Simplifying A Ratio Of Decimals - Tutorialspoint

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Home Ratios_and_unit_rates Simplifying Ratios and Decimals Simplifying a Ratio of Decimals Previous Quiz Next

Introduction

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.

Example 1

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

Example 2

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

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