Answer :
Below is a step‐by‐step explanation for solving each part of the exercise.
--------------------------------------------------
Step 1. Convert the given fractions to percentages.
(a) For the fraction
[tex]$$\frac{3}{10},$$[/tex]
multiply by 100 to convert it into a percentage:
[tex]$$
\frac{3}{10} \times 100 = 30\%.
$$[/tex]
(b) For the fraction
[tex]$$\frac{4}{50},$$[/tex]
multiply by 100:
[tex]$$
\frac{4}{50} \times 100 = 8\%.
$$[/tex]
(c) For the fraction
[tex]$$\frac{3}{20},$$[/tex]
multiply by 100:
[tex]$$
\frac{3}{20} \times 100 = 15\%.
$$[/tex]
(d) For the fraction
[tex]$$\frac{7}{25},$$[/tex]
multiply by 100:
[tex]$$
\frac{7}{25} \times 100 = 28\%.
$$[/tex]
(e) For the fraction
[tex]$$\frac{4}{5},$$[/tex]
multiply by 100:
[tex]$$
\frac{4}{5} \times 100 = 80\%.
$$[/tex]
--------------------------------------------------
Step 2. Write the given fractions in their simplest form.
(a) Simplify
[tex]$$\frac{20}{50}.$$[/tex]
Find the greatest common divisor (GCD) of 20 and 50, which is 10. Then divide both the numerator and the denominator by 10:
[tex]$$
\frac{20 \div 10}{50 \div 10} = \frac{2}{5}.
$$[/tex]
(b) Simplify
[tex]$$\frac{12}{16}.$$[/tex]
The GCD of 12 and 16 is 4. Dividing both by 4:
[tex]$$
\frac{12 \div 4}{16 \div 4} = \frac{3}{4}.
$$[/tex]
(c) Simplify
[tex]$$\frac{24}{30}.$$[/tex]
The GCD of 24 and 30 is 6. Dividing both by 6:
[tex]$$
\frac{24 \div 6}{30 \div 6} = \frac{4}{5}.
$$[/tex]
(d) Simplify
[tex]$$\frac{32}{54}.$$[/tex]
The GCD of 32 and 54 is 2. Dividing both by 2:
[tex]$$
\frac{32 \div 2}{54 \div 2} = \frac{16}{27}.
$$[/tex]
--------------------------------------------------
Step 3. Determine the ratio of green to white in the Nigerian flag.
The Nigerian national flag is divided into three parts, with 2 parts green and 1 part white. Therefore, the ratio of green to white is:
[tex]$$
2:1.
$$[/tex]
--------------------------------------------------
Final Answers
1. Converting fractions to percentages:
- (a) [tex]$\frac{3}{10}=30\%$[/tex]
- (b) [tex]$\frac{4}{50}=8\%$[/tex]
- (c) [tex]$\frac{3}{20}=15\%$[/tex]
- (d) [tex]$\frac{7}{25}=28\%$[/tex]
- (e) [tex]$\frac{4}{5}=80\%$[/tex]
2. Fractions in simplest form:
- (a) [tex]$\frac{20}{50}=\frac{2}{5}$[/tex]
- (b) [tex]$\frac{12}{16}=\frac{3}{4}$[/tex]
- (c) [tex]$\frac{24}{30}=\frac{4}{5}$[/tex]
- (d) [tex]$\frac{32}{54}=\frac{16}{27}$[/tex]
3. Ratio of green to white in the Nigerian flag:
[tex]$$2:1.$$[/tex]
--------------------------------------------------
Step 1. Convert the given fractions to percentages.
(a) For the fraction
[tex]$$\frac{3}{10},$$[/tex]
multiply by 100 to convert it into a percentage:
[tex]$$
\frac{3}{10} \times 100 = 30\%.
$$[/tex]
(b) For the fraction
[tex]$$\frac{4}{50},$$[/tex]
multiply by 100:
[tex]$$
\frac{4}{50} \times 100 = 8\%.
$$[/tex]
(c) For the fraction
[tex]$$\frac{3}{20},$$[/tex]
multiply by 100:
[tex]$$
\frac{3}{20} \times 100 = 15\%.
$$[/tex]
(d) For the fraction
[tex]$$\frac{7}{25},$$[/tex]
multiply by 100:
[tex]$$
\frac{7}{25} \times 100 = 28\%.
$$[/tex]
(e) For the fraction
[tex]$$\frac{4}{5},$$[/tex]
multiply by 100:
[tex]$$
\frac{4}{5} \times 100 = 80\%.
$$[/tex]
--------------------------------------------------
Step 2. Write the given fractions in their simplest form.
(a) Simplify
[tex]$$\frac{20}{50}.$$[/tex]
Find the greatest common divisor (GCD) of 20 and 50, which is 10. Then divide both the numerator and the denominator by 10:
[tex]$$
\frac{20 \div 10}{50 \div 10} = \frac{2}{5}.
$$[/tex]
(b) Simplify
[tex]$$\frac{12}{16}.$$[/tex]
The GCD of 12 and 16 is 4. Dividing both by 4:
[tex]$$
\frac{12 \div 4}{16 \div 4} = \frac{3}{4}.
$$[/tex]
(c) Simplify
[tex]$$\frac{24}{30}.$$[/tex]
The GCD of 24 and 30 is 6. Dividing both by 6:
[tex]$$
\frac{24 \div 6}{30 \div 6} = \frac{4}{5}.
$$[/tex]
(d) Simplify
[tex]$$\frac{32}{54}.$$[/tex]
The GCD of 32 and 54 is 2. Dividing both by 2:
[tex]$$
\frac{32 \div 2}{54 \div 2} = \frac{16}{27}.
$$[/tex]
--------------------------------------------------
Step 3. Determine the ratio of green to white in the Nigerian flag.
The Nigerian national flag is divided into three parts, with 2 parts green and 1 part white. Therefore, the ratio of green to white is:
[tex]$$
2:1.
$$[/tex]
--------------------------------------------------
Final Answers
1. Converting fractions to percentages:
- (a) [tex]$\frac{3}{10}=30\%$[/tex]
- (b) [tex]$\frac{4}{50}=8\%$[/tex]
- (c) [tex]$\frac{3}{20}=15\%$[/tex]
- (d) [tex]$\frac{7}{25}=28\%$[/tex]
- (e) [tex]$\frac{4}{5}=80\%$[/tex]
2. Fractions in simplest form:
- (a) [tex]$\frac{20}{50}=\frac{2}{5}$[/tex]
- (b) [tex]$\frac{12}{16}=\frac{3}{4}$[/tex]
- (c) [tex]$\frac{24}{30}=\frac{4}{5}$[/tex]
- (d) [tex]$\frac{32}{54}=\frac{16}{27}$[/tex]
3. Ratio of green to white in the Nigerian flag:
[tex]$$2:1.$$[/tex]
