Math Expressions Grade 5, Unit 3: Multiplication and Division with Fractions
In this unit, your child multiplies and divides with fractions. They see a fraction as division, so 7 ÷ 2 = 7/2 = 3 1/2; multiply whole numbers and fractions by fractions; and learn when a product is smaller than what they started with. They also divide with unit fractions and whole numbers. Next, the class multiplies whole numbers and decimals.
By Robert “Bobby” BarnettMath teacher, parent, and founder of Bobby’s Math Club
What is my child learning in Unit 3?
- Interpreting a fraction as division, so 7 brownies shared by 2 people means 3 1/2 brownies each. Learn more: Fractions as sharing, like 3 ÷ 4 = 3/4
- Finding a fraction of a whole number or of another fraction, like 5/8 × 16 or 2/3 × 4/5. Learn more: Multiplying fractions, like 2/3 × 4/5
- Explaining why multiplying by a fraction less than 1 gives a smaller product and by a fraction greater than 1 gives a larger one. Learn more: When multiplying makes a number smaller
- Solving everyday problems with fractions and mixed numbers, like finding 2/3 of a 4 1/2-foot ribbon or scaling a recipe. Learn more: Multiplying fractions in real life, like recipes
- Dividing with unit fractions, like finding how many 1/4-cup scoops are in 3 cups or sharing 1/2 a pan among 4. Learn more: Dividing with fractions, like 1/2 ÷ 4
Sample questions to try together
These are real questions from our practice. Tap the speaker to hear one read aloud, or the light bulb for a hint, and talk about the answer together.
Question 1 of 3
What is 4 ÷ 7?
- 0
- 4/7
- 7/4
How you can help
- Share a pan of brownies or a pizza fairly. Ask what each person gets when 7 pieces go to 2 people, and write it as a fraction and as a division.
- Fill a container using a 1/3 cup or 1/4 cup measure. Ask your child how many scoops will fill 2 cups before you start, then count together.
- Ask your child to predict before figuring: will 3/4 of 12 cookies be more or less than 12? Will 1 1/2 batches of a recipe need more or less of each ingredient?
Where kids can get stuck
- Writing a sharing answer upside down, so 3 pizzas shared by 4 people becomes 4/3 instead of 3/4.
- Assuming any fraction makes a number smaller, so they expect 7/6 × 12 to be less than 12.
- Confusing sharing with grouping, so 'how many 1/4-cup scoops are in 3 cups' gets 3/4 instead of 12.
Practice makes perfect
Bobby's Math Club has practice problems that adapt to your child’s level, each with a detailed explanation and an easy-to-follow video, so your child can build confidence in these skills one step at a time.
Words your child will hear
- numerator
- The top number in a fraction, telling how many parts you have.
- denominator
- The bottom number in a fraction, telling how many equal parts make a whole.
- quotient
- The answer to a division problem.
- unit fraction
- A fraction with 1 as its numerator, like 1/3.
- scaling
- Resizing a number by multiplying, making it bigger, smaller, or the same.
- mixed number
- A whole number and a fraction together, like 2 1/2.
- product
- The answer to a multiplication problem.
- divisor
- The number you divide by.
- dividend
- The number being divided.
Want to help your child master multiplying with fractions?
In Bobby's Math Club, your child practices these skills at just the right level, with a hint when they need one, a clear explanation after every question, and kid-friendly videos. Unlimited practice is free.
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Written by Robert “Bobby” Barnett
Bobby is an award-winning math teacher, the author of Meet Every Learner’s Needs, and the father of two elementary-school math learners. He uses Bobby’s Math Club with his own kids a few times every week. Learn more or contact Bobby.
Which math standards does Math Expressions Grade 5 Unit 3 cover?
Math Expressions Grade 5 Unit 3 covers these math standards. Each one links to what it means, sample questions, and teaching strategies.
- 5.NF.B.3: Understand a fraction as division, like 2 ÷ 3 = 2/3.
- 5.NF.B.4: Multiply fractions, like 2/3 × 4/5 or 5/8 × 16.
- 5.NF.B.5: See how multiplying by a fraction can make a number bigger or smaller.
- 5.NF.B.6: Solve word problems that multiply fractions and mixed numbers.
- 5.NF.B.7: Divide with fractions, like 1/2 ÷ 4 and 5 ÷ 1/3.
For teachers: Unit names and order vary between editions and districts, so your school’s own materials have the exact sequence. Learn how Bobby's Math Club can help your students grow.