Which of the following options has the same value as $20\%$ of $45$ ? $\newline$ Choose $3$ answers: $\newline$ (A) $\frac{20}{45}\times100$ $\newline$ (B) $\frac{1}{5}\times45$ $\newline$ (C) $20\times45$ $\newline$ (D) $\frac{20}{100}\times45$ $\newline$ (E) $0.2\times45$

Full solution

Q. Which of the following options has the same value as

20\%

45

\newline

Choose

3

answers:

\newline

(A)

\frac{20}{45}\times100

\newline

(B)

\frac{1}{5}\times45

\newline

(C)

20\times45

\newline

(D)

\frac{20}{100}\times45

\newline

(E)

0.2\times45

Understand the meaning: Understand the meaning of $20\%$ of a number. $\newline$ $20\%$ of a number means $20$ per $100$ of that number, which can be written as $(\frac{20}{100})$ times the number.
Convert to fraction and multiply: Convert the percentage to a fraction and multiply by $45$ . $20\%$ as a fraction is $\frac{20}{100}$ , so $20\%$ of $45$ is $(\frac{20}{100}) \times 45$ .
Simplify the expression: Simplify the expression from Step $2$ . $\newline$ $(\frac{20}{100}) \times 45$ simplifies to $(\frac{1}{5}) \times 45$ because $\frac{20}{100}$ reduces to $\frac{1}{5}$ .
Calculate the value: Calculate the value of the simplified expression. $(\frac{1}{5}) \times 45 = 9$ .
Compare with options: Compare the options to the simplified expression $(\frac{1}{5}) \times 45$ . $\newline$ Option A: $(\frac{20}{45})\times100$ is not equivalent to $(\frac{1}{5})\times45$ . $\newline$ Option B: $(\frac{1}{5})\times45$ is exactly the expression we have, so it is equivalent. $\newline$ Option C: $20\times45$ is not a percentage of $45$ , it's a multiplication, so it's not equivalent. $\newline$ Option D: $(\frac{20}{100})\times45$ is the same as $(\frac{1}{5})\times45$ after simplifying, so it is equivalent. $\newline$ Option E: $0.2\times45$ is equivalent because $0.2$ is the decimal form of $(\frac{20}{45})\times100$ $0$ .