Express one quantity as a fraction of another

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Express one quantity as a fraction of another

Identify the comparison quantity before writing a fraction. Expressing 6 as a fraction of 4 gives 6/4 = 3/2, which is greater than one. A fraction used for comparison need not be less than one.

Convert quantities to matching units first. To compare 150 cm with 2 m, use 150/200 = 3/4. Keeping unlike units in the fraction would obscure the intended relationship.

Part of a whole and one part compared with another are different comparisons. With blue: gold = 3: 2, blue is 3/5 of the whole but 3/2 as much as gold. Label the denominator meaning explicitly.

Worked example: Express 150 cm as a fraction of 2 m.

Convert 2 m to 200 cm.

Write 150/200.

Divide numerator and denominator by 50.

Answer: 3/4.

Check your understanding: For a ratio 3: 2, is the first part 3/2 of the whole?

Answer: No; it is 3/5 of the whole.

Why: The whole contains five equal ratio parts.