What is $12 / 16$ reduced to its lowest terms?
A. $5 / 8$
B. $8 / 12$
C. $3 / 4$
D. $12 / 8$
Answer (2)
Find the greatest common divisor (GCD) of 12 and 16, which is 4.
Divide both the numerator and the denominator of the fraction 16 12 by the GCD: 16 ÷ 4 12 ÷ 4 .
Simplify the fraction: 4 3 .
The fraction 16 12 reduced to its lowest terms is 4 3 .
Explanation
Understanding the Problem We need to reduce the fraction 16 12 to its lowest terms. This means we need to find the greatest common divisor (GCD) of 12 and 16 and then divide both the numerator and the denominator by their GCD.
Finding the Greatest Common Divisor (GCD) To find the GCD of 12 and 16, we can list the factors of each number: Factors of 12: 1, 2, 3, 4, 6, 12 Factors of 16: 1, 2, 4, 8, 16 The greatest common factor is 4.
Reducing the Fraction Now, we divide both the numerator and the denominator of the fraction 16 12 by their GCD, which is 4: 16 ÷ 4 12 ÷ 4 = 4 3
Final Result So, the fraction 16 12 reduced to its lowest terms is 4 3 .
Examples
Imagine you're baking a cake and the recipe calls for 16 12 of a cup of flour. To simplify the measurement, you reduce the fraction to its simplest form, which is 4 3 of a cup. This makes it easier to measure and ensures the cake turns out perfectly. Reducing fractions is useful in many real-life situations, from cooking to construction, where precise measurements are essential.
The fraction 16 12 reduced to its lowest terms is 4 3 , so the correct answer is C . By finding the greatest common divisor (GCD) of 12 and 16, which is 4, we divide both the numerator and denominator by this number to simplify the fraction. This process makes the fraction easier to work with and understand.
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