Multiply. Write your answer in simplest form.
$\frac{5}{12} \times \frac{4}{5}$
Answer (2)
To multiply 12 5 by 5 4 , first multiply the numerators to get 20 and the denominators to get 60, resulting in 60 20 . Simplifying 60 20 gives 3 1 as the final answer. Thus, 12 5 × 5 4 = 3 1 .
;
Multiply the numerators and denominators: 12 5 × 5 4 = 12 × 5 5 × 4 = 60 20 .
Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 20: 60 20 = 60 ÷ 20 20 ÷ 20 = 3 1 .
Alternatively, cancel the common factor 5 from the numerator and denominator before multiplying: 12 5 × 5 4 = 12 1 × 4 = 12 4 .
Simplify the resulting fraction 12 4 by dividing both the numerator and denominator by their GCD, which is 4: 12 4 = 12 ÷ 4 4 ÷ 4 = 3 1 . The final answer is 3 1 .
Explanation
Understanding the Problem We are asked to multiply two fractions, 12 5 and 5 4 , and simplify the result.
Multiplying Numerators and Denominators To multiply fractions, we multiply the numerators together and the denominators together: 12 5 × 5 4 = 12 × 5 5 × 4 = 60 20
Simplifying the Fraction Now we simplify the fraction 60 20 by finding the greatest common divisor (GCD) of the numerator and the denominator. The GCD of 20 and 60 is 20. We divide both the numerator and the denominator by 20: 60 20 = 60 ÷ 20 20 ÷ 20 = 3 1 Alternatively, we can cancel common factors before multiplying: 12 5 × 5 4 = 12 5 × 5 4 = 12 1 × 4 = 12 4 = 12 ÷ 4 4 ÷ 4 = 3 1
Final Answer The simplified form of the product is 3 1 .
Examples
Fractions are used in everyday life, such as when baking a cake. If a recipe calls for 12 5 of a cup of flour and you only want to make 5 4 of the recipe, you would multiply 12 5 × 5 4 to find out how much flour you need. This calculation shows that you would need 3 1 of a cup of flour.
