Lesson 9, Topic 6
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# Expressing one Quantity as a Percentage of Another

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To express one quantity as a percentage of another, write the first quantity as a fraction of the second and then multiply by 100.

Example 1

a. What percentage of 550g  is 11g?

b. What percentage of 800 is 300?

c. What percentage of ₦2 is 50 kobo?

d. What percentage of 3kg  is 300g

Solution

a. Fraction of the quantity =  $$\frac{11g}{550g} \\ = \frac{1}{50}$$

% of quantity  =  $$\frac{1}{50} \scriptsize \: \times \: 100\% \scriptsize = 20\%$$

b. Fraction of the quantity =  $$\frac{300}{800}= \frac{3}{8}$$

% of quantity  =  $$\frac{3}{8} \scriptsize \: \times \: 100\% \scriptsize = 20\% \\ = \frac{3 \: \times \: 100}{8}\\ = \frac{3 \: \times \: 25}{2} \\ = \frac{75}{2} \\ = \scriptsize 37.5\%$$

c. Fraction of the quantity =  $$\frac{50 \: kobo}{₦2}$$

₦  and kobo are different units.

Convert  ₦ to kobo

₦1 = 100 kobo

₦2  = 100 x 2 =  200 kobo

Fraction of the quantity =  $$\frac{50 \: kobo}{200 \: kobo} \\ = \frac{1}{4}$$

% of quantity  =  $$\frac{1}{4} \scriptsize \: \times \: 100\% \scriptsize = 25\%$$

d. Fraction of the quantity =  $$\frac{300g}{3kg}$$

But g and kg are different units.

Convert kg to g.

1kg  = 1000g

3kg  = 3 x 1000g   =   3000g

Fraction of the quantity =  $$\frac{300g}{3000g} = \frac{3\not{0}\not{0}g}{30\not{0}\not{0}g} \\ = \frac{3}{30} \\ = \frac{1}{10}$$

% of quantity  =  $$\frac{1}{10} \scriptsize \: \times \: 100\%\\ = \scriptsize 10\%$$ error: