One Quantity as a Fraction
Express one quantity as a fraction of another where the result may be less than 1 or greater than 1, and interpret the meaning in context
What a learner can do afterwards
- Express 45 minutes as a fraction of 2 hours (= 3/8)
- Express a larger quantity as a fraction of a smaller one and explain why the result exceeds 1
- Simplify the resulting fraction and interpret its meaning in the original context
1 · Read
You can compare two quantities by writing one as a fraction of the other. Put the first quantity on top and the second on the bottom, but only once both are measured in the same unit.
45 minutes and 2 hours are not in the same unit yet. Change 2 hours into minutes: 2 x 60 = 120 minutes. Now write 45 over 120: 45/120. Divide top and bottom by 15 to simplify: 3/8.
Sometimes the first quantity is bigger than the second. Then the fraction comes out greater than 1. That is not a mistake, it just means the first amount is more than a whole of the second amount.
A recipe uses 9 cups of flour and 6 cups of sugar. Flour as a fraction of sugar is 9/6. Simplify by dividing by 3: 3/2. Since 3/2 is greater than 1, there is one and a half times as much flour as sugar.
Always simplify your fraction at the end, and check what the number tells you: less than 1 means a smaller part, more than 1 means more than a whole.
Match the units, put one quantity over the other, then simplify. The size of the fraction shows how the two quantities compare.
More to read
Introduction to Fractions
A fraction is a neat way to say one amount as part of another. Saying 45 minutes as a fraction of 2 hours means writing 45 over the whole, but only after both use the same units. Two hours is 120 minutes, so the fraction is 45/120, not 45 over 2.
The unit rule is the whole trick of this topic. Metres with centimetres, litres with millilitres, hours with minutes: always convert first, then write the fraction. Skipping the conversion is the most common mistake, and it always gives a wrong answer.
4.1 Visualize Fractions
Simplifying keeps the value while shrinking the numbers. The fraction 45/120 looks clumsy, but dividing top and bottom by 15 gives 3/8, which means the same thing. Always divide both parts by their highest common factor to finish the job.
Sometimes the answer tops 1, and that is fine. Writing 150 cm as a fraction of 1 m gives 150/100, which simplifies past 1. A fraction above 1 simply says the first quantity is bigger than the second, which you should expect before you even calculate.
5.3 Decimals and Fractions
Decimals give a second way to report the same fraction. Once 15 minutes of an hour simplifies to 1/4, dividing 1 by 4 gives 0.25. Converting this way makes comparing easy: 0.75 of a film watched beats 0.5 remaining without any further work.
Reading the context matters as much as the maths. A question asking for a fraction of a jug wants the drink over the capacity, in matching units, simplified. State the units, convert, write, simplify, and, when asked, convert to a decimal.
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2 · Watch
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Where it sits
Learn first
Optional connections
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
17 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.