Multiplication and Division of Fractions

Lesson 5

Math

Unit 5

5th Grade

Lesson 5 of 24

Objective


Multiply a non-unit fraction by a whole number.

Common Core Standards


Core Standards

  • 5.NF.B.4.A — Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)
  • 5.NF.B.6 — Solve real-world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

Foundational Standards

  • 4.NF.B.4

Criteria for Success


  1. Multiply a non-unit fraction by a whole number using tape diagrams.
  2. Look for and express regularity in repeated reasoning to deduce that $$\frac{a}{b} \times q$$ is $$a$$ times as much as $$\frac{1}{b} \times q$$, or $$\frac{a}{b} \times q = a \times q \div b$$ (MP.8).

  3. Solve contextual problems involving finding the product of a non-unit fraction and a whole number, including multiplicative comparison problems (MP.4).

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Anchor Tasks

25-30 minutes


Problem 1

a.   Find the value of each of the following. Draw a diagram if it will help you.

  1. $$\frac{1}{3} \times 5$$
  1. $$\frac{2}{3} \times 5$$
  1. $$\frac{1}{4} \times 9$$
  1. $$\frac{3}{4} \times 9$$
  1. $$\frac{1}{5} \times 10$$
  1. $$\frac{4}{5} \times 10$$

b.   What do you notice about the solutions in each row of the table? What do you wonder?

c.   Yesterday, Frederick wrote the equation $$\frac{1}{5} \times 6 = 6 \div 5$$. Based on what you noticed in Part (a), how can you modify Frederick’s equation to represent $$\frac{3}{5} \times 6$$?

Guiding Questions

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Student Response

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Problem 2

Find the values of the following expressions.

a.   $${2\over5} \times 7$$

b.   $$\frac{3}{8} \times 11$$

c.   $${2\over5} \times30$$

d.   $${5\over4} \times46$$

Guiding Questions

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Student Response

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Problem 3

a.   A new bike costs $80. A used bike costs half as much. How much does a used bike cost? 

b.   Nadra is $$\frac34$$ as tall as her dad. Her dad is 6 feet tall. How tall, in feet, is Nadra?

Guiding Questions

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Student Response

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Problem Set

15-20 minutes


Discussion of Problem Set

  • Look at #1(a) and 1(b). What do you notice about your solutions?
  • Look at #1(c) and 1(d). What do you notice about your solutions?
  • Look at #3(b). How did you solve? How many degrees is a straight angle? (This is connected to Grade 4 content of 4.MD.5—7.) 
  • In #2, how does knowing $$\frac{1}{6}$$ of 12 help you find $$\frac{5}{6}$$ of 12?
  • Look at #3(d). What made this problem a bit challenging? How did you solve? Was there more than one correct way to solve? (Students could have (1) found the amount of chocolate used to make frosting and the amount of chocolate used to make brownies and subtracted those quantities, or (2) they could have found how much more chocolate was used to make brownies than for frosting (i.e. one fifth of the chocolate) and then figured out how much of the chocolate that was.) 
  • Look at #4. Why does Alicia’s thinking make sense?

Target Task

5-10 minutes


Problem 1

Solve. Show or explain your work.

a.   $${{3\over4} \times 32}$$

b.   $${{2\over5} \times 8}$$

Student Response

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Problem 2

On Monday, Mrs. Johnson went on a walk that was $$4$$ miles long. On Tuesday, she goes on a walk that is $${{2\over3}}$$ as long as her walk on Monday. How long was Mrs. Johnson’s walk on Tuesday?

Student Response

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Additional Practice


The Extra Practice Problems can be used as additional practice for homework, during an intervention block, etc. Daily Word Problems and Fluency Activities are aligned to the content of the unit but not necessarily to the lesson objective, therefore feel free to use them anytime during your school day.

Word Problems and Fluency Activities

Word Problems and Fluency Activities

Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.

Next

Relate multiplication of a fraction by a whole number to multiplication of a whole number by a fraction and use this to develop a general method to multiply any fraction by any whole number (or vice versa).

Lesson 6
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Fractions as Division

Topic B: Multiplying a Fraction by a Whole Number

Topic C: Multiplying a Fraction by a Fraction

Topic D: Multiplying with Mixed Numbers

Topic E: Dividing with Fractions

Topic F: Fraction Real-World Problems and Line Plots

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