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 â‚¦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 =  $$\frac{50 \: kobo}{â‚¦2}$$

â‚¦  and kobo are different units.

Convert  â‚¦ to kobo

â‚¦1 = 100 kobo

â‚¦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.Â Â Â  0.4
b.Â Â Â  0.15
c.Â Â Â  0.025
d.Â Â Â  0.375
e.Â Â Â  0.468
f.Â Â Â  0.0425
g.Â Â Â  38.25
h.Â Â Â  0.0001

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

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

a.Â Â Â  20% of 240
b.Â Â Â  5% of 500
c. Â Â Â  2 Â½ % of 400
d.Â Â Â  25% of 600kg
e.Â Â Â  20% of â‚¦250
f.Â Â Â  25% of 120 girls
g.Â Â Â  2.5% of 800
h.Â Â Â  4 Â½% of 1000g

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