Find two rational numbers between 4 5 and 7 13

We know that, A rational number is any number that can be named in the form a b where a and b are integers and b ≠ 0 . Between any two different rational numbers, there are infinitely many rational numbers. For any two rational numbers a and b , the number between them can be found using the formula 1 2 a + b . Let the given rational numbers be a = 4 5 and b = 7 13 . Then by mean method, q 1 = 1 2 ( a + b ) = 1 2 4 5 + 7 13 = 1 2 52 + 35 65 ⇒ q 1 = 1 2 × 87 65 = 87 130 Similarly, q 2 = 1 2 q 1 + b ⇒ q 2 = 1 2 87 130 + 7 13 = 157 260 Hence, two rational numbers between 4 5 and 7 13 are 87 130 and 157 260 .

Find two rational numbers between 3 4 and 1 1 5 .

We know that, A rational number is any number that can be named in the form a b where a and b are integers and b ≠ 0 . Between any two different rational numbers, there are infinitely many rational numbers. For any two rational numbers a and b , the number between them can be found using the formula 1 2 a + b . Let the given rational numbers be a = 3 4 and b = 1 1 5 = 6 5 . ⇒ q 1 = 1 2 ( a + b ) = 1 2 3 4 + 6 5 ⇒ q 1 = 1 2 15 + 24 20 ⇒ q 1 = 1 2 39 20 = 39 40 ⇒ q 2 = 1 2 q 1 + b = 1 2 39 40 + 6 5 ⇒ q 2 = 1 2 39 + 48 40 ⇒ q 2 = 1 2 87 40 = 87 80 Hence, two rational numbers between 3 4 and 1 1 5 are 39 40 and 87 80 .

Write the repeating decimal for 1 9 and use a bar to show the repeated.

Let the rational number a b = 1 9 A rational number can be expressed as a decimal by simplify dividing a by b . 1 9 = 1 ÷ 9 Hence, the repeating decimal for 1 9 = 0 . 1 ¯

Write the repeating decimal for - 4 3 and use a bar to show the repeated.

Let the rational number a b = - 4 3 A rational number can be expressed as a decimal by simply dividing a by b . - 4 3 = - 4 ÷ 3 Hence, the repeating decimal number for - 4 3 = - 1 . 3 ¯

Write the repeating decimal for 1 6 and use a bar to show the repeated.

Let the rational number a b = 1 6 A rational number can be expressed as a decimal by simply dividing a by b . 1 6 = 1 ÷ 6 Hence, the repeating decimal number for 1 6 = 0 . 1 6 ¯

E M B I B E

ICSE Mathematics>Pure Arithmetic>Chapter 1 - Rational and Irrational Numbers>Exercise

O P Malhotra, S K Gupta and, Anubhuti Gangal Solutions for Exercise 1: Exercise

Author:O P Malhotra, S K Gupta & Anubhuti Gangal

O P Malhotra Mathematics Solutions for Exercise - O P Malhotra, S K Gupta and, Anubhuti Gangal Solutions for Exercise 1: Exercise

Attempt the practice questions from Exercise 1: Exercise with hints and solutions to strengthen your understanding. ICSE Mathematics solutions are prepared by Experienced Embibe Experts.