Multiplicative Comparison Word Problems
Solve word problems involving multiplicative comparison using drawings and equations with a symbol for the unknown number
What a learner can do afterwards
- A blue ribbon is 3 times as long as a red ribbon of 7 cm — how long is the blue ribbon?
- 36 is 4 times a number — what is the number?
- Explain why 'Sam has 5 more' is additive but 'Sam has 5 times as many' is multiplicative
1 · Read
You already know that 'times as many' means multiply, not add. 'Sam has 5 more' tells you to add 5. 'Sam has 5 times as many' tells you to multiply by 5. Now you will write that idea as an equation, using a letter or symbol for the number you do not know yet.
A red ribbon is 9 cm long. A blue ribbon is 3 times as long. Write it as an equation: 3 x 9 = b, where b is the blue ribbon's length. Solve: b = 27 cm.
Sometimes the unknown sits inside the multiplication. '30 is 5 times a number' becomes 5 x n = 30. Ask yourself: 5 times what lands on 30? Count up in 5s: 5, 10, 15, 20, 25, 30. That took 6 jumps, so n = 6.
The symbol can be a letter like n or a box like this: ▢. Read the equation like a sentence: '3 times a number equals 12' becomes 3 x n = 12.
Turn a 'times as many' problem into a multiplication equation with a symbol for the unknown, then solve for that symbol.
2 · Watch
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Where it sits
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.