerators by keeping the denominator same. ⇒ - 1 2 + 1 3 ÷ 1 4 - - 1 5 LCM of 2 , 3 = 6 and 4 , 5 = 20 ⇒ - 1 × 3 2 × 3 + 1 × 2 3 × 2 ÷ 1 × 5 4 × 5 - - 1 × 4 5 × 4 ⇒ - 3 6 + 2 6 ÷ 5 20 - - 4 20 ⇒ - 3 + 2 6 ÷ 5 - - 4 20 ⇒ - 1 6 ÷ 9 20 ⇒ - 1 6 × 20 9 ⇒ - 1 3 × 10 9 ⇒ - 10 27 Hence, - 10 27 is the required answer.

Simplify the following: 11 12 ÷ 7 + - 1 3

We need to find the value of 11 12 ÷ 7 + - 1 3 First, we will solve the brackets We know that, to add or subtract fractions first convert them into like fractions and then add or subtract the numerators by keeping the denominator same. ⇒ 11 12 ÷ 7 + - 1 3 ⇒ 11 12 × 1 7 + - 1 3 ⇒ 11 84 + - 1 3 LCM of 84 , 3 = 84 ⇒ 11 84 + - 1 × 28 3 × 28 ⇒ 11 - 28 84 ⇒ - 17 84 Hence, - 17 84 is the required answer.

Simplify the following: 5 4 + 10 5 × - 5 12

We need to find the value of 5 4 + 10 5 × - 5 12 First, we will solve the bracket We know that, to add or subtract fractions first convert them into like fractions and then add or subtract the numerators by keeping the denominator same. ⇒ 5 4 + 10 5 × - 5 12 ⇒ 5 4 + 2 × - 5 12 ⇒ 5 4 + - 5 6 LCM of 4 , 6 = 12 ⇒ 5 × 3 4 × 3 + - 5 × 2 6 × 2 ⇒ 15 12 + - 10 12 ⇒ 15 - 10 12 = 5 12 Hence, 5 12 is the required answer.

Simplify the following: 3 5 - 6 10 ÷ - 1 2 + - 2 5

We need to find the value of 3 5 - 6 10 ÷ - 1 2 + - 2 5 First, we will solve the brackets We know that, to add or subtract fractions first convert them into like fractions and then add or subtract the numerators by keeping the denominator same. ⇒ 3 5 - 6 10 ÷ - 1 2 + - 2 5 LCM of 5 , 10 = 10 and 2 , 5 = 10 ⇒ 3 × 2 5 × 2 - 6 × 1 10 × 1 ÷ - 1 × 5 2 × 5 + - 2 × 5 5 × 2 ⇒ 6 10 - 6 10 ÷ - 5 10 + - 10 10 ⇒ 0 ÷ - 5 - 10 10 ⇒ 0 Hence, 0 is the required answer.

What should be added to - 1 6 to obtain the nearest natural number?

Natural numbers are a part of the number system, including all the positive numbers from 1 to infinity. Now, we are asked that what should be added to - 1 6 to obtain the nearest natural number. The nearest natural number to - 1 6 is 1 . Let us assume the number to be x ⇒ x - 1 6 = 1 ⇒ x = 1 + 1 6 LCM of 1 , 6 = 6 ⇒ x = 1 6 + 1 = 1 × 1 6 × 1 + 1 × 6 1 × 6 ⇒ x = 1 + 6 6 ⇒ x = 7 6 That means the required answer is 7 6 .

E M B I B E

Cambridge connection Mathematics>Chapter 4 - Rational numbers>Let's Practice

Prakash Tiwari and Ishita Joshi Solutions for Chapter: Rational numbers, Exercise 2: Let's Practice

Author:Prakash Tiwari & Ishita Joshi

Prakash Tiwari Mathematics Solutions for Exercise - Prakash Tiwari and Ishita Joshi Solutions for Chapter: Rational numbers, Exercise 2: Let's Practice

Attempt the practice questions on Chapter 4: Rational numbers, Exercise 2: Let's Practice with hints and solutions to strengthen your understanding. Cambridge connection Mathematics solutions are prepared by Experienced Embibe Experts.