Multiply. Write your answer in simplest form.
$\frac{3}{8} \times \frac{5}{7}$
Answer (2)
To multiply 8 3 and 7 5 , we multiply the numerators to get 15 and the denominators to get 56, resulting in 56 15 . This fraction is already in simplest form. Therefore, the answer is 56 15 .
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Multiply the numerators: 3 × 5 = 15 .
Multiply the denominators: 8 × 7 = 56 .
The resulting fraction is 56 15 .
The fraction 56 15 is in simplest form: 56 15 .
Explanation
Problem Analysis We are asked to multiply two fractions, 8 3 and 7 5 , and express the result in simplest form.
Multiplying Fractions To multiply fractions, we multiply the numerators together and the denominators together. So, we have: 8 3 × 7 5 = 8 × 7 3 × 5
Calculating Numerator and Denominator Now, we calculate the numerator and the denominator: 3 × 5 = 15 8 × 7 = 56 So, the fraction becomes: 56 15
Checking for Simplification To check if the fraction can be simplified, we need to find the greatest common divisor (GCD) of the numerator and the denominator. The factors of 15 are 1, 3, 5, and 15. The factors of 56 are 1, 2, 4, 7, 8, 14, 28, and 56. The only common factor is 1, so the GCD of 15 and 56 is 1.
Final Answer Since the GCD of the numerator and the denominator is 1, the fraction is already in its simplest form. Therefore, the answer is 56 15 .
Examples
In baking, if a recipe calls for 8 3 of a cup of flour and you only want to make 7 5 of the recipe, you would multiply these fractions to determine how much flour you need. The calculation 8 3 × 7 5 = 56 15 tells you that you need 56 15 of a cup of flour.
