To convert a fractional ratio into a whole number ratio, you need to eliminate the fractions by finding a common multiple of the denominators and multiplying each part of the ratio. Here's a step-by-step guide:
Steps to Convert Fractional Ratios to Whole Number Ratios
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Find the Least Common Multiple (LCM) of the Denominators: Identify the denominators of all the fractions in the ratio and determine their least common multiple. The LCM is the smallest number that is a multiple of all the denominators.
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Multiply Each Term of the Ratio by the LCM: Multiply each part (term) of the fractional ratio by the LCM you found in the previous step. This will eliminate the fractions.
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Simplify: Reduce the resulting whole numbers to their simplest form by dividing each number by their greatest common factor (GCF). This gives you the equivalent whole number ratio in its simplest terms.
Example
Let's convert the fractional ratio 1/2 : 2/3 into a whole number ratio.
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Find the LCM: The denominators are 2 and 3. The LCM of 2 and 3 is 6.
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Multiply by the LCM: Multiply each term by 6:
- (1/2) * 6 = 3
- (2/3) * 6 = 4
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Simplify: The resulting ratio is 3 : 4. Since 3 and 4 have no common factors other than 1, the ratio is already in its simplest form.
Therefore, the whole number ratio equivalent to 1/2 : 2/3 is 3 : 4.
Another Example
Convert the ratio 1/4 : 1/6 : 1/8 to a whole number ratio.
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Find the LCM: The denominators are 4, 6, and 8. The LCM of 4, 6, and 8 is 24.
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Multiply by the LCM:
- (1/4) * 24 = 6
- (1/6) * 24 = 4
- (1/8) * 24 = 3
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Simplify: The resulting ratio is 6 : 4 : 3. Since 6, 4, and 3 have no common factors other than 1, this is the simplest form.
Therefore, the equivalent whole number ratio is 6:4:3.
