Question

1. what is 2% of 9? select all the expressions that apply.

a. \\(\frac{2}{100} \times 9\\)
b. \\(\frac{2}{10} \times 9\\)
c. \\(0.02 \times 9\\)
d. \\(0.2 \times 9\\)
e. \\(0.002 \times 9\\)
problems 9–10: maria needs to calculate 20% of 90. she sets up the expression as \\(\frac{1}{5} \cdot 90\\)

1. is her expression correct? explain your thinking.
2. what is 20% of 90?

a. 15
b. 16
c. 17
d. 18

Explanation:

Question 8

To determine which expressions represent 2% of 9, we recall that "percent" means "per hundred," so 2% can be written as a fraction \(\frac{2}{100}\) or as a decimal \(0.02\). To find a percentage of a number, we multiply the percentage (in fraction or decimal form) by the number.

Step 1: Analyze Option A

2% is \(\frac{2}{100}\), so "2% of 9" is \(\frac{2}{100} \times 9\). This matches the formula for finding a percentage of a number. So A is correct.

Step 2: Analyze Option B

\(\frac{2}{10}\) is 20% (not 2%), so \(\frac{2}{10} \times 9\) represents 20% of 9, not 2% of 9. So B is incorrect.

Step 3: Analyze Option C

2% as a decimal is \(0.02\) (since \(\frac{2}{100} = 0.02\)). Thus, "2% of 9" is \(0.02 \times 9\). This matches the formula. So C is correct.

Step 4: Analyze Option D

\(0.002\) is 0.2% (since \(\frac{0.2}{100} = 0.002\)), so \(0.002 \times 9\) represents 0.2% of 9, not 2% of 9. So D is incorrect.

Thus, the correct options are A and C.

Question 9

Maria needs to calculate 20% of 90. She sets up the expression as \(\frac{1}{5} \times 90\).

To check if this is correct:

• Recall that 20% as a fraction: \(20\% = \frac{20}{100} = \frac{1}{5}\) (since \(\frac{20 \div 20}{100 \div 20} = \frac{1}{5}\)).
• To find a percentage of a number, we multiply the percentage (as a fraction or decimal) by the number. So 20% of 90 is \(\frac{20}{100} \times 90\) or \(\frac{1}{5} \times 90\).

Thus, Maria’s expression is correct because 20% is equivalent to \(\frac{1}{5}\), and "of" in mathematics means multiplication. So \(\frac{1}{5} \times 90\) correctly represents 20% of 90.

Question 10

To find 20% of 90:

Step 1: Convert 20% to a fraction or decimal

• As a fraction: \(20\% = \frac{20}{100} = \frac{1}{5}\).
• As a decimal: \(20\% = 0.2\).

Step 2: Multiply by 90

Using the fraction: \(\frac{1}{5} \times 90 = \frac{90}{5} = 18\).
Using the decimal: \(0.2 \times 90 = 18\).

Thus, 20% of 90 is 18, so the correct option is D.

Answer:

Question 8

To determine which expressions represent 2% of 9, we recall that "percent" means "per hundred," so 2% can be written as a fraction \(\frac{2}{100}\) or as a decimal \(0.02\). To find a percentage of a number, we multiply the percentage (in fraction or decimal form) by the number.

Step 1: Analyze Option A

2% is \(\frac{2}{100}\), so "2% of 9" is \(\frac{2}{100} \times 9\). This matches the formula for finding a percentage of a number. So A is correct.

Step 2: Analyze Option B

\(\frac{2}{10}\) is 20% (not 2%), so \(\frac{2}{10} \times 9\) represents 20% of 9, not 2% of 9. So B is incorrect.

Step 3: Analyze Option C

2% as a decimal is \(0.02\) (since \(\frac{2}{100} = 0.02\)). Thus, "2% of 9" is \(0.02 \times 9\). This matches the formula. So C is correct.

Step 4: Analyze Option D

\(0.002\) is 0.2% (since \(\frac{0.2}{100} = 0.002\)), so \(0.002 \times 9\) represents 0.2% of 9, not 2% of 9. So D is incorrect.

Thus, the correct options are A and C.

Question 9

Maria needs to calculate 20% of 90. She sets up the expression as \(\frac{1}{5} \times 90\).

To check if this is correct:

• Recall that 20% as a fraction: \(20\% = \frac{20}{100} = \frac{1}{5}\) (since \(\frac{20 \div 20}{100 \div 20} = \frac{1}{5}\)).
• To find a percentage of a number, we multiply the percentage (as a fraction or decimal) by the number. So 20% of 90 is \(\frac{20}{100} \times 90\) or \(\frac{1}{5} \times 90\).

Thus, Maria’s expression is correct because 20% is equivalent to \(\frac{1}{5}\), and "of" in mathematics means multiplication. So \(\frac{1}{5} \times 90\) correctly represents 20% of 90.

Question 10

To find 20% of 90:

Step 1: Convert 20% to a fraction or decimal

• As a fraction: \(20\% = \frac{20}{100} = \frac{1}{5}\).
• As a decimal: \(20\% = 0.2\).

Step 2: Multiply by 90

Using the fraction: \(\frac{1}{5} \times 90 = \frac{90}{5} = 18\).
Using the decimal: \(0.2 \times 90 = 18\).

Thus, 20% of 90 is 18, so the correct option is D.