Multiplication as scaling
Interpret multiplication as scaling (resizing): compare the size of a product to a factor based on the size of the other factor without computing; explain the effect of multiplying by fractions greater than, equal to, or less than 1
What a learner can do afterwards
- Predict without calculating whether 3/4 × 7 is greater or less than 7
- Explain why multiplying by 5/3 makes a number larger and multiplying by 2/5 makes it smaller
- Relate multiplying a/b by n/n = 1 to the principle of fraction equivalence
The lesson
You already know how to multiply fractions. Now you can predict the size of the answer before you calculate anything. Look at the fraction you are multiplying by. Is it less than 1, equal to 1, or greater than 1? That tells you whether your number will shrink, stay the same, or grow.
Multiply by a fraction less than 1, like 2/5, and the answer shrinks smaller than you started. Multiply by exactly 1, like 6/6, and nothing changes at all. That is the same idea behind equivalent fractions: you are showing the same size in different pieces. Multiply by a fraction greater than 1, like 5/3, and the answer grows bigger than you started.
Mia sees the problem 3/4 × 7. Before she multiplies, she checks the fraction. 3/4 is less than 1, so she predicts the answer will be smaller than 7. Then she calculates: 3/4 × 7 = 21/4 = 5 and 1/4. Smaller than 7, just like she predicted.
Check the fraction first. Less than 1 shrinks, equal to 1 stays the same, greater than 1 grows. You do not need to multiply to know which one will happen.
Look at the fraction: less than 1 shrinks, equal to 1 stays the same, greater than 1 grows, no calculating needed.
Watch it
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 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.