$\frac{5}{8} \times \frac{14}{15}$
Answer (2)
Multiply the numerators and denominators: 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, then simplify the resulting fraction.
Multiplying Fractions First, multiply the numerators and denominators: 8 5 × 15 14 = 8 × 15 5 × 14 = 120 70 .
Finding the GCD Now, we simplify the fraction 120 70 by finding the greatest common divisor (GCD) of 70 and 120. We can factorize both numbers: 70 = 2 × 5 × 7 120 = 2 × 2 × 2 × 3 × 5 = 2 3 × 3 × 5 The GCD of 70 and 120 is 2 × 5 = 10 .
Simplifying the Fraction Divide both the numerator and the denominator by their GCD, which is 10: 120 70 = 120 ÷ 10 70 ÷ 10 = 12 7 .
Final Result Therefore, the simplified fraction is 12 7 .
Examples
In baking, if a recipe calls for 8 5 of a cup of flour and you only want to make 15 14 of the recipe, you would multiply these fractions to find out how much flour you need. The result, 12 7 of a cup, tells you the adjusted amount of flour for the reduced recipe. This kind of calculation is essential for scaling recipes up or down.
The product of 8 5 and 15 14 simplifies to 12 7 after multiplying the numerators and denominators and reducing the fraction. The GCD of 70 and 120 is 10, which helps us simplify the fraction. Thus, the solution to the multiplication of the two fractions is 12 7 .
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