3.3: Multiplication

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Amy Lagusker
College of the Canyons

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Definition: Multiplication

What is the definition of Multiplication? Repeated Addition

Common Core has slightly changed the WHY behind Repeated Addition

Repeated addition

Example $\PageIndex{1}$

Watermelons cost $3 per pound. How much does a watermelon cost which weighs five pounds?
1. We could answer this question two different ways
  1. $5+5+5=5 \times 3=\$ 15$ (3 groups of 5)
  2. $3+3+3+3+3=3 \times 5=\$ 15$ (5 groups of 3)
2. Which method is correct? The first one, only.
3. Why? Two reasons.
  1. Think farther ahead in math: $5^{3}=5 \times 5 \times 5$, which matches how we write. Do keep in mind that multiplication is communitive, and.
  2. The watermelon is the subject of the problem. Its weight is the first issue. We pick up a watermelon and then look at the price. 5 pounds multiplies to $3 because we have 5 pounds for each dollar.
Are we able to use repeated addition for decimals like $0.3 \times 6=1.8$
1. Six boxes weigh 0.3 pounds each. What is the total weight?
  1. Are you able to write a repeated 6, 0.3 times? No. So instead we write: $6 \times 0.3=0.3+0.3+0.3+0.3+0.3+0.3=1.8$
2. What is 30% of 6 pounds?
  1. $6 \times 0.3=0.3+0.3+0.3+0.3+0.3+0.3=1.8$ (6 groups of 0.3)

Sketching Multiplication

Common Core is very big on visualizing mathematics. Students are expected to make drawings to show how multiplication works.

Example $\PageIndex{2}$

Sketch $3 \times 2$

Sketch $2 \times 3$

Multiplying with Decimals

Example $\PageIndex{3}$

Step 1: Multiply 7 to each digit in the top number from right to left.

Step 2: Multiply 4 to each digit in the top number from right to left.

Step 3: Multiply 2 to each digit in the top number from right to left.

Step 4: Add

Step 5: Move the decimal three spots to the left. Since there are three digits to the right of the decimals, we move the final decimal three spots to the left. (bold numbers)

\[\begin{array}{r}
123.8 \\
\times 2.47 \\
\hline 28666 \\
49520 \\
+247600 \\
\hline 305.\mathbf{786}
\end{array} \nonumber \]

Practice Problems

Expand out $7 \times 4$
Expand out $2 \times 6$
Multiply $4.61 \times 7.94$ (do not round)
Multiply $516.4 \times 0.347$ (do not round)