Multiplying fractions
Understand a/b as a multiple of 1/b; multiply proper fractions and mixed numbers by whole numbers, supported by visual models (e.g. 3 × 2/5 = 6/5 = 1 1/5)
What a learner can do afterwards
- Calculate 4 × 3/8 using repeated addition or the rule n × a/b = (n×a)/b
- Multiply mixed numbers by whole numbers and express the product as a whole number or mixed number; find a missing whole-number factor from a given mixed-number group size and total
- Use a visual model to show why 5 × 1/4 = 5/4
1 · Read
Multiplying a fraction by a whole number collects that many equal groups. Multiply the numerator by the number of groups and keep the denominator for this step. The parts keep their size. Compare the resulting numerator with the denominator to see whether the product is below one whole. One group leaves the fraction unchanged; zero groups give zero.
For a mixed number, first multiply its whole part by its denominator and add its numerator. Then multiply this new numerator by the number of groups. For 1 2/5 × 2, 1 × 5 + 2 = 7, so use 7/5. Two groups make 14/5. Divide 14 by 5: two wholes and four fifths remain, giving 2 4/5.
Keep the denominator during the multiplication step. You may change both numbers afterward to simplify the product without changing its value.
A unit fraction counts one equal part. Two groups of 1/6 make two sixths, or 2/6. To model a unit-fraction product on a number line, start at zero and make one equal hop for each group. Every hop has the size of the unit fraction.
You can find a missing number of groups by counting in the same small parts. If each group has 1 1/4 units and the total is 5 units, each group contains five quarters and the total contains twenty quarters. Divide 20 by 5 to get four groups. Check by multiplying the group size by four.
To multiply a fraction by a whole number, multiply the top number and keep the bottom number the same. Change mixed numbers into a single fraction first.
Questions and the readings 'Count the small parts first' and 'Equal groups keep equal parts' written for this learning dataset. 'Multiply fractions: FAQ' adapted from Khan Academy. Linked videos by Khan Academy.
2 · Watch
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