Express 2 9 as a rational number with denominator 54

Given: 2 9 Therefore, find equivalent fractions by multiply or divide 54 ÷ 9 = 6 Multiplying numerator and denominator by 6 2 × 6 9 × 6 = 12 54 Hence, the required rational number is 12 54 .

Do + 3 - 7 and - 7 3 represent the same negative rational number?

Given: + 3 - 7 and - 7 3 Using the property of cross product. ⇒ 3 × 3 = 9 ⇒ - 7 × - 7 = 49 Therefore, ⇒ 9 < 49 ⇒ + 3 - 7 < - 7 3 Hence, + 3 - 7 and - 7 3 does not represent the same negative rational numbers.

Compare the following rational numbers using > , < or = . 23 46 and 81 99

Given rational numbers are 23 46 and 81 99 We know that, Rational numbers can be compared by evaluating their cross products. Therefore, using cross product method to compare rational numbers. 23 46 = 81 99 23 × 99 = 2277 81 × 46 = 3726 ∴ 2277 < 3726 Hence, 23 46 < 81 99

Compare the following rational numbers using > , < or = . - 1 5 and - 1 7

Given rational numbers are - 1 5 and - 1 7 We know that, Rational numbers can be compared by evaluating their cross products. Therefore, Using cross product method to compare rational numbers. - 1 5 = - 1 7 - 1 × 7 = - 7 - 1 × 5 = - 5 ∴ - 7 < - 5 Hence, - 1 5 < - 1 7 .

Compare the following rational numbers using > , < or = . - 9 17 and 6 - 19

Given rational numbers are - 9 17 and 6 - 19 We know that, Rational numbers can be compared by evaluating their cross products. Therefore, Using the property of cross products such that If a × d = b × c , then a b = c d - 9 17 = 6 - 19 - 9 × - 19 = 171 17 × 6 = 102 ∴ 171 > 102 Hence, - 9 17 < 6 - 19 .