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

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

Evaluation Questions:

1. Change the following to a terminating decimal:

a. $$\frac{3}{5}$$

b. $$\frac{3}{4}$$

c. $$\scriptsize 5 \frac{3}{4}$$

d. $$\frac{1}{2}$$

e. $$\frac{3}{8}$$

2. Change the following to recurring decimals:

a. $$\frac{2}{3}$$

b. $$\frac{4}{7}$$

c. $$\frac{5}{7}$$

d. $$\scriptsize 5 \frac{1}{3}$$

e. $$\frac{5}{6}$$

f. $$\frac{1}{9}$$

g. $$\scriptsize 8 \frac{2}{3}$$

h. $$\frac{2}{11}$$

3. Express the following as percentages

a.    0.4
b.    0.15
c.    0.025
d.    0.375
e.    0.468
f.    0.0425
g.    38.25
h.    0.0001

4. Convert the following  percentage to fraction in its simplest form

a.    25%
b.    150%
c.    32%
d.    50%
e.    42%
f.    64%
g.    24.2%

5. Change the following to decimal:

a. $$\scriptsize 80 \frac{2}{5} \%$$

b. 36.05%

c. 50%

d. 25%

e. $$\scriptsize 80 \frac{2}{5} \%$$

f. 20%

6. Calculate the following

a.    20% of 240
b.    5% of 500
c.     2 ½ % of 400
d.    25% of 600kg
e.    20% of ₦250
f.    25% of 120 girls
g.    2.5% of 800
h.    4 ½% of 1000g

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