Reduce the fraction [tex]$36 / 48$[/tex] to its lowest terms.
Answer (2)
Find the greatest common divisor (GCD) of 36 and 48, which is 12.
Divide both the numerator and the denominator by the GCD: 48 ÷ 12 36 ÷ 12 .
Simplify the fraction: 4 3 .
The reduced fraction is 4 3 .
Explanation
Problem Analysis We are asked to reduce the fraction 48 36 to its lowest terms. This means we need to find the greatest common divisor (GCD) of 36 and 48, and then divide both the numerator and the denominator by their GCD.
Finding the GCD To find the GCD of 36 and 48, we can list the factors of each number: Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36 Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 The common factors are: 1, 2, 3, 4, 6, 12. The greatest common factor is 12.
Dividing by the GCD Now, we divide both the numerator and the denominator by the GCD, which is 12: 12 36 = 3 12 48 = 4
Final Result So, the reduced fraction is 4 3 .
Examples
Reducing fractions is a fundamental skill with many practical applications. For example, if you are baking and a recipe calls for 48 36 of a cup of flour, you can simplify this to 4 3 of a cup, making it easier to measure. Similarly, in construction or engineering, simplifying fractions can help in calculating dimensions and proportions accurately.
To reduce the fraction 48 36 , we find the greatest common divisor (GCD), which is 12. Dividing both the numerator and denominator by the GCD gives us the simplified fraction 4 3 . Therefore, the reduced fraction is 4 3 .
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