Final answer:
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
- To find the reciprocal of a fraction, simply flip the numerator and denominator.
- The reciprocal of 11/13 is therefore 13/11.
- 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.