Find the product
$\frac{3}{20} \times \frac{4}{12}$
Enter your simplified answer.
Answer (2)
Multiply the numerators and denominators: 20 3 × 12 4 = 240 12 .
Find the greatest common divisor (GCD) of 12 and 240, which is 12.
Divide both the numerator and the denominator by the GCD: 240 ÷ 12 12 ÷ 12 = 20 1 .
The simplified product is 20 1 .
Explanation
Understanding the Problem We are asked to find the product of two fractions, 20 3 and 12 4 , and simplify the result.
Multiplying the Fractions First, we multiply the numerators and the denominators: 20 3 × 12 4 = 20 × 12 3 × 4 = 240 12
Finding the Greatest Common Divisor Now, we simplify the fraction 240 12 by finding the greatest common divisor (GCD) of the numerator and the denominator. The GCD of 12 and 240 is 12.
Simplifying the Fraction We divide both the numerator and the denominator by their GCD: 240 12 = 240 ÷ 12 12 ÷ 12 = 20 1
Final Answer Therefore, the simplified product of the two fractions is 20 1 .
Examples
Fractions are used in everyday life, such as when calculating proportions in recipes, determining discounts while shopping, or understanding probabilities. For example, if a recipe calls for 4 1 cup of sugar and you want to make half the recipe, you need to calculate 2 1 × 4 1 = 8 1 cup of sugar. Understanding how to multiply and simplify fractions is essential for accurate measurements and calculations in various real-world scenarios.
The product of 20 3 and 12 4 is calculated by first multiplying them to get 240 12 . This fraction is simplified by dividing the numerator and denominator by their greatest common divisor, which is 12, resulting in 20 1 .
;
