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.
More to read
Times as many
Multiplicative comparison uses times as many to compare two amounts. If Tom has 7 stickers and Sarah has 3 times as many, Sarah has 3 x 7 = 21 stickers. The word times tells you to multiply. Additive comparison instead uses more or fewer and needs adding or subtracting. Spot which word the problem uses before you calculate.
Ten times as many
Ten times as many means multiply by 10. A blue ribbon that is 3 times as long as a 7 cm red ribbon measures 3 x 7 = 21 cm. Drawing a bar split into equal parts helps: draw one small bar for the red ribbon and three matching bars for the blue one. Counting the parts shows why multiplication fits.
Solve problems using the four operations
Word problems hide the operation in words. Times as many, twice and triple all signal multiplication. Altogether, left and difference usually signal addition or subtraction. If 36 is 4 times a number, undo the multiplication with division: 36 / 4 = 9. Reading the sentence twice keeps you from mixing the two kinds up.
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2 · Watch
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Where it sits
17 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.