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Ratio and Proportion

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Question : 51 of 112

Marks: +1, -0

A fraction bears the same ratio to

\frac{1}{27}

\frac{3}{7}

\frac{5}{9} .

The fraction is :

$\frac{7}{45}$
$\frac{1}{35}$
$\frac{45}{7}$
$\frac{5}{21}$

Solution:

Concept:

Set up a proportion between two ratios and solve for the unknown fraction.

Explanation:

Let the fraction be

x

.

The condition means:

x : \frac{1}{27}

is equal to

\frac{3}{7} : \frac{5}{9}

.

So

\frac{x}{\frac{1}{27}} = \frac{\frac{3}{7}}{\frac{5}{9}}

.

Simplify the right side:

\frac{3}{7} \div \frac{5}{9} = \frac{3}{7} \times \frac{9}{5} = \frac{27}{35}

.

Thus

\frac{x}{\frac{1}{27}} = \frac{27}{35}

.

Multiply both sides by

\frac{1}{27}

:

x = \frac{1}{27} \times \frac{27}{35} = \frac{1}{35}

.

Answer:

\frac{1}{35}

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