Question

Directions: Solve the following by multiplying by the inverse of the fractional coefficient. 1. \frac{2}{5} t = 20 2. \frac{7}{8} p = 56 3. \frac{5}{6} x = 30 4. \frac{1}{2} x = 20 5. \frac{3}{5} s = 60 6. \frac{1}{3} t = 3 7. \frac{3}{4} x = 9 8. \frac{11}{12} x = 11 9. \frac{8}{10} t = 80 10. \frac{p}{3} = 9 11. \frac{n}{5} = 30 12. \frac{6a}{7} = 36 13. \frac{1}{2} t + 3 = 28 14. \frac{1}{6} r = 12 15. \frac{11}{12} b = 32

Answer 1

The answer of the following options are as 50, 64, 36, 40, 100, 9, 12, 12 100, 27, 150 42, 50 72, 28.3.

How to interpret the fraction?

Suppose the fraction is proper (the numerator is smaller than the denominator).

Let it be

$\dfrac{a}{b}$

Then, we can interpret it as:

a parts out of b parts of a thing.

$1. \dfrac{2}{5} t = 20\\\\t = 20 \times \dfrac{5}{2}\\\\t= 50$

$2. \frac{7}{8} p = 56\\\\p = 56 \times \frac{8}{7} \\\\ p= 64$

$3. \frac{5}{6} x = 30 \\\\x = 30 \times \frac{6}{5} = 36$

$4. \frac{1}{2} x = 20\\\\x = 20 \times 2 = 40$

$5. \frac{3}{5} s = 60\\\\s = 60 \times \frac{5}{3} = 100$

$6. \frac{1}{3} t = 3 \\\\t = 3\times 3 = 9$

$7. \frac{3}{4} x = 9\\\\x = 12$

$8. \frac{11}{12} x = 11\\\\x = 11 \times 12/11 = 12$

$9. \frac{8}{10} t = 80\\\\t = 80 \times 10/8 = 100$

$10. \frac{p}{3} = 9 \\\\p = 9 \times 3 = 27$

$11. \frac{n}{5} = 30\\\\n = 30 \times 5 = 150$

$12. \frac{6a}{7} = 36 \\\\a = 36 \times 7/6 = 42$

$13. \frac{1}{2} t + 3 = 28\\\\t = (28 - 3)2 = 50$

$14. \frac{1}{6} r = 12\\\\r = 12\times 6 = 72$

$15. \frac{11}{12} b = 32\\ \\b = 32 \times 11/12 = 29.33$

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