Adding and subtracting fractions and mixed numbers
In 4th grade, children learn that 5/4 is five one-fourths, which can also be split as 2/4 + 3/4; and how to use that to add and subtract fractions and mixed numbers with like denominators.
By Robert “Bobby” BarnettMath teacher, parent, and founder of Bobby’s Math Club
Try these with your child
These are real questions from our 4th 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
Which sum is equal to 4/5?
- 1/5 + 1/5 + 1/5
- 1/4 + 1/4 + 1/4 + 1/4
- 1/5 + 1/5 + 1/5 + 1/5
Why this matters
Once your child sees a fraction as a count of equal pieces, fraction arithmetic starts to make sense, and they avoid the common slip of adding tops and bottoms, which turns 1/4 + 1/4 into 2/8. It comes up in daily life, like adding 1 3/4 cups of flour to 1/2 cup. Next year they add fractions with different denominators, and later use fractions in measurement, science, and algebra.
Where kids can get stuck
- Adding the denominators too, writing 5/12 + 6/12 = 11/24, an answer smaller than one of the starting fractions.
- Subtracting the smaller fraction from the larger, so 3 1/4 − 1 3/4 comes out as 2 2/4 instead of 1 2/4.
- Thinking a fraction can never be more than 1, so 7/4 looks like a mistake rather than one whole and three fourths.
How you can help
- Make 3/4 cup of flour as many ways as you can with a 1/4 cup and a 1/2 cup. Your child might find 1/4 + 1/4 + 1/4, or 1/2 + 1/4, which is 2/4 + 1/4. Say each way aloud as a sum.
- Talk about pizza leftovers. If a pizza is cut into 8 slices and your family eats 3/8 at lunch and 4/8 at dinner, ask your child how much was eaten and how much is left.
- Measure a walk in parts of a mile. If you walk 1 1/2 miles one day and 2 1/2 miles the next, ask your child to find the total and explain how the halves combine.
Bobby's Math Club offers free practice that grows with your child.
Questions parents ask
Why is my child learning to add fractions this way?
Thinking of 5/12 as five one-twelfths makes adding fractions with the same denominator a matter of counting pieces of the same size. That explains why the denominator does not change: twelfths plus twelfths are still twelfths. Children who learn only a rule often add the denominators too, which gives answers that make no sense. Building from unit fractions helps your child reason about each step.
What is a mixed number, and why does my child keep changing it into a fraction?
A mixed number is a whole number and a fraction together, like 2 1/4, which means 2 wholes and one fourth more. Sometimes it is easier to add or subtract after rewriting it as a fraction greater than 1: 2 1/4 is 9/4, since each whole is 4 fourths. Your child may switch back and forth depending on the problem. Both forms name the same amount.
Does my child need to add fractions with different denominators in 4th grade?
Mostly no. In 4th grade, adding and subtracting is done with like denominators, meaning the pieces are the same size, such as fourths with fourths. The one exception is tenths and hundredths, which your child learns to combine this year. Adding fractions with unlike denominators, such as 1/3 + 1/4, is a 5th-grade skill.
Make learning math fun
Bobby's Math Club turns 4th grade math practice into something fun to do together.
- Unlimited free practice
- A few minutes a day, at just the right level
- You see their progress and what to work on next
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 4.NF.B.3: “Understand a fraction a/b with a > 1 as a sum of fractions 1/b. a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8. c. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. d. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.” Learn how Bobby's Math Club can help your students grow. (Common Core 4.NF.3)