Find the percent 33 1/3% of 180 = ? 66 2/3% of 630 = ?
The correct answer and explanation is:
Correct Answers:
- 33 1/3% of 180 = 60
- 66 2/3% of 630 = 420
Explanation:
To find a percent of a number, convert the percentage into a fraction or a decimal, then multiply by the number.
1. 33 1/3% of 180
Step 1: Convert 33 1/3% to a fraction.
33 1/3% = one-third = 1/3
Step 2: Multiply this fraction by 180
(1/3) × 180 = 60
So, 33 1/3% of 180 is 60.
2. 66 2/3% of 630
Step 1: Convert 66 2/3% to a fraction.
66 2/3% = two-thirds = 2/3
Step 2: Multiply this fraction by 630
(2/3) × 630 = 420
So, 66 2/3% of 630 is 420.
Understanding the Concept
Percent means “per hundred.” When a percent includes a fraction like 1/3 or 2/3, it often helps to convert it into a simpler fraction instead of a decimal to avoid long division or rounding.
For example:
- 33 1/3% is one-third of 100, which is written as 1/3.
- 66 2/3% is two-thirds of 100, written as 2/3.
Multiplying a number by a fraction means finding that part of the whole. For instance, one-third of 180 means splitting 180 into 3 equal parts, each being 60. Similarly, two-thirds of 630 means dividing 630 by 3 to get 210, then multiplying by 2 to get 420.
This method is often faster and more accurate, especially when the percentage is a repeating decimal. It helps students build number sense and confidence in mental math.