Find the answer when 6/13 is multiplied by the reciprocal of 12/5.

To solve the problem, we need to find the product of 6/13 and the reciprocal of 12/5. Let's break it down step by step:

Understand the reciprocal of 12/5: The reciprocal of a fraction is obtained by swapping its numerator and denominator. Therefore, the reciprocal of 12/5 is 5/12.

Multiply 6/13 by 5/12: To multiply two fractions, multiply their numerators and denominators: Numerator: 6 × 5 = 30
Denominator: 13 × 12 = 156

So, the product is 30/156.

Simplify the fraction 30/156: Find the greatest common divisor (GCD) of 30 and 156, which is 6.
Divide both the numerator and denominator by their GCD:
30 ÷ 6 = 5
156 ÷ 6 = 26

Therefore, 30/156 simplifies to 5/26.

Final Answer: 5/26