Reduce this fraction to its simplest form: [tex]$\frac{16}{24}=?$\tex]
Answer (2)
Find the greatest common divisor (GCD) of the numerator and the denominator. In this case, GCD(16, 24) = 8.
Divide both the numerator and the denominator by the GCD: 24 ÷ 8 16 ÷ 8 = 3 2 .
The simplified fraction is 3 2 .
Therefore, the simplest form of the fraction is 3 2 .
Explanation
Problem Analysis We are asked to reduce the fraction 24 16 to its simplest form. This means we need to find a common factor of both the numerator (16) and the denominator (24) and divide both by that factor. Ideally, we want to find the greatest common divisor (GCD) to simplify the fraction in one step.
Finding the Greatest Common Divisor (GCD) To find the greatest common divisor (GCD) of 16 and 24, we can list the factors of each number:
Factors of 16: 1, 2, 4, 8, 16 Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
The common factors are 1, 2, 4, and 8. The greatest of these is 8. Therefore, the GCD(16, 24) = 8. Alternatively, we can use the Euclidean algorithm to find the GCD. The result of this operation is 8.
Simplifying the Fraction Now, we divide both the numerator and the denominator by their GCD, which is 8:
8 16 = 2 8 24 = 3
So, the simplified fraction is 3 2 .
Final Answer Therefore, the simplest form of the fraction 24 16 is 3 2 .
Examples
Imagine you're baking a cake and the recipe calls for 24 16 of a cup of flour. To make it easier to measure, you simplify the fraction to 3 2 of a cup. This way, you're using the same proportion of ingredients but with simpler numbers, making your baking experience smoother and more intuitive. Simplifying fractions is a practical skill that helps in everyday tasks like cooking, measuring, and understanding proportions.
To simplify the fraction 24 16 , we find that the greatest common divisor is 8. Dividing the numerator and denominator by 8 results in 3 2 . Therefore, the simplest form of the fraction is 3 2 .
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