Expressing One Quantity as a Percentage of Another

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

Worked Example 9.6.1:

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  =  \( \frac{3}{8} \scriptsize \: \times \: 100\% \\ = \frac{3 \: \times \: 100}{8}\\ = \frac{3 \: \times \: 25}{2} \\ = \frac{75}{2} \\ = \scriptsize 37.5\%\)

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

₦  and kobo are different units.

Convert  ₦ to kobo

₦1 = 100 kobo

₦2  = 100 × 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

3 kg  = 3 × 1000 g   =   3000 g

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  =  \( \frac{1}{10} \scriptsize \: \times \: 100\%\\ = \scriptsize 10\%\)