Reduce each fraction to simplest form/lowest term. Show your solution in the space provided. 10/20, 12/26
The Correct Answer and Explanation is:
To reduce the fractions 10/20 and 12/26 to their simplest form, we will follow these steps:
1. Simplifying 10/20:
- Step 1: Identify the greatest common divisor (GCD) of the numerator and denominator.
- The factors of 10 are 1, 2, 5, and 10.
- The factors of 20 are 1, 2, 4, 5, 10, and 20.
- The greatest common factor between 10 and 20 is 10.
- Step 2: Divide both the numerator and the denominator by their GCD.
- 1020=10÷1020÷10=12\frac{10}{20} = \frac{10 \div 10}{20 \div 10} = \frac{1}{2}2010=20÷1010÷10=21
Thus, 10/20 simplifies to 1/2.
2. Simplifying 12/26:
- Step 1: Identify the greatest common divisor (GCD) of the numerator and denominator.
- The factors of 12 are 1, 2, 3, 4, 6, and 12.
- The factors of 26 are 1, 2, 13, and 26.
- The greatest common factor between 12 and 26 is 2.
- Step 2: Divide both the numerator and the denominator by their GCD.
- 1226=12÷226÷2=613\frac{12}{26} = \frac{12 \div 2}{26 \div 2} = \frac{6}{13}2612=26÷212÷2=136
Thus, 12/26 simplifies to 6/13.
Summary:
- The simplified form of 10/20 is 1/2.
- The simplified form of 12/26 is 6/13.
To reduce a fraction, you always find the greatest common divisor of the numerator and denominator and divide both by it. The process ensures that the fraction is expressed in its simplest or lowest terms.
