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:
Let’s simplify and convert each of the given fractions into their lowest terms, decimal form, and percent form:
1. Fraction: 6/12
- Lowest terms:
The greatest common divisor (GCD) of 6 and 12 is 6.
6 divided by 6 = 1
12 divided by 6 = 2
Lowest terms: 1/2 - Decimal:
1 ÷ 2 = 0.5 - Percent:
0.5 × 100 = 50%
2. Mixed Number: 2 6/8
- Step 1: Simplify the fractional part 6/8
GCD of 6 and 8 is 2
6 divided by 2 = 3
8 divided by 2 = 4
So, 6/8 simplifies to 3/4 - Lowest terms:
2 6/8 = 2 3/4 (which is simplified) - Decimal:
3 divided by 4 = 0.75
So, 2 + 0.75 = 2.75 - Percent:
2.75 × 100 = 275%
3. Fraction: 10/16
- Lowest terms:
GCD of 10 and 16 is 2
10 divided by 2 = 5
16 divided by 2 = 8
Lowest terms: 5/8 - Decimal:
5 ÷ 8 = 0.625 - Percent:
0.625 × 100 = 62.5%
300-word Explanation
Understanding how to simplify and convert fractions into decimals and percentages is essential for solving everyday math problems. It helps compare values, interpret data, and make decisions. We begin by simplifying the fractions using the greatest common divisor (GCD), which is the largest number that divides both the numerator and denominator without leaving a remainder.
For 6/12, both numbers are divisible by 6, giving us 1/2. This is its simplest form. When we divide 1 by 2, we get 0.5. Multiplying the decimal by 100 converts it to a percentage: 50%.
In the case of mixed numbers like 2 6/8, we simplify the fraction part first. The GCD of 6 and 8 is 2, so 6/8 becomes 3/4. That makes the mixed number 2 3/4. To find the decimal, we convert 3/4 to 0.75 and add it to 2, resulting in 2.75. Multiplying 2.75 by 100 gives 275%.
For 10/16, we divide both the numerator and denominator by 2, simplifying it to 5/8. Converting 5/8 to decimal form gives 0.625. As a percent, that’s 62.5%.
This process of simplification and conversion makes numerical data easier to compare and understand, especially when interpreting results in school, business, and real-life decisions.
