5th Grade · Number & Operations - Fractions
5.NF.B.7: Divide with fractions, like 1/2 ÷ 4 and 5 ÷ 1/3
5.NF.B.7 is a 5th grade Common Core math standard in Number & Operations - Fractions. Here’s what it really covers, and how you can help your students learn it.
By Robert “Bobby” BarnettMath teacher, parent, and founder of Bobby’s Math Club
The standard
Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. a. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. b. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. c. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?
In plain words
Divide with fractions, like 1/2 ÷ 4 and 5 ÷ 1/3.
Sample questions from student practice
These questions from Bobby's Math Club are the kinds of questions your students will see. You can try answering them to see what a student might see.
Question 1 of 3
What is 3 divided by 1/5?
- 15
- 1/15
- 3/5
Where students can get stuck
- Dividing the whole number by the denominator, so 1/2 ÷ 4 becomes 2 instead of 1/8.
- Multiplying instead of dividing, so 5 ÷ 1/3 becomes 5/3 instead of 15, because they expect division to shrink things.
- Confusing sharing with grouping, so "how many 1/4 cup scoops are in 3 cups" gets 3/4 instead of 12.
Effective teaching strategies
- Fold a paper strip in half, cut that half into 4 equal parts, and have students name each part as 1/8 of the whole strip to show 1/2 ÷ 4.
- Draw 5 wholes each cut into thirds and ask how many 1/3 pieces there are in all, so students see why 5 ÷ 1/3 is 15.
- Write one story for 3 ÷ 1/4 and one for 1/4 ÷ 3 with students, and have them tell which counts groups and which shares equally.
Units that teach this standard
Find where 5.NF.B.7 lands in the program you teach. Each unit has a guide written for families. Unit names and order vary between editions and districts, so your school’s own materials have the exact sequence.
Bridges in Mathematics
enVision Mathematics
Everyday Mathematics
i-Ready Classroom Mathematics
Illustrative Mathematics
Math Expressions
Reveal Math
Don’t see your curriculum? Contact Bobby and we’ll see if we can help!
Share it with families
Families can read Dividing with fractions, like 1/2 ÷ 4 for a plain-language look at this skill, with three questions to try together and ideas for helping at home.
Help every student practice fractions at home
In Bobby's Math Club, students practice 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 for every family.
See how it works for teachers
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.