Find the product
$\frac{5}{24} \times \frac{3}{10}$
Enter your simplified answer.
Answer (2)
Multiply the numerators and denominators: 24 5 × 10 3 = 24 × 10 5 × 3 = 240 15 .
Find the greatest common divisor (GCD) of 15 and 240, which is 15.
Divide both the numerator and the denominator by the GCD: 240 ÷ 15 15 ÷ 15 = 16 1 .
The simplified product is 16 1 .
Explanation
Understanding the Problem We are asked to find the product of two fractions, 24 5 and 10 3 , and simplify the result.
Multiplying the Fractions To multiply fractions, we multiply the numerators together and the denominators together: 24 5 × 10 3 = 24 × 10 5 × 3 = 240 15
Simplifying the Fraction Now we need to simplify the fraction 240 15 . We can do this by finding the greatest common divisor (GCD) of 15 and 240 and dividing both the numerator and the denominator by the GCD. The GCD of 15 and 240 is 15.
Dividing by the GCD Dividing both the numerator and the denominator by 15, we get: 240 15 = 240 ÷ 15 15 ÷ 15 = 16 1
Final Answer Therefore, the simplified product of the two fractions is 16 1 .
Examples
Fractions are used in everyday life, such as when cooking, baking, or measuring ingredients. For example, if a recipe calls for 24 5 of a cup of flour and you only want to make 10 3 of the recipe, you would need to calculate 24 5 × 10 3 to determine how much flour to use. This problem demonstrates how to multiply and simplify fractions, which is a useful skill in many real-world situations.
The product of the fractions 24 5 and 10 3 is 240 15 , which simplifies to 16 1 .
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