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• Word Problems Involving Multiplication

a. 8 and 6.5

b. 9.2 and -4.6

1d.p  × 1d.p = 2d.p’s (decimal places)

Here, we also added the negative sign after multiplying. (+ × – = – )

Find the product of \( \scriptsize – 3 \frac{1}{9} \: and \: – 4 \frac{2}{7} \)

first, convert to improper fractions.

⇒ \( -\frac{28}{9} \: \times \: -\frac{30}{7} \\= + \frac{4 \: \times \: 10}{3} \\= +\frac {40}{3} \\ = \scriptsize 13 \frac{1}{3} \; or \; 13.33 \)

Note:   \( \scriptsize – \; \times \; – \; = + \)

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

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

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

⇒ \(\normalsize \frac{-2x}{-2} = \frac{ \large \frac{37}{10}}{-2}\)

x = \(\large \frac{ \frac{37}{10}}{\frac{-2}{1}}\)

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