Finding equal fractions, like 1/2 = 2/4
In 3rd grade, children learn to spot fractions of the same size, like 1/2 and 2/4; to make equal fractions, like 2/3 and 4/6; and to write whole numbers as fractions, like 3 = 3/1.
By Robert “Bobby” BarnettMath teacher, parent, and founder of Bobby’s Math Club
Try these with your child
These are real questions from our 3rd 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
A pizza is cut into 6 equal slices. Which fraction names the whole pizza?
- 1/6
- 6/1
- 6/6
Why this matters
Seeing that 1/2 and 2/4 are the same amount shows your child that one number can have more than one name. Fractions like these are called equivalent, which means equal. In 4th grade your child uses them to compare any two fractions, and in 5th grade to add fractions with different-sized pieces. At home, it is the moment two 1/4 cups of flour do the job of one 1/2 cup.
Next comes comparing fractions by size, which asks which of two fractions is the larger amount.
Where kids can get stuck
- Adding 1 to both the numerator and denominator (the top and bottom numbers), so 1/2 becomes 2/3, which is a different amount.
- Placing 1/2 and 2/4 at different spots on a number line from 0 to 1, as if they were different numbers.
- Thinking 6/6 is bigger than 1 because 6 is a big number, when six sixths make exactly one whole.
How you can help
- Cut two identical sandwiches, one into 2 equal pieces and one into 4. Ask your child how many fourths cover the same amount as one half, and let them lay the pieces on top to check.
- Swap measuring cups when you bake. If the recipe calls for 1/2 cup of flour, hand your child the 1/4 cup instead and ask how many scoops it will take.
- Fold a strip of paper in half, then in half again, then once more, shading the same part each time. Ask your child to name the shaded part after each fold: 1/2, 2/4, then 4/8.
For more, Bobby's Math Club has free practice at your child’s level.
Questions parents ask
Why is my child learning equal fractions with pictures instead of a rule?
Pictures and number lines show why 1/2 and 2/4 are the same amount: the shaded part does not change, only the number of pieces it is cut into. A shortcut rule usually comes in 4th grade. It makes much more sense to a child who has already watched the pieces line up, because they know what the rule is doing.
How do I explain why 1/2 equals 2/4?
Use a ruler. The mark for half an inch is the same mark as two fourths of an inch, the same spot with two names. Then point out that the inch did not change; it was only split into more pieces. Showing it on something real, like a ruler or a measuring cup, is more convincing than any explanation.
How can a fraction equal a whole number?
The denominator says how many equal parts make one whole, and the numerator says how many of those parts you have. So 4/4 is all four parts of one whole, which is 1. And 3/1 means 3 parts that are each a whole, which is 3. In the same way, 6 halves make 3 wholes, so 6/2 = 3.
Make learning math fun
Bobby's Math Club turns 3rd grade math practice into something fun to do together.
- Free, unlimited practice for every child in your family
- Practice that starts where your child is and grows with them
- Level-ups, badges, and a cheer for every win
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 3.NF.A.3: “Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. a. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. b. Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent, e.g., by using a visual fraction model. c. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1, recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram. d. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.” Learn how Bobby's Math Club can help your students grow. (Common Core 3.NF.3)