Simplifying a Ratio of Whole Numbers: Problem Type 1

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A ratio is in its simplest form when both sides are whole numbers and there is no whole number that both sides can be divided by. Consider ratios of whole numbers for example, 6:4. It can be written as the fraction $\frac{6}{4}$. To write a ratio in its simplest form, keep dividing both sides by the same number until you cannot go any further without going into decimals.

Alternatively, to simplify a ratio of whole numbers, we simplify the corresponding fraction of the whole numbers. We write the prime factors of both the whole numbers and then cancel out the highest common factor from both the numerator and the denominator of the fraction. For the ratio 6:4, $\frac{6}{4} = \frac{6}{2} \div \frac{4}{2} = \frac{3}{2}$ The fraction can be written back into ratio form as 3:2. So the ratio of whole numbers 6:4 when simplified is 3:2

Simplify the ratio 42:54

Solution

Step 1:

The ratio $42:54 = \frac{42}{54}$

Step 2:

HCF of 42 and 54 is 6

Simplifying

$\frac{\left ( \frac{42}{6} \right )}{\left ( \frac{54}{6} \right )} = \frac{7}{9} \space or \space 7:9$

Step 3:

So, the simplified ratio of 42:54 is 7:9

Simplify the ratio 33:21

Solution

Step 1:

The ratio $33:21 = \frac{33}{21}$

Step 2:

HCF of 33 and 21 is 3

Simplifying

$\frac{\left ( \frac{33}{3} \right )}{\left ( \frac{21}{3} \right )} = \frac{11}{7} \space or \space 11:7$

Step 3:

So, the simplified ratio of 33:21 is 11:7