Question

Match the column

Column I	Column II
a. The equivalent rational number of $\frac{5}{7}$ , whose numerator is $35$ , is	(i) $\frac{21}{8}$
b. Rational number $\frac{57}{1140}$ is equivalent to	(ii) $\frac{104}{21}$
c. If $a = \frac{1}{4}$ and $b = \frac{3}{2}$ , then $(a + b) + (a - b)$ is equal to	(iii) $\frac{- 7}{6}$
d. The reciprocal of $\frac{- 3}{8} \times (\frac{- 7}{13})$ is	(iv) $\frac{- 15}{4}$
e. The multiplicative inverse of $- 1 \frac{1}{7}$ is	(v) $\frac{35}{49}$
f. To get the product $1$ , we should multiply $\frac{8}{21}$ by	(vi) $\frac{1}{20}$
g. The reciprocal of $\frac{3}{5} \times (\frac{- 4}{9})$ is	(vii) $\frac{1}{2}$

Accepted Answer

For (a).

The equivalent rational number of a given rational number is obtained by dividing or multiplying the numerator and denominator by the same number.

For rational number, $\frac{5}{7}$ , we get,

$\frac{5 \times 7}{7 \times 7} = \frac{35}{49}$ ,

$∴$ (a) matches with (v).

For (b).

For rational number, $\frac{57}{1140}$ , we get,

$\frac{\frac{57}{57}}{\frac{1140}{57}} = \frac{1}{20}$

$∴$ (b) matches with (vi).

For (c).

If $a = \frac{1}{4} a n d b = \frac{3}{2}$

$\Rightarrow (a + b) + (a - b) = a + b + a - b = 2 a = 2 \times \frac{1}{4} = \frac{1}{2}$

$∴$ (c) matches with (vii).

For (d).

For a rational number $x$ , its reciprocal is $\frac{1}{x}$

The reciprocal of $\frac{- 3}{8} \times (\frac{- 7}{13})$ is $\frac{8}{- 3} \times (\frac{13}{- 7}) = \frac{104}{21}$

$∴$ (d) matches with (ii).

For (e).

Multiplicative of a rational number is nothing but the reciprocal of a rational number.

The multiplicative inverse of $- 1 \frac{1}{7} = \frac{- 6}{7}$ is $\frac{- 7}{6}$

$∴$ (e) matches with (iii).

For (f).

To get the product $1$ , we should multiply $\frac{8}{21}$ by its reciprocal i.e. by $\frac{21}{8}$

$∴$ (f) matches with (i).

For (g).

The reciprocal of $\frac{3}{5} \times (\frac{- 4}{9})$ is $\frac{5}{3} \times (\frac{9}{- 4}) = \frac{45}{- 12} = \frac{- 15}{4}$

$∴$ (g) matches with (iv).

Subject Experts Solutions for Chapter: Rational Numbers, Exercise 3: Worksheet 3

Subject Experts Mathematics Solutions for Exercise - Subject Experts Solutions for Chapter: Rational Numbers, Exercise 3: Worksheet 3

Questions from Subject Experts Solutions for Chapter: Rational Numbers, Exercise 3: Worksheet 3 with Hints & Solutions

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