Find the missing number and express it as a fraction in its simplest form.$\frac{3}{14} \div .... = \frac{3}{10}$

Given :

The given expression is $\frac{3}{14}  \div .... = \frac{3}{10}$ 

To do :

We have to find the missing number and express it as a simple fraction.

Solution :

Let the missing number be a.

This implies,

$\frac{3}{14}  \div a = \frac{3}{10}$

We know that,

$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$

Therefore,

$\frac{3}{14}  \div \frac{a}{1} = \frac{3}{10}$

$\frac{3}{14}  \times \frac{1}{a} = \frac{3}{10}$

$\frac{3\times 1}{14\times a} =\frac{3}{10}$

$ 3\times 10 = 3 \times 14a$

$30 = 42a$

$a = \frac{30}{42}$

$a = \frac{5}{7}$

The missing number in its simplest form is $\frac{5}{7}$.

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Updated on: 10-Oct-2022

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