1. Visual Fraction Models
and Equations
Lesson 6.2.7

2. Division Relative to Multiplication
Determine the number that correctly completes both equations.
Answer

3. Dividing Unit Fractions
Answer each problem.
Answer

4. Multiplicative Inverse
Two numbers whose product is 1
are multiplicative inverses of one another. 2 3 3 2 3 4 4 3 3 4 = 1 x 5 8 8 5 1 3 3 1 1 3 = x 1 4 4

5. Practice #1 ÷ 3 2 4 5 Make sense of the problem. 3 4 ?
Which fraction strip should be used?
How did we know to shade in two sections?
How did we know to put the 3/4 in the brace that shows 2/5?
What about the bottom brace?

6. Practice #1 ÷ 3 2 4 5 A different look: Make sense of the problem. ÷ 3?
A different look:
2 units = 3 4
Make sense of the problem.
1 unit is half of = 3 4 1 2 3 4 8 3 8
5 units = 15 8
5 units = ÷ 3 4 2 5
So, = 15 8

7. Practice #1 A Different Method3 4 ?
Using the commutative property, we can say the following:
So and
Therefore, 1 2
5 = 3 4 3 4
5 = 1 2 3 4 = 5 2 15 8 3 4 = 2 5 15 8 ÷ 3 4 = 5 2 15 8 3 4 = 2 5 ÷
invert and multiply

8. Problem #1 Multiplicative Inverse÷ 1 4 2 3 1 4 ?
Which fraction strip should be used?
How did we know to shade in two sections?
How did we know to put the 1/4 in the brace that shows 2/3?
What about the bottom brace?

9. Problem #1 Multiplicative Inverse÷ 1 4 2 3 1 4
2 units = 1 4
1 unit is half of = 1 4 1 2 4 8 ? 1 8
3 units = 3 8
3 units = ÷ 1 4 2 3
So, = 8

10. Problem #1 Multiplicative Inverse÷ 1 4 2 3 1 4 1 4
3 = 2 1 4 = 3 2 8 ? 1 4 = 3 2 8 1 4 = 2 3 ÷
invert and multiply

11. Lesson Summary
Connecting models of fraction division to multiplication through the use of reciprocals helps in understanding the “invert and multiply” rule.

12. Problem #2
Solve the following problem with both a tape diagram and the “invert and multiply” rule. ÷ 2 3 4
Which fraction strip should be used?
How many section should be shaded?
Where does the top brace go?
What fraction goes on the top brace?
What about the bottom brace?
fourths
three
Across 3 of the 4 sections
2/3
That is our unknown

13. ÷ 2 3 4
Problem #2 ÷ 2 3 4 = 8 12 9

14. Independent Practice Draw models that show: 1) 25÷13 2) 34÷12
1) 25÷13 2) 34÷12
Find the answer as well.
Independent Practice
Which fraction strip should be used?
How many section should be shaded?
Where does the top brace go?
What fraction goes on the top brace?
What about the bottom brace?

15. Math Talk . Lesson Summary Math Talk: Lesson Summary
Dividing by a fraction is equivalent to multiplying by its reciprocal, or inverse. Connecting the models of division by a fraction to multiplication by its inverse strengthens your understanding.
Lesson Summary
Math Talk .
Lesson Summary
Connecting models of fraction division to multiplication through the use of reciprocals helps in understanding the “invert and multiply” rule.

16. Exit Ticket 1) Write the reciprocal of the following numbers: 7 10 1 25 2)
Rewrite this division problem as a multiplication problem:
Exit Ticket 5 8 2 3 3)
Solve problem 2 using models.

17. Division Relative to Multiplication
Determine the number that correctly completes both equations.
Next Slide

18. Dividing Unit Fractions
Answer each problem.
Next Slide