What's the fraction $18 / 24$ reduced to its lowest terms?
Answer (2)
Find the greatest common divisor (GCD) of 18 and 24, which is 6.
Divide both the numerator and the denominator by the GCD: 24 ÷ 6 18 ÷ 6 .
Simplify the fraction: 4 3 .
The fraction 24 18 reduced to its lowest terms is 4 3 .
Explanation
Problem Analysis We are asked to reduce the fraction 24 18 to its lowest terms. This means we need to find the greatest common divisor (GCD) of 18 and 24 and then divide both the numerator and the denominator by their GCD.
Finding the GCD To find the greatest common divisor (GCD) of 18 and 24, we can list the factors of each number:
Factors of 18: 1, 2, 3, 6, 9, 18 Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
The common factors are 1, 2, 3, and 6. The greatest of these is 6. Therefore, the GCD of 18 and 24 is 6.
Euclidean Algorithm Alternatively, we can use the Euclidean algorithm to find the GCD of 18 and 24:
24 = 1 × 18 + 6 18 = 3 × 6 + 0
The last non-zero remainder is 6, so the GCD of 18 and 24 is 6.
Reducing the Fraction Now, we divide both the numerator and the denominator of the fraction 24 18 by their GCD, which is 6:
24 ÷ 6 18 ÷ 6 = 4 3
Final Answer Therefore, the fraction 24 18 reduced to its lowest terms is 4 3 .
Examples
Reducing fractions is a fundamental skill with many practical applications. For instance, when baking, you might need to adjust a recipe that calls for 24 18 of a cup of flour. Simplifying this fraction to 4 3 makes it easier to measure and ensures the recipe turns out correctly. This skill is also useful in everyday situations like splitting a pizza fairly or understanding proportions in various contexts.
The fraction 24 18 can be reduced by finding the greatest common divisor, which is 6. Dividing both the numerator and denominator by this GCD gives us 4 3 . Thus, the reduced form of the fraction is 4 3 .
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