### Hard Multiplication, Hard Measurement and Hard Partition Word Problems

Just as Hard Addition and Hard Subtraction problems involves 2 sets and the relationship between those 2 sets, so also with Hard Multiplication, Hard Measurement and Hard Division.

Suppose that Trixie has 2 fish and that Rose has 3 times as many fish. Then Rose has 6 fish altogether. Here is a representation of that situation.

Trixie
 fish fish

Rose
 fish fish

 fish fish

 fish fish

The number 2 (of fish that Trixie has) is called the multiplicand and the number 3 is called the multiplier. (The multiplier tells the relationship between the number of fish that Trixie has and the number of fish that Rose has.) The number 6 is called the product. All Hard Multiplication, all Hard Measurement, and all Hard Partition word problems involve 3 numbers - a multiplier, a multiplicand and a product. We can make up word problems involving these numbers in 3 different ways.

1. Hard Multiplication: Trixie has 2 fish. Rose has 3 times as many fish as Trixie has. How many fish does Rose have? (We are given the number 2, the multiplicand, and the number 3 the multiplier. We need to find the product. 2 x 3 = □)

2. Hard Measurement: Rose has 6 fish. Trixie has 2 fish. Rose has how many times as many fish as Trixie has? (We are given the number 6, the product, and the number 2, the multiplicand. We need to find the multiplier. 6 ÷ 2 = □)

3. Hard Partition: Rose has 6 fish. She has 3 times as many fish as Trixie has. How many fish does Trixie have? (We are given the number 6, the product, and the number 3, the multiplier. We need to find the multiplicand. 6 ÷ 3 = □)

This chart summarizes the relationship between Easy Multiplication, Easy Partition and Easy Measurement.

 multiplier (relationship) multiplicand product Hard Multiplication given given find Hard Measurement find given given Hard Partition given find given

It is worthwhile comparing this chart with the charts for

Together, these 4 charts describe 11 of the 12 different types of word problems that are part of the typical elementary school arithmetic curriculum.

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