Find the product
$\frac{5}{6} \times \frac{12}{15}$
Enter your simplified answer.
Answer (2)
Multiply the numerators and denominators: 6 5 × 15 12 = 6 × 15 5 × 12 = 90 60 .
Find the greatest common divisor (GCD) of 60 and 90, which is 30.
Divide both the numerator and the denominator by the GCD: 90 60 = 90 ÷ 30 60 ÷ 30 = 3 2 .
The simplified answer is 3 2 .
Explanation
Understanding the Problem We are asked to find the product of two fractions, 6 5 and 15 12 , and simplify the result.
Multiplying the Fractions To multiply fractions, we multiply the numerators together and the denominators together: 6 5 × 15 12 = 6 × 15 5 × 12 = 90 60 .
Simplifying the Fraction Now we simplify the fraction 90 60 by finding the greatest common divisor (GCD) of 60 and 90. The GCD of 60 and 90 is 30. We divide both the numerator and the denominator by 30: 90 60 = 90 ÷ 30 60 ÷ 30 = 3 2 . Alternatively, we can simplify before multiplying by canceling common factors. Notice that 12 = 2 × 6 and 15 = 3 × 5 . Thus, we can rewrite the fraction as 6 × 15 5 × 12 = 6 × ( 3 × 5 ) 5 × ( 2 × 6 ) = 6 × 3 × 5 5 × 2 × 6 . Now, we cancel out the common factors 5 and 6: 6 × 3 × 5 5 × 2 × 6 = 3 2 .
Final Answer The simplified product of the two fractions is 3 2 .
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 6 slices and you eat 5 of those slices, you have eaten 6 5 of the pizza. If you then share 2 1 of your portion with a friend, you are giving them 2 1 × 6 5 = 12 5 of the whole pizza. Understanding how to multiply and simplify fractions is essential for many real-world applications.
The product of the fractions 6 5 and 15 12 is 90 60 , which simplifies to 3 2 . This simplification is achieved by finding the greatest common divisor and dividing both the numerator and the denominator accordingly. Another method involves canceling common factors before multiplying for a quicker result.
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