Visual Fraction Models and Equations Lesson 6.2.7

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

Dividing Unit Fractions Answer each problem. Answer

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

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?

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

Practice #1 A Different Method 3 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

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?

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

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

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

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

÷ 2 3 4 Problem #2 ÷ 2 3 4 = 8 12 9

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?

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.

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

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

Dividing Unit Fractions Answer each problem. Next Slide