➕ 5th Grade Math · Unit 6

Multiplying and Dividing Fractions

20 short narrated lessons in 4 chapters, each with pictures, a quiz with a hint and a second try, and an explanation for every answer.

Standards: 5.NF.B.3 5.NF.B.4 5.NF.B.6 5.NF.B.5 5.NF.B.7

5th Grade Math · 8 units
  1. 1Volume
  2. 2Expressions and Whole Number Operations
  3. 3Place Value with Decimals
  4. 4Decimal Operations
  5. 5Adding and Subtracting Fractions
  6. 6Multiplying and Dividing Fractions
  7. 7Coordinate Plane and Patterns
  8. 8Classifying Shapes
Picture from the lesson “Sharing Makes Fractions”
Sharing Makes Fractions
Picture from the lesson “A Fraction Is a Division”
A Fraction Is a Division
Picture from the lesson “Division Answers as Mixed Numbers”
Division Answers as Mixed Numbers

What your child will learn

Fractions as division

  1. Sharing Makes FractionsShow that sharing three sandwiches among four people gives each person three fourths of a sandwich.
  2. A Fraction Is a DivisionExplain that a fraction like three fourths means three divided by four.
  3. Division Answers as Mixed NumbersSolve division word problems whose answers are fractions or mixed numbers.
  4. Fractions Are Division: Review ReviewReview how a fraction shows division.

Multiplying fractions

  1. Finding a Fraction of a NumberFind a fraction of a whole number, like two thirds of twelve, using a model.
  2. Multiplying a Fraction by a FractionMultiply a fraction by a fraction using an area model, like one half of three fourths.
  3. The Fraction Multiplying ShortcutMultiply two fractions by multiplying the numerators and multiplying the denominators.
  4. Area with Fraction Side LengthsFind the area of a rectangle with fraction side lengths by tiling it with unit fraction squares and by multiplying.
  5. Fraction Multiplication Word ProblemsSolve real-world problems that multiply fractions and mixed numbers.
  6. Multiplying Fractions: Review ReviewReview multiplying fractions and mixed numbers.

Multiplication as scaling

  1. Multiplying Is ResizingExplain multiplication as resizing, and compare the size of a product to one factor without multiplying.
  2. Multiplying by More Than OneExplain why multiplying a number by a fraction greater than one gives a product greater than that number.
  3. Multiplying by Less Than OneExplain why multiplying a number by a fraction less than one gives a product smaller than that number.
  4. Multiplication as Scaling: Review ReviewReview multiplication as scaling.

Dividing with unit fractions

  1. How Many Thirds Fit?Divide a whole number by a unit fraction, like four divided by one third, by asking how many thirds fit in four.
  2. Sharing a Unit FractionDivide a unit fraction by a whole number, like one third divided by four, by sharing it into equal parts.
  3. Checking Fraction DivisionUse multiplication to check an answer to a division with a unit fraction.
  4. Fraction Division StoriesSolve word problems that divide with unit fractions using drawings and equations.
  5. Dividing with Unit Fractions: Review ReviewReview dividing whole numbers and unit fractions.
  6. Unit 6 Test: Multiplying and Dividing FractionsShow what you learned in the whole unit (Fractions as division, Multiplying fractions, Multiplication as scaling, Dividing with unit fractions) by answering mixed questions.

Try a question from this unit

From the lesson “Sharing Makes Fractions”

Two granola bars, each cut into 5 equal colored parts.

Five kids share 2 granola bars equally. How much does each kid get?

  • 5/2 of a bar
  • 2/5 of a bar
  • 1/5 of a bar
  • 2 bars
Show the answer

2/5 of a bar. Each kid gets 1 part of 1/5 from each bar. That is 2/5 of a bar.

Hint kids see after a wrong try: “Each bar is cut into 5 equal parts. How many parts does each kid get?”

Key words

  • share
  • equal parts
  • fraction
  • quotient
  • mixed number
  • of
  • product
  • area model
  • numerator
  • denominator
  • area
  • side length
  • scaling
  • factor
  • greater than one
  • less than one
  • unit fraction
  • divide
  • check
  • inverse operation
  • word problem
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