Lesson 10 of 10 · Grades 3 to 5
Fractions in real life
Fractions are not only a school topic. They show up in recipes, on clock faces, in money and whenever people share food. This lesson puts everything you have learned to work on small, everyday problems.
Fractions on the clock
Fractions are already part of your day. When someone says "half an hour", they mean 1/2 of an hour. A quarter of an hour is 15 minutes, and three quarters of an hour is 45 minutes. To change a fraction of an hour into minutes, divide 60 by the denominator, then multiply by the numerator. For 5/6 of an hour: 60 divided by 6 is 10, and 5 x 10 is 50 minutes.
Fractions and money
Money splits into fractions neatly because 100 cents and 60 minutes both divide by many numbers. One quarter of $8 is $2, because 8 divided by 4 is 2. Half of $10 is $5. Two fifths of $15 is $6, because 15 divided by 5 is 3 and 2 x 3 = 6. The method is the same two-step method from the lesson on fractions of a whole number: divide by the denominator, multiply by the numerator.
Fractions in the kitchen
Recipes are full of fractions: 1/2 cup of milk, 3/4 teaspoon of cinnamon, 1 1/2 cups of flour. Cooking for more people often means multiplying those fractions. If a recipe for 4 people uses 3/4 cup of milk, a recipe for 8 people uses double: 2 x 3/4 = 6/4, which is 1 1/2 cups. If you halve a recipe that needs 2 1/2 cups of flour, you need 1 1/4 cups, because half of 2 is 1 and half of 1/2 is 1/4.
Sharing and measuring
Sharing food is fraction practice in disguise. Cut a pizza into 8 equal slices and let three friends take 2 slices each: 6 slices are eaten, so 6/8 of the pizza is gone, and 2/8, or 1/4, is left. Measuring works the same way. Half a metre of ribbon is 50 centimetres, because a metre has 100 centimetres and half of 100 is 50.
Worked example
A cake recipe needs 3/4 cup of milk and makes 12 cupcakes. You want to make 24 cupcakes, so you double every ingredient. Milk: 2 x 3/4 = 6/4 cups, which is 1 1/2 cups. Flour: the recipe uses 2 1/4 cups, so double it: 2 x 2 1/4 = 4 1/2 cups. Check the logic: doubling the cupcakes doubles the ingredients, and every answer is twice the original amount.
Watch out for this
Do not read a quarter of an hour as 25 minutes. A quarter of 60 is 15, not 25. If the numbers feel wrong, use the two-step method and check with a sensible estimate: a quarter should be a small part, and 45 minutes is most of an hour. Also, when a recipe is halved or doubled, all the ingredients change together; a single fraction cannot be left at its original size.
Remember
- Use divide-then-multiply for fractions of time, money and amounts.
- Doubling a recipe doubles every fraction in it.
- Halving a mixed number halves the whole and the fraction.
- Estimate first, so you notice an answer that is wildly wrong.
Try it
Answer the five questions below. Work them out first, then open each answer to check.
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How many minutes are in 1/4 of an hour?
Show answer
15 minutes. 60 divided by 4 is 15.
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What is 1/2 of $10?
Show answer
$5.
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A recipe uses 1/2 cup of oil. You double the recipe. How much oil do you need?
Show answer
1 cup, because 2 x 1/2 = 1.
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How many minutes are in 3/4 of an hour?
Show answer
45 minutes. 60 divided by 4 is 15, and 3 x 15 = 45.
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A bike ride is 12 km long. You complete 2/3 of it. How far have you ridden?
Show answer
8 km. 12 divided by 3 is 4, and 2 x 4 = 8.
Puzzle · Clock puzzle
Puzzle time
After school, Sam reads for 1/4 of an hour, draws for 1/3 of an hour and tidies up for 1/6 of an hour. How many minutes is that in total?
Show a hint
Change each fraction of an hour into minutes. One hour is 60 minutes, and 1/4 of 60 is 15.
Show the answer
Answer: 45. Sam is busy for 45 minutes. 1/4 of an hour is 15 minutes, 1/3 of an hour is 20 minutes and 1/6 of an hour is 10 minutes. 15 + 20 + 10 = 45 minutes, which is 3/4 of an hour.