$\frac{5}{8} \times \frac{14}{15}$
Answer (2)
Multiply the numerators and denominators: 8 5 × 15 14 = 8 × 15 5 × 14 = 120 70 .
Find the greatest common divisor (GCD) of 70 and 120, which is 10.
Divide both the numerator and the denominator by the GCD: 120 ÷ 10 70 ÷ 10 = 12 7 .
The simplified fraction is 12 7 .
Explanation
Problem Analysis We are asked to compute the product of two fractions: 8 5 × 15 14 . To do this, we multiply the numerators and the denominators.
Multiplying Numerators and Denominators First, multiply the numerators: 5 × 14 = 70 . Then, multiply the denominators: 8 × 15 = 120 . So, we have 8 5 × 15 14 = 120 70 .
Finding the Greatest Common Divisor (GCD) Now, we simplify the fraction 120 70 by finding the greatest common divisor (GCD) of 70 and 120. The prime factorization of 70 is 2 × 5 × 7 , and the prime factorization of 120 is 2 3 × 3 × 5 . The GCD is 2 × 5 = 10 .
Simplifying the Fraction Divide both the numerator and the denominator by the GCD: 120 ÷ 10 70 ÷ 10 = 12 7 . Therefore, 8 5 × 15 14 = 12 7 .
Final Answer Thus, the simplified form of the expression is 12 7 .
Examples
Fractions are used in everyday life, such as when cooking, measuring ingredients, or splitting a pizza. For example, if you have 8 5 of a pizza and you eat 15 14 of that portion, you have eaten 12 7 of the whole pizza. Understanding how to multiply fractions is essential for these types of calculations.
To multiply the fractions 8 5 and 15 14 , you first multiply the numerators to get 70 and the denominators to get 120, leading to 120 70 . This fraction can then be simplified to 12 7 by dividing both the numerator and the denominator by their greatest common divisor, which is 10. Therefore, the final answer is 12 7 .
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