A ratio is a comparison of two measurements by division.

For example, 40 and 10 can be compared by division viz, 40÷10. This is called ratio.

Symbolically, ratios can be written as:

40:10, $\frac{40}{10}$, 40 to 10

As can be seen, the ratio is written as a fraction. This is because the ratio is a fraction, therefore, we can also simplify the ratio just as we can simplify fractions.

__Example 1__

Write the ratio of 440 to 550 in the most simplified form possible

**Solution:**

$\frac{440}{550}=\frac{4\times 110}{5\times 110}=\frac{4}{5}$

In ratio, it is written as 4:5

__Example 2__

Write 78 to 624 as a ratio in simplified form

**Solution:**

$\frac{78}{624}=\frac{78\times 1}{78\times 6}=\frac{1}{6}$

Which can be expressed as 1:6

__Example 3__

Write 35 to 105 as a ratio in simplified form

**Solution:**

$\frac{35}{105}=\frac{35\times 1}{35\times 3}=\frac{1}{3}$

In standard ratio form, it is 1:6.

__Example 4__

Write 32 to 480 as a ratio in simplified form

**Solution:**

$\frac{32}{480}=\frac{32\times 1}{32\times 15}=\frac{1}{15}$

In standard ratio form, it is 1:15

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