Convert the fractions into equivalent lowest term fraction, decimal number, and percent. 6/12, 2 6/8, 10/16
The Correct Answer and Explanation is:
Here are the simplified forms, decimal equivalents, and percentages for each of the given fractions:
1. 6/12
- Lowest Term Fraction: 1/2
- Decimal: 0.5
- Percent: 50%
2. 2 6/8
- Lowest Term Fraction: 2 3/4
- Decimal: 2.75
- Percent: 275%
3. 10/16
- Lowest Term Fraction: 5/8
- Decimal: 0.625
- Percent: 62.5%
Explanation
Fractions, decimals, and percentages are different ways of representing the same value. To convert fractions to their lowest terms, we divide both the numerator and the denominator by their greatest common divisor (GCD). This process reduces the fraction to its simplest form.
Let’s break it down:
1. 6/12
The GCD of 6 and 12 is 6. Divide both by 6:
6 ÷ 6 = 1, 12 ÷ 6 = 2, so 6/12 simplifies to 1/2.
To convert 1/2 to a decimal, divide 1 by 2 = 0.5.
To convert to a percent, multiply the decimal by 100: 0.5 × 100 = 50%.
2. 2 6/8
First, simplify the fraction part 6/8. The GCD of 6 and 8 is 2.
6 ÷ 2 = 3, 8 ÷ 2 = 4, so 6/8 becomes 3/4.
So, 2 6/8 becomes 2 3/4.
Convert 3/4 to decimal: 3 ÷ 4 = 0.75.
Add it to the whole number: 2 + 0.75 = 2.75.
Convert to percent: 2.75 × 100 = 275%.
3. 10/16
The GCD of 10 and 16 is 2. Divide both by 2:
10 ÷ 2 = 5, 16 ÷ 2 = 8, so 10/16 becomes 5/8.
Convert 5 ÷ 8 = 0.625.
Convert to percent: 0.625 × 100 = 62.5%.
Understanding how to convert between these forms improves number sense and is essential in math, science, and everyday life such as shopping, measuring, or budgeting.
