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Solve multiplicative comparison problems

Multiplicative comparison describes one whole-number quantity as a specified number of times another, distinguishing the reference quantity, multiplier, and compared quantity; learners solve for any one of these using multiplication or division and represent relationships with equations or bar models. They distinguish “times as many” from additive difference, working with familiar whole-number factors and products; fractional, decimal, ratio, and generalized proportional comparisons are beyond this scope.

Detailed Explanation: Solve multiplicative comparison problems

A multiplicative comparison tells how many times as much one amount is as another.

  • Reference quantity: the amount you start with
  • Multiplier: how many times
  • Compared quantity: the amount you find

“Times as many” means multiply, not add.

Example:
Lena has 44 stickers. Omar has 33 times as many stickers as Lena. How many stickers does Omar have?

  1. Find the reference quantity: Lena has 44 stickers.
  2. Find the multiplier: Omar has 33 times as many.
  3. Write an equation:
3×4=3 \times 4 = \Box
  1. Solve:
3×4=123 \times 4 = 12

Omar has (12)(12) stickers.

You can picture it as three equal groups:

4+4+4=124 + 4 + 4 = 12

Do not add 33 and 44. The word times tells you to multiply.

Learn by doing: Solve multiplicative comparison problems

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Competition Math - Grade 11


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