Solve multiplicative comparison problems

Multiplicative comparison interprets one whole-number quantity as a specified number of times another, expressed through relationships such as “4 times as many” and represented with equations, tape diagrams, or arrays. The learner determines an unknown compared amount, reference amount, or whole-number factor using multiplication or division, while distinguishing multiplicative relationships from additive differences; fractional factors, decimal comparisons, and more general ratio reasoning are beyond this scope.

Detailed Explanation: Solve multiplicative comparison problems

When a problem says “times as many”, use multiplication. The number being compared is made of equal groups of the reference amount.

Example

Mia has $6$ stickers. Leo has $4$ times as many stickers as Mia. How many stickers does Leo have?

Find the reference amount.
Mia has $6$ stickers.
Find the number of groups.
“ $4$ times as many” means $4$ groups of Mia’s amount.
Write a multiplication equation.

4 \times 6 = \text{Leo's stickers}

Solve.

4 \times 6 = 24

Leo has $(24)$ stickers.

You can picture the comparison as four equal groups:

6+6+6+6=24

Remember, “ $4$ times as many” is different from “ $4$ more.” Times as many uses multiplication, while more uses addition.

Learn by doing: Solve multiplicative comparison problems

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Competition Math - Grade 11

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