Fractions of a whole (age 10+)
Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b); solve word problems involving division of whole numbers leading to fractional or mixed-number answers
What a learner can do afterwards
- Explain that 3/4 means 3 ÷ 4 and verify by showing 3/4 × 4 = 3
- Solve: '9 people share a 50-pound sack equally — how many pounds each?' and express the answer as 5 5/9
- Use a visual model to show that sharing 3 wholes among 4 people gives each person 3/4
1 · Read
A fraction means its numerator divided by its denominator. In a/b, a names the amount being shared and b names the number of equal shares. The denominator cannot be zero. A shaded fraction of one whole also names this division result: count the shaded equal parts for the numerator and all the equal parts for the denominator.
Six people share 17 litres equally. Give each 2 litres, using 6 × 2 = 12 litres. Five litres remain. Share those five litres six ways: each gets another 5/6 litre. The full share is 2 5/6 litres. In general, divide to find the whole part, then write the remainder over the number of people. The remainder must be smaller than that number.
Check equal sharing by multiplying one person's share by the number of people. For a fraction, multiply its numerator by that number, then divide by its denominator. For a mixed-number share, multiply its whole part and fraction part separately, then add. Five shares of 2 1/5 give 5 × 2 = 10 and 5 × 1/5 = 1, making 11 in total.
Four equal-size loaves are shared by seven people. Cut every loaf into seven equal pieces. Each row here represents one loaf, and each dot represents one seventh of a loaf. Give each person one piece from every row. Each column contains four pieces, so each person gets 4/7 of a loaf. This is why 4 ÷ 7 = 4/7.
A fraction a/b always means a ÷ b, and multiplying the fraction by b brings you back to a.
Questions and the readings 'Separate complete wholes' and 'Share the leftover amount' written for this learning dataset. Other readings adapted from Khan Academy reviews of fractions, decimals and mixed numbers. The linked video is by Khan Academy.
2 · Watch
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Where it sits
Where this leads
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16 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.