Question

Which of the following options have the same value as
65% of 20?
Choose 2 answers:

Answer 1

Answer:

A) 0.65 · 20

D) $\mathsf{\dfrac{65}{100} \cdot 20}$

Step-by-step explanation:

To find 65% of 20:

Method 1

65% in decimal form is:  65% = 65/100 = 0.65

Therefore, to find a percentage of a number, multiply the percentage in decimal form by the number:

$\mathsf{\implies 65\% \ of \ 20 = 0.65 \cdot 20}$

Method 2

Divide the number by 100 to get 1%, then multiply this by 20 to get 20%.

$\mathsf{\implies \dfrac{65}{100} \cdot 20}$

Answer 2

Solution:

Step-1: Find the expression of 65% of 20

• Given sentence: 65% of 20

~The word "of" stands for multiplication.~

• 65/100 × 20                                                                     [65% = 65/100]

Step-2: Verify all the options

Option A) 0.65 × 20

~0.65 can be converted to fraction, which is 65/100.~

• ⇒ 65/100 × 20 = 65/100 × 20                                        [0.65 = 65/100]

~This expression correctly matches with the resulting expression.~

Thus, option A is correct.

Option B) 65/100 ÷ 20

• ⇒ 65/100 ÷ 20 = 65/100 × 20        

This could've been equivalent to the resulting expression. However, the expression has a division sign.

Thus, Option B is incorrect.

Option C) 65/20 × 100

~To avoid confusion, let's further solve the expression.~

• 65/20 × 100
• ⇒ 65/1 × 5
• ⇒ 325

~Now, let's solve the resulting expression.~

• 65/100 × 20
• ⇒ 65/100 × 20
• ⇒ 65/5 × 1
• ⇒ 13

~Since 13 does not equal 325, "65/20 × 100" does not equal "65/100 × 20".~

Thus, option C is incorrect.

Option D) 65/100 × 20

~This equation is the resulting equation.~

Thus, option D is correct.

Option E) 65 × 20

~To avoid confusion, let's further solve the expression.~

• 65 × 20
• ⇒ 650 × 2
• ⇒ 1300

~Now, let's solve the resulting expression.~

• 65/100 × 20
• ⇒ 65/100 × 20
• ⇒ 65/5 × 1
• ⇒ 13

Since 1300 does not equal 13, 65 × 20 does not equal 65/100 × 20.

Thus, option E is incorrect.

Step-3: Make a conclusion

Option A and D were equivalent to 65/100 × 20.