Unit 4, Lesson 11
Using an Algorithm to Divide Fractions
Grade 6
Student Lesson Summary
We can think of the division in terms of finding the size of 1 group: “If there is in of a group, how much is in 1 group?” or “If of a number is , what is that number?”
On a tape diagram, we can show of a group having a value of and the whole group having an unknown value.
Fraction bar diagram. 4 equal parts. 3 parts shaded. First 3 parts labeled the fraction 3 over 4 and a. Total labeled unknown quantity and 1 group.
If of a number is , then to find the number, we can first divide by 3 to find of the number. Then we multiply the result by 4 to find the number.
These steps can be written as: . Dividing by 3 is the same as multiplying by , so we can also write the steps as: , which is .
In other words: .
In general, dividing a number by a fraction is the same as multiplying the number by , which is the reciprocal of the fraction. Reciprocals are numbers that when multiplied equal 1.
Two numbers that multiply to equal 1 are reciprocals.
- 8 and are reciprocals because .
- is a reciprocal of because .