Question

The reciprocal of a fraction is its "flipped" counterpart--the denominator of one is the numerator of the other, and vice versa. The reciprocal of 2 ⁄ 3 is 3 ⁄ 2, and the reciprocal of 5 ⁄ 6 is 6 ⁄ 5. Dividing by a fraction and multiplying by that fraction's reciprocal will always give you the same thing. 7 ÷ ________ = 7 × 11/13

Answer 1

To solve the equation 7 ÷ ________ = 7 × 11/13, you must fill in the blank with the reciprocal of 11/13, which is 13/11. This is because dividing by a fraction is equivalent to multiplying by its reciprocal.

Step-by-step explanation:

The question asks what fraction should be filled in the blank so that the statement 7 ÷ ________ = 7 × 11/13 is true. The operation on the right side of the equation is multiplication by the fraction 11/13. To maintain balance, the left side must involve the reciprocal of 11/13, because dividing by a fraction is the same as multiplying by its reciprocal. Hence, the blank should be filled with the reciprocal of 11/13, which is 13/11.

Step-by-Step Explanation

1. To find the reciprocal of a fraction, simply flip the numerator and denominator.
2. The reciprocal of 11/13 is therefore 13/11.
3. To verify, we multiply 7 by 11/13 and divide 7 by 13/11 and confirm they yield the same result.

Multiplication and division by fractions can be understood by remembering that these operations are linked: dividing by a fraction is equivalent to multiplying by its reciprocal. It's similar to how dividing by 8 is akin to multiplying by 1/8, and multiplying by 1/2 is the same as dividing by 2, but with fractions involved instead.