Illustrative Mathematics Grade 5, Unit 2: Fractions as Quotients and Fraction Multiplication
In this unit, your child sees that a fraction can be a division: 3 people sharing 2 pizzas equally each get 2/3 of a pizza. They then multiply a whole number by a fraction and a fraction by a fraction, and ask whether a product will be bigger or smaller. It follows the volume unit, where multiplication described space, and leads into multiplying and dividing fractions.
By Robert “Bobby” BarnettMath teacher, parent, and founder of Bobby’s Math Club
What is my child learning in Unit 2?
- Seeing a fraction as a quotient, so 2 pizzas shared by 3 people means each gets 2 ÷ 3 = 2/3. Learn more: Fractions as sharing, like 3 ÷ 4 = 3/4
- Multiplying a whole number by a fraction, like 5 × 2/3 = 10/3, and a fraction by a fraction, like 1/2 × 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 one greater than 1 a larger one. Learn more: When multiplying makes a number smaller
- Solving problems with fraction products, like finding 2/3 of a 3/4-mile trail or 4 batches of 2/3 cup. Learn more: Multiplying fractions in real life, like recipes
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 2 sandwiches among 3 people at lunch. Ask your child how much each person gets, 2/3 of a sandwich, and to draw how they would cut them.
- Ask how much of a 3/4-mile walk you have done when you are 2/3 of the way. Let your child sketch a strip and find 1/2 mile.
- Make 4 batches of a recipe that uses 2/3 cup of oats. Ask your child to predict whether it is more or less than 4 cups, then find 2 2/3 cups.
Where kids can get stuck
- Writing 2 pizzas shared by 3 people as 3/2 instead of 2/3, flipping the fraction.
- Multiplying 5 × 2/3 as 10/15, putting the whole number on both the top and the bottom.
- Missing that multiplying by 3/3 keeps a number the same, so 2/3 = 6/9 feels like a trick.
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
- quotient
- What you get when you divide one number by another.
- numerator
- The top number of a fraction, which counts how many parts you have.
- denominator
- The bottom number of a fraction, which tells how many equal parts make a whole.
- fraction
- A number that names part of a whole, like 2/3.
- product
- What you get when you multiply numbers together.
- unit fraction
- One equal part of a whole, like 1/4.
- scaling
- Resizing a number by multiplying, making it larger, smaller, or keeping it the same.
- mixed number
- A number written as a whole number plus a fraction, like 3 3/4.
Ready to build your child’s confidence with fractions as division?
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 Illustrative Mathematics Grade 5 Unit 2 cover?
Illustrative Mathematics Grade 5 Unit 2 covers these math standards. Each one links to what it means, sample questions, and teaching strategies.
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.