Multiplicative Comparison as an Equation
Interpret a multiplication equation as a comparison (e.g. 35 = 5 × 7 means 35 is 5 times as many as 7); represent verbal statements of multiplicative comparisons as equations
What a learner can do afterwards
- Explain that '4 times as many' means multiply by 4
- Write an equation for: Sarah has 3 times as many stickers as Tom, who has 8 stickers
- Distinguish multiplicative comparison from additive comparison in word problems
1 · Read
You already know that multiplication makes equal groups. Multiplicative comparison uses that same idea to compare two amounts. When you hear the words 'times as many,' that phrase tells you to multiply.
Jack has 6 shells. Nina has 4 times as many shells as Jack. To find Nina's total, multiply: 4 × 6 = 24. Written as an equation, that is 24 = 4 × 6. You can read any multiplication equation the same way round: 24 = 4 × 6 says 24 is 4 times as many as 6.
Watch the exact words. 'Sarah has 5 more stickers than Tom' is additive: you add. 'Sarah has 5 times as many stickers as Tom' is multiplicative: you multiply. The sentences look almost the same, but the answer is very different.
The words 'times as many' mean multiply, not add.
More to read
Ten times as many
4 times as many means multiply by 4. If Dan owns 9 toy cars and Ella owns 4 times as many, Ella owns 4 x 9 = 36. Writing it as e = 4 x 9 turns the words into an equation. The letter stands for the unknown amount. Once the equation is written, the calculation is easy.
Times as many
Equations capture comparison stories in symbols. Tom has 8 stickers and Sarah has 3 times as many, so s = 3 x 8 and s = 24. The multiplication sign shows it is multiplicative comparison. If the story had said 3 more, the equation would use a plus sign instead.
Multiplication equations
Multiplication equations have matching sides. In t = 5 x 6, the letter t must equal 30. You can check any equation by working out the numbers side: 5 x 6 = 30. Bar pictures help too: draw one small bar for the bucket and five matching bars for the tank. The picture and the equation tell the same story.
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2 · Watch
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Learn first
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.