Calculate $\frac{5}{8} \times \frac{4}{15}$. Give your answer in its simplest form.
Answer (2)
The product of 8 5 and 15 4 is 120 20 , which simplifies to 6 1 . By multiplying the numerators and denominators, we arrive at the final simplified form. This process involves finding the greatest common divisor and dividing both parts accordingly.
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Multiply the numerators and denominators: 8 5 × 15 4 = 8 × 15 5 × 4 = 120 20 .
Find the greatest common divisor (GCD) of 20 and 120, which is 20.
Divide both the numerator and the denominator by the GCD: 120 ÷ 20 20 ÷ 20 = 6 1 .
The simplified fraction is 6 1 .
Explanation
Problem Analysis We need to calculate the product of two fractions, 8 5 and 15 4 , and express the result in its simplest form.
Multiplying Numerators and Denominators To multiply fractions, we multiply the numerators together and the denominators together: 8 5 × 15 4 = 8 × 15 5 × 4 = 120 20
Finding the Greatest Common Divisor (GCD) Now, we simplify the fraction 120 20 by finding the greatest common divisor (GCD) of the numerator and the denominator. The GCD of 20 and 120 is 20.
Simplifying the Fraction Divide both the numerator and the denominator by their GCD: 120 20 = 120 ÷ 20 20 ÷ 20 = 6 1
Final Answer The simplified fraction is 6 1 .
Examples
Fractions are used in everyday life, such as when cooking, measuring ingredients, or splitting a bill with friends. For example, if you have a pizza that is cut into 8 slices and you eat 5 of those slices, you have eaten 8 5 of the pizza. If you then give 15 4 of your remaining pizza to a friend, you need to calculate 8 5 × 15 4 to determine how much of the whole pizza your friend received, which in this case is 6 1 of the whole pizza.
