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Lesson 3, Topic 2
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# Product

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This is the result obtained when two numbers are multiplied together.

N.B. When multiplying decimals, remove the decimal point before you multiply and replace it after multiplying.

Example 1

a. 8 and 6.5

b. 9.2 and -4.6

1d.p  x 1d.p = 2d.ps

c. Find the product of $$\scriptsize – 3 \frac{1}{9} \; and \; – 4 \frac{2}{7}$$

First, convert to improper fractions.

$$-\frac{28}{9} \; \times \; -\frac{30}{7} = +\frac {40}{3} \\ = \scriptsize 13 \frac{1}{3} \; or \; 13.33$$

Note:   $$\scriptsize – \; \times \; – \; = +$$

d. The product of a positive number and itself is $$\;\scriptsize 3 \frac{1}{16}$$ What is the number

Solution

Let the number be x

$$\scriptsize x \; \times \; x = 3 \frac{1}{16}\\ \scriptsize x^2 = \normalsize \frac{49}{16}$$

Take the square root of both sides

$$\scriptsize \sqrt{x^2} = \sqrt{\normalsize \frac{49}{16}}\\ \scriptsize x = \normalsize \frac{7}{4} = \scriptsize 1 \frac{3}{4}$$

e. When a number is tripled and five times the number is subtracted, the result is 3.7. What is the number?

Solution

Let the number be x

3x  – 5x  = 3.7

-2x  =  3.7

-2x  =  $$\frac{37}{10}$$

Divide both sides by -2

:- $$\frac{-2x}{-2} =\frac{ \frac{37}{10}}{-2}$$

x = $$\frac{37}{10} \; \times \; \frac{1}{-2} \\ = -\frac{37}{20}\scriptsize = -1\frac{17}{20}$$

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