Reduce this fraction to its simplest form: [tex]$\frac{40}{48}=?$\ [/tex]
Answer (2)
Find the greatest common divisor (GCD) of 40 and 48, which is 8.
Divide both the numerator and the denominator by the GCD: 48 ÷ 8 40 ÷ 8 .
Simplify the fraction: 6 5 .
The simplest form of the fraction is 6 5 .
Explanation
Problem Analysis We are asked to reduce the fraction 48 40 to its simplest form. This means we need to find the greatest common divisor (GCD) of the numerator (40) and the denominator (48) and then divide both by their GCD.
Finding the GCD To find the GCD of 40 and 48, we can use prime factorization. The prime factorization of 40 is 2 3 × 5 , and the prime factorization of 48 is 2 4 × 3 . The GCD is the product of the common prime factors raised to the lowest power, which is 2 3 = 8 .
Reducing the Fraction Now, we divide both the numerator and the denominator by the GCD, which is 8: 48 ÷ 8 40 ÷ 8 = 6 5 .
Final Answer The simplified fraction is 6 5 .
Examples
Fractions are used in everyday life, such as when cooking, baking, or measuring ingredients. For example, if a recipe calls for 48 40 of a cup of flour, you can simplify this fraction to 6 5 of a cup to make measuring easier. Understanding how to simplify fractions helps in accurately following recipes and adjusting quantities as needed. This ensures that the proportions of ingredients remain consistent, leading to better cooking and baking outcomes.
To simplify the fraction 48 40 , find the greatest common divisor, which is 8. Dividing both the numerator and the denominator by 8 gives 6 5 . Therefore, the simplest form is 6 5 .
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