Answer :
Below is a detailed step‐by‐step solution.
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Step 1. Convert Fractions to Percentages
Remember that to convert a fraction to a percentage you multiply by 100.
1a) For the fraction
[tex]$$
\frac{3}{10},
$$[/tex]
we have
[tex]$$
\frac{3}{10} \times 100 = 30\%.
$$[/tex]
Also, for the expression
[tex]$$
\frac{\sqrt{13}}{100},
$$[/tex]
multiplying by 100 gives
[tex]$$
\frac{\sqrt{13}}{100}\times 100 = \sqrt{13}\%.
$$[/tex]
Numerically, since
[tex]$$
\sqrt{13}\approx 3.605551275463989,
$$[/tex]
this is approximately
[tex]$$
3.61\%.
$$[/tex]
1b) For the fraction
[tex]$$
\frac{4}{50},
$$[/tex]
note that
[tex]$$
\frac{4}{50} \times 100 = 8\%.
$$[/tex]
1c) For the fraction
[tex]$$
\frac{3}{20},
$$[/tex]
we calculate
[tex]$$
\frac{3}{20} \times 100 = 15\%.
$$[/tex]
1d) For the fraction
[tex]$$
\frac{7}{25},
$$[/tex]
we have
[tex]$$
\frac{7}{25} \times 100 = 28\%.
$$[/tex]
1e) For the fraction
[tex]$$
\frac{4}{5},
$$[/tex]
calculating gives
[tex]$$
\frac{4}{5} \times 100 = 80\%.
$$[/tex]
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Step 2. Simplify the Given Fractions
To simplify a fraction, divide the numerator and the denominator by their greatest common divisor (GCD).
2a) Simplify
[tex]$$
\frac{20}{50}.
$$[/tex]
The GCD of 20 and 50 is 10, so
[tex]$$
\frac{20}{50} = \frac{20\div10}{50\div10} = \frac{2}{5}.
$$[/tex]
2b) Simplify
[tex]$$
\frac{12}{16}.
$$[/tex]
The GCD of 12 and 16 is 4, so
[tex]$$
\frac{12}{16} = \frac{12\div4}{16\div4} = \frac{3}{4}.
$$[/tex]
2c) Simplify
[tex]$$
\frac{24}{30}.
$$[/tex]
The GCD of 24 and 30 is 6, so
[tex]$$
\frac{24}{30} = \frac{24\div6}{30\div6} = \frac{4}{5}.
$$[/tex]
2d) Simplify
[tex]$$
\frac{32}{54}.
$$[/tex]
The GCD of 32 and 54 is 2, so
[tex]$$
\frac{32}{54} = \frac{32\div2}{54\div2} = \frac{16}{27}.
$$[/tex]
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Step 3. The Nigerian National Flag
The Nigerian national flag is composed of three vertical parts:
- A left green stripe,
- A central white stripe,
- A right green stripe.
Thus, there are 3 parts.
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Summary of Answers
1. Percentages:
[tex]$$\frac{3}{10} = 30\%,$$[/tex]
[tex]$$\frac{\sqrt{13}}{100} = \sqrt{13}\% \approx 3.61\%,$$[/tex]
[tex]$$\frac{4}{50} = 8\%,$$[/tex]
[tex]$$\frac{3}{20} = 15\%,$$[/tex]
[tex]$$\frac{7}{25} = 28\%,$$[/tex]
[tex]$$\frac{4}{5} = 80\%.$$[/tex]
2. Simplified Fractions:
[tex]$$\frac{20}{50} = \frac{2}{5},$$[/tex]
[tex]$$\frac{12}{16} = \frac{3}{4},$$[/tex]
[tex]$$\frac{24}{30} = \frac{4}{5},$$[/tex]
[tex]$$\frac{32}{54} = \frac{16}{27}.$$[/tex]
3. The Nigerian national flag has 3 parts (left green, central white, right green).
This completes the solution.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Step 1. Convert Fractions to Percentages
Remember that to convert a fraction to a percentage you multiply by 100.
1a) For the fraction
[tex]$$
\frac{3}{10},
$$[/tex]
we have
[tex]$$
\frac{3}{10} \times 100 = 30\%.
$$[/tex]
Also, for the expression
[tex]$$
\frac{\sqrt{13}}{100},
$$[/tex]
multiplying by 100 gives
[tex]$$
\frac{\sqrt{13}}{100}\times 100 = \sqrt{13}\%.
$$[/tex]
Numerically, since
[tex]$$
\sqrt{13}\approx 3.605551275463989,
$$[/tex]
this is approximately
[tex]$$
3.61\%.
$$[/tex]
1b) For the fraction
[tex]$$
\frac{4}{50},
$$[/tex]
note that
[tex]$$
\frac{4}{50} \times 100 = 8\%.
$$[/tex]
1c) For the fraction
[tex]$$
\frac{3}{20},
$$[/tex]
we calculate
[tex]$$
\frac{3}{20} \times 100 = 15\%.
$$[/tex]
1d) For the fraction
[tex]$$
\frac{7}{25},
$$[/tex]
we have
[tex]$$
\frac{7}{25} \times 100 = 28\%.
$$[/tex]
1e) For the fraction
[tex]$$
\frac{4}{5},
$$[/tex]
calculating gives
[tex]$$
\frac{4}{5} \times 100 = 80\%.
$$[/tex]
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Step 2. Simplify the Given Fractions
To simplify a fraction, divide the numerator and the denominator by their greatest common divisor (GCD).
2a) Simplify
[tex]$$
\frac{20}{50}.
$$[/tex]
The GCD of 20 and 50 is 10, so
[tex]$$
\frac{20}{50} = \frac{20\div10}{50\div10} = \frac{2}{5}.
$$[/tex]
2b) Simplify
[tex]$$
\frac{12}{16}.
$$[/tex]
The GCD of 12 and 16 is 4, so
[tex]$$
\frac{12}{16} = \frac{12\div4}{16\div4} = \frac{3}{4}.
$$[/tex]
2c) Simplify
[tex]$$
\frac{24}{30}.
$$[/tex]
The GCD of 24 and 30 is 6, so
[tex]$$
\frac{24}{30} = \frac{24\div6}{30\div6} = \frac{4}{5}.
$$[/tex]
2d) Simplify
[tex]$$
\frac{32}{54}.
$$[/tex]
The GCD of 32 and 54 is 2, so
[tex]$$
\frac{32}{54} = \frac{32\div2}{54\div2} = \frac{16}{27}.
$$[/tex]
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Step 3. The Nigerian National Flag
The Nigerian national flag is composed of three vertical parts:
- A left green stripe,
- A central white stripe,
- A right green stripe.
Thus, there are 3 parts.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Summary of Answers
1. Percentages:
[tex]$$\frac{3}{10} = 30\%,$$[/tex]
[tex]$$\frac{\sqrt{13}}{100} = \sqrt{13}\% \approx 3.61\%,$$[/tex]
[tex]$$\frac{4}{50} = 8\%,$$[/tex]
[tex]$$\frac{3}{20} = 15\%,$$[/tex]
[tex]$$\frac{7}{25} = 28\%,$$[/tex]
[tex]$$\frac{4}{5} = 80\%.$$[/tex]
2. Simplified Fractions:
[tex]$$\frac{20}{50} = \frac{2}{5},$$[/tex]
[tex]$$\frac{12}{16} = \frac{3}{4},$$[/tex]
[tex]$$\frac{24}{30} = \frac{4}{5},$$[/tex]
[tex]$$\frac{32}{54} = \frac{16}{27}.$$[/tex]
3. The Nigerian national flag has 3 parts (left green, central white, right green).
This completes the solution.
