Lesson 3, Topic 4
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# Word Problems with Fractions

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The quotient of two numbers is the result obtained by dividing one number by another.

a. Find two-thirds of the sum of 23 and 19.

Solution

$$\frac{2}{3} \: \times \: \scriptsize \left (23 \: + \: 19 \right)$$

= $$\frac{2}{3} \: \times \: \frac{42}{1}$$

= $$\scriptsize 2 \: \times \: 14 = 28$$

b. Divide 88 by the sum of 2 and the product of 3 and 3.

Solution

product of 3 and 3

3 x 3 = 9

Add 2 to it = $$\scriptsize 2 + (3 \: \times \: 3) \\ \scriptsize = 2 + 9 = 11$$

Divide 88 by the sum which is 11 = $$\frac{88}{11} \\ \scriptsize = 8$$

c. Add the square of 9 to the product of the square roots of 25 and 4, and divide the result by the square root of 100.

Solution

$$\frac{9^2 \: + \: \left(\sqrt{25}\: \times \: \sqrt{4}\right)}{\sqrt{100}} \\ = \frac{81 \: + \: \left (5 \: \times \: 2 \right) }{10} \\ = \frac{81 \: + \: 10}{10} \\ = \frac{91}{10} \scriptsize = 9.1$$

d. Find four-fifth of the difference between the product of 0.25 and 128 and the difference between 32.8 and 25.8

$$\frac{4}{5} \scriptsize \: \times \: \left(0.25 \: \times \: 128 \right) \: – \: \left(32.8 \: – \: 25.8 \right)$$

$$\frac{4}{5} \scriptsize \: \times \: 32 \:\: – \: 7$$

$$\frac{4}{5} \scriptsize \: \times \: 25$$

$$\scriptsize = 4 \: \times \: 5 = 20$$

e. Divide the square root of 81 by the difference between the product of

-1 and -3 and the square root of 4.

Solution

$$\frac {\sqrt{81}}{(-1 \; \times \: -3) \; – \: \sqrt{4}} \\ = \frac{9}{+3 \: – \: 2}\\ = \frac{9}{1} \\ \scriptsize = 9$$
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