Multiplying a fraction by a whole number
In 4th grade, children learn to multiply a fraction by a whole number, like 2 × 3/4, by seeing it as repeated groups of the same fraction.
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 7 × 1/10?
- 7/70
- 1/70
- 7/10
Why this matters
This is your child's first step into multiplying with fractions, and it ties fractions back to the multiplication they already know. It shows up in the kitchen, such as tripling a recipe that needs 3/4 cup of milk. In 5th grade, they multiply a fraction by a fraction, like 1/2 × 3/4, and learn why multiplying by a number less than 1 gives a smaller answer.
Where kids can get stuck
- Multiplying both the top and bottom by the whole number, so 2 × 3/4 becomes 6/8, which still equals 3/4.
- Getting the right fraction without a sense of its size, leaving 15/8 unrecognized as almost 2, or 1 7/8.
- Adding 5 and 3/8 in a word problem that calls for 5 groups of 3/8.
How you can help
- Double a recipe together. If cookies need 3/4 cup of sugar, ask your child how much sugar a double batch needs, and measure it out to show 6/4 cups is 1 1/2 cups.
- Talk about time in fractions of an hour. If each of 3 chores takes 1/4 of an hour, ask your child how long all three take, then connect 3/4 of an hour to 45 minutes.
- Use a ruler and a quarter-inch mark. Have your child lay down 5 lengths of 1/4 inch and read the total, linking it to 5 × 1/4 = 5/4 = 1 1/4 inches.
Bobby's Math Club offers free practice that grows with your child.
Questions parents ask
Why is my child learning to multiply fractions this way?
Treating 3 × 2/5 as 2/5 + 2/5 + 2/5 builds on what your child already knows about multiplication as equal groups. It shows why the answer is 6/5 and why the bottom number does not change. Children who learn a rule without that picture often multiply the bottom too, which changes nothing about the size. The repeated-groups idea keeps the meaning clear.
Should my child turn answers like 6/4 into mixed numbers?
Both 6/4 and 1 2/4 are correct, and many teachers accept either in 4th grade. Changing to a mixed number helps your child see how big the answer is: 1 2/4 is a little more than one whole. Your child may also notice 1 2/4 is the same as 1 1/2. Ask what your child's teacher prefers, since expectations vary by class.
What comes after multiplying a fraction by a whole number?
In 5th grade, your child multiplies a fraction by a fraction, such as 1/2 × 3/4, and learns that this means taking part of a part. They also learn that multiplying by a fraction less than 1 makes a smaller answer, which surprises many children. Later in 5th grade, they begin dividing with unit fractions. This year's repeated-groups thinking is the foundation for all of that.
Make learning math fun
Bobby's Math Club turns 4th grade math practice into something fun to do together.
- Unlimited practice, completely free
- A few minutes a day, at just the right level
- 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 4.NF.B.4: “Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. a. Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4). b. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. c. Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?” Learn how Bobby's Math Club can help your students grow. (Common Core 4.NF.4)