In the previous lesson we learned how to write variable and numerical expressions involving addition and subtraction. In this lesson we learn how to use multiplication and division to write expressions.
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Here is a table of key words that indicate multiplication and division.
Operation |
Verbal expressions (key words) |
Variable expression |
$\large~\times~$ |
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$2m\mbox{ or }2\cdot~m$ |
$\large~\div~$ |
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$a\div~6\mbox{ or }\frac{a}{6}$ |
Example 1:
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To find the total number of apples in n bags, make a table an fill in some values.
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If n = 7, how many apples are there altogether? [There would be 28 apples.] If n = 12, how many apples are there altogether? [There would be 48 apples.] Can you see that the total number of apples is always 4 times the number of bags? If there were n bags, then we would have "4 times n" number of apples. "4 times n" is written as 4n. NOTE: A number right next to a variable is assumed to represent multiplication. |
Example 2: A stick is x inches long and is cut into 4 equal pieces. How long is each of the pieces?
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To understand this question, first suppose you had a 78-inch long stick and you cut it into 6 equal-sized pieces. How long would each piece be?
Dividing 78 by 6 would give the lenth of each piece. $$\frac{78}{6}=13$$
Each piece would be 13 inches long.
Now replace the "78" with x and 6 with 4.
$$\frac{x}{4}\mbox{ is the length of each of the four pieces.}$$
EXPLORE!
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Question 1 Imagine a sheet of stamps. Each stamp costs 35 cents. Write a variable expression for the cost of n stamps.
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[show answer] |
Question 2 David has 9 bags. He places an equal number of coins in each bag. If there are n coins total, write an expression for the number of coins in each bag.
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[show answer] |
Question 3 Each side of a regular pentagon measures m inches. Write a variable expression for the perimeter of this pentagon.
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[show answer] |