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There are three types of multiplication word problems:
- Repeated Addition
- Cartesian Multiplication
- Multiplicative Comparison Problems - This type of problem might look like a repeated addition or Cartesian multiplication problem, but you are missing part of the problem. If you know one number and a multiplier this is called a "Product Unknown Comparison Problem". If you know the product and the multiplier, but not the original set this is called a "Set Size Unknown problem", and finally if you are given the size of two sets, one of which is a multiple of the other than this is a "Multiplier Unknown" problem
The picture to the right shows stamps, arranged in four groups of four.
How many stamps are in that image? While you can count them individually, there is a much faster way of getting the total.
Multiplicative Comparison Problems:
Multiplier Unknown Comparison Problem:
Mary is collecting bottles to return for deposit. There are 24 bottles in a case. This month she has collected 3 cases of bottles. How many bottles has she collected?
Product Unknown Comparison Problem:
If the deposit on each bottle is 5 cents, how much money will Mary collect for her 3 cases of bottles?
Set Size Unknown Comparison Problem:
Mary's younger brother also collected bottles. He received $2.40 for the bottles he collected. How many cases did he collect?