Why fractions like 3/4 and 6/8 are equal
In 4th grade, children learn why multiplying the top and bottom of a fraction by the same number gives an equal fraction, like 3/4 = 6/8, and how to show it with a picture.
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
What is the missing number? 4/5 = ?/10
- 4
- 9
- 8
Why this matters
Equal fractions open the door to most of the fraction work ahead for your child, starting this year with comparing fractions and renaming tenths as hundredths. In 5th grade, adding 1/2 + 1/3 means rewriting both as sixths, and simplifying an answer like 6/8 to 3/4 relies on the same idea. Later, ratios and percents work the same way: 3/4 is 75/100, or 75%.
Where kids can get stuck
- Multiplying only the bottom number and saying 3/4 equals 3/8, which is a smaller amount.
- Adding the same number to the top and bottom, so 2/3 seems equal to 4/5.
- Using the multiplying rule without being able to draw or explain why 2/5 and 4/10 are the same amount.
How you can help
- Fold a sheet of paper into fourths and shade 1/4. Fold it again so there are eighths, and ask your child how many eighths are shaded now and why the shaded amount did not change.
- Cut a sandwich or tortilla into halves, then cut each half into thirds. Ask your child to name the same amount two ways: 1/2 and 3/6.
- Use a measuring cup while cooking. Ask whether two 1/4 cups fill the same amount as one 1/2 cup, then pour to check, and link it to 2/4 = 1/2.
Bobby's Math Club offers free practice that grows with your child.
Questions parents ask
Why is my child learning equivalent fractions this way?
Drawing fraction models shows your child why multiplying top and bottom by the same number works: each piece is cut into equal smaller pieces, so there are more pieces but the total amount stays the same. Without that picture, the rule can feel random, and children often apply it wrongly, such as changing only the bottom number. The drawings make the rule something your child can reason through.
Will my child learn to simplify fractions this year?
Your child may notice that 6/8 can be written as 3/4 by dividing the top and bottom by 2, and some classes talk about this. But the main goal in 4th grade is understanding and creating equivalent fractions. Formally simplifying fractions to lowest terms, using common factors, becomes more important in 5th and 6th grade.
What denominators does my child work with in 4th grade?
In 4th grade, fraction work usually uses denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. These are numbers that are easy to draw and that connect well to each other, such as halves, fourths, and eighths. Working with this smaller set lets your child focus on the idea of equivalence rather than on difficult arithmetic.
Make learning math fun
Bobby's Math Club turns 4th 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
- 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.
Ready to watch your child’s confidence grow?
Your 4th grade child can start today with free, unlimited practice that grows with them.
Join the clubNote for teachers: This skill is covered by Common Core math standard 4.NF.A.1: “Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.” Learn how Bobby's Math Club can help your students grow. (Common Core 4.NF.1)