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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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