Fractions as sharing, like 3 ÷ 4 = 3/4
In 5th grade, children learn to see a fraction as a division, so 3 ÷ 4 equals 3/4, and to solve sharing problems whose answers are fractions or mixed numbers.
By Robert “Bobby” BarnettMath teacher, parent, and founder of Bobby’s Math Club
Try these with your child
These are real questions from our 5th grade 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
Why this matters
Your child is about to discover that fractions and division, two ideas that used to live apart, are the same thing. That changes what division can do: a sharing problem no longer needs a remainder. It sets up dividing with fractions later this year, turning fractions into decimals in 6th grade, and the ratios and rates of middle school, like 50 pounds of rice shared among 9 families.
Where kids can get stuck
- Saying 3 ÷ 4 cannot be done because 3 is smaller than 4, instead of seeing that each share is 3/4.
- Writing the fraction upside down, so 3 pizzas shared among 4 people becomes 4/3 instead of 3/4.
- Giving a remainder when a fraction fits better, so 7 brownies shared by 2 is "3 remainder 1" instead of 3 1/2 each.
How you can help
- Share a real snack, like 3 granola bars among 4 people. Before cutting, ask your child how much each person will get. Cut each bar into fourths and hand them out to check that everyone gets 3/4.
- Ask a sharing question at dinner: 5 slices of pie split among 2 people. Let your child explain why each person gets 5/2, or 2 1/2 slices.
- Use a length of string or ribbon: cut 2 feet of ribbon into 3 equal pieces and ask how long each piece is. Your child can reason that 2 ÷ 3 is 2/3 of a foot.
Bobby's Math Club offers free practice that grows with your child.
Questions parents ask
Why is my child learning fractions as division?
Fractions and division describe the same thing: sharing a quantity into equal parts. Showing your child that 3/4 means 3 ÷ 4 ties together ideas they used to see as separate. It also explains why a division like 7 ÷ 2 can have an exact answer, 3 1/2, instead of always ending with a remainder. This connection is used constantly in later math.
How do I explain that 3 ÷ 4 is 3/4?
Use something you can share. With 3 sandwiches and 4 people, cut each sandwich into 4 equal pieces. That makes 12 pieces, and each person gets 3 of them. Each piece is 1/4 of a sandwich, so each person gets 3/4 of a sandwich. Seeing the pieces handed out is often more convincing than any explanation.
When should the answer be a remainder and when a fraction?
It depends on what is being shared. Things that can be cut, like pizza, ribbon, or time, usually get a fractional answer. Things that cannot be split, like people or cars, usually need a whole number and a remainder, or rounding up. Asking "Can this be cut?" helps your child decide which answer fits.
Make learning math fun
Bobby's Math Club turns 5th grade math practice into something fun to do together.
- Unlimited practice, completely free
- A few minutes a day, at just the right level
- Hints when they are stuck, and a celebration when it clicks
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.
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Join the clubNote for teachers: This skill is covered by Common Core math standard 5.NF.B.3: “Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?” Learn how Bobby's Math Club can help your students grow. (Common Core 5.NF.3)