Word Problems with Fractions

Topic Content:

• Word Problems with Fractions

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

Solution

= \( \frac{2}{3} \: \times \: \frac{42}{1} \)

= \( \scriptsize 2 \: \times \: 14 = 28 \)

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

Solution

product of 3 and 3

⇒ 3 × 3 = 9

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

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

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

Step 1: square of 9 = 9²

Step 2: product of the square roots of 25 and 4 = \( \scriptsize \left(\sqrt{25}\: \times \: \sqrt{4}\right)\)

Step 3: square root of 100 = \( \scriptsize \sqrt{100}\\ = \scriptsize 10 \)

Putting all the steps together and solving the word problem, we get:

Find four-fifths of the difference between the product of 0.25 and 128 and the difference between 32.8 and 25.8

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

⇒ \( \frac{4}{5} \scriptsize \: \times \: 32 \:\: – \: 7 \)

⇒ \( \frac{4}{5} \scriptsize \: \times \: 25 \)

⇒ \( \scriptsize 4 \: \times \: 5 \\ \scriptsize = 20 \)

Divide the square root of 81 by the difference between the product of  -1 and -3 and the square root of 4.

Solution