# Simplifying a Ratio of Decimals

We have ratios of whole numbers and ratios of decimal numbers too. It is required that ratios in simplified form have whole numbers.

Rules to simplify a ratio of decimals

• To simplify a ratio of decimals we remove the decimal point and reduce the ratio to a ratio of whole numbers.

• We multiply the numerator and denominator of the ratio in fraction form by a 10, 100, 1000 i.e., a power of ten to eliminate the decimal.

• Then the fraction is simplified to be in its lowest terms.

• This gives simplified ratio of decimals as a ratio of whole numbers in simplest form.

Simplify the ratio 4.8:5.6

### Solution

Step 1:

The ratio $4.8:5.6 = \frac{4.8}{5.6}$

Step 2:

We multiply and divide the fraction by 10

$\frac{4.8}{5.6} = \frac{\left ( 4.8 \times 10 \right )}{\left ( 5.6 \times 10 \right )} = \frac{48}{56}$

Step 3:

HCF of 48 and 56 is 8

Simplifying

$\frac{\left ( \frac{48}{8} \right )}{\left ( \frac{56}{8} \right )} = \frac{6}{7} \space or \space 6:7$

Step 4:

So, the simplified ratio of 4.8:5.6 is 6:7

Simplify the ratio 6.3:1.89

### Solution

Step 1:

The ratio $6.3:1.89 = \frac{6.3}{1.89}$

Step 2:

We multiply and divide the fraction by 100

$\frac{6.3}{1.89} = \frac{\left ( 6.3 \times 100 \right )}{\left ( 1.89 \times 100 \right )} = \frac{630}{189}$

Step 3:

HCF of 630 and 189 is 63

Simplifying

$\frac{\left ( \frac{630}{63} \right )}{\left ( \frac{189}{63} \right )} = \frac{10}{3} \space or \space 10:3$

Step 4:

So, the simplified ratio of 6.3:1.89 is 10:3 