Represent - 4 7 on a number line.

The given rational number is - 4 7 . To represent - 4 7 on the number line, divide the number line into seven equal parts. In the figure number line is divided into seven equal parts to either sides of 0 . From the figure, we observe that point D represents - 4 7 on the number line.

Represent - 4 7 on a number line.

The given rational number is - 4 7 . To represent - 4 7 on the number line, divide the number line into seven equal parts. In the figure number line is divided into seven equal parts to either sides of 0 . From the figure, we observe that point D represents - 4 7 on the number line.

Write the multiplicative inverse of 2 9 11 .

The given fraction is 2 9 11 . Converting the same in p q , the form of a rational number = 2 9 11 = ( 2 × 11 ) + 9 11 = 31 11 . The rational number b a is called the multiplicative inverse or reciprocal of a b and is obtained by exchanging the numerator and denominator. So, the multiplicative inverse of 31 11 is 11 31 .

Express 42 63 into its simplest form.

The given fraction is 42 63 . A rational number is said to be in the simplest form if its denominator is a positive integer and the numerator and denominator have no common factor other than 1 . The HCF of 42 and 63 is 21 . Now, to find the simplest form, we can divide numerator and denominator by the HCF . So, 42 63 = 42 ÷ 21 63 ÷ 21 = 2 3 Hence, 2 3 is the standard form of the given fraction.

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 .