Fraction word problems are math questions that put fractions into everyday situations like splitting a pizza, scaling a recipe, or figuring out how far you still have to walk. Instead of just solving 1/2 + 1/3, you read a short scenario and decide which operation fits before you do any math. They show up in the Common Core State Standards starting in grade 3 (standard 3.NF) and keep going through grade 7.
Most kids don't struggle with the actual arithmetic. They struggle with the reading part. A sentence says "Maria ate 2/8 of a pizza and then 3/8 more," and the student has to recognize that means adding fractions with like denominators. That translation from words to numbers is the whole skill here, and it only gets better with practice.
Below you'll find 22 problems organized from the easiest (same-denominator addition in grades 3-4) up through some genuinely tricky multi-step problems with mixed numbers and probability (grade 7+). Try the hint first before peeking at the answer. And when you're done, run your solutions through our free fractions calculator to see how you did.
Quick Summary
- 22 practice problems sorted into three levels: grades 3-4, grades 5-6, and grade 7+.
- Every problem has a hint you can open first and a full worked solution with the math shown.
- Grades 3-4 cover addition, subtraction, and comparing with like denominators.
- Grades 5-6 introduce unlike denominators, mixed numbers, and all four operations including the Keep-Change-Flip method for division.
- Grade 7+ problems are multi-step: recipe scaling, work rates, probability, and mixed number subtraction.
- Scroll past the problems for a clue-words table that tells you which operation to use, plus the three most common mistakes to avoid.
Grades 3–4 Grade 3–4 Fraction Word Problems
All same-denominator problems, plus a few "fraction of a whole number" questions. These line up with Common Core standards 3.NF and 4.NF, so you're looking at unit fractions, simple addition and subtraction where the denominators already match, comparing fractions on a number line or with an area model, and figuring out what "one-fourth of 24" actually means. Good starting point if fractions are still new.
Problem 1
Addition (Like Denominators)
Maria ate 2/8 of a pizza for lunch and 3/8 of the same pizza for dinner. What fraction of the pizza did Maria eat in total?
Hint
The denominators already match (both eighths), so just add the numerators. No need to find a common denominator.
Solution
Set up the addition:
2/8 + 3/8
Add the numerators (denominator stays the same):
(2 + 3) / 8 = 5/8
Answer: Maria ate 5/8 of the pizza.
Problem 2
Subtraction (Like Denominators)
A jar is 5/6 full of marbles. Jake removes 2/6 of the jar's worth. What fraction of the jar still has marbles?
Hint
Removing means subtraction. Both fractions share the denominator 6, so subtract the numerators.
Solution
Subtract:
5/6 − 2/6 = 3/6
Reduce to lowest terms (the GCF of 3 and 6 is 3):
3/6 = 1/2
Answer: The jar is 1/2 full.
Want to double-check? Our Simplify Fractions Calculator can do it instantly.
Problem 3
Comparing Fractions
Emma has 1/3 of a chocolate bar. Liam has 1/4 of an identical bar. Who has more chocolate?
Hint
Same numerator, different denominators. The smaller the denominator, the bigger each piece. Would you rather cut a bar into 3 slices or 4?
Solution
Convert to equivalent fractions with a common denominator (3 × 4 = 12):
1/3 = 4/12
1/4 = 3/12
Compare the numerators:
4/12 > 3/12
Answer: Emma has more chocolate (1/3 > 1/4).
Problem 4
Addition (Like Denominators)
A painter uses 1/5 of a can of paint on Monday and 2/5 on Tuesday. How much paint has the painter used so far?
Hint
"So far" means combine both amounts. Same denominators, so add straight across.
Solution
Add:
1/5 + 2/5 = 3/5
Answer: The painter used 3/5 of the can.
Problem 5
Subtraction (Like Denominators)
A water bottle is 7/10 full. After a hike, Sam drinks 4/10 of the bottle. How much water is left?
Hint
"How much is left" means subtract what was used up.
Solution
Subtract:
7/10 − 4/10 = 3/10
Answer: 3/10 of the bottle remains.
Problem 6
Fraction of a Whole Number
A class has 24 students. One-fourth of them are wearing red shirts. How many students are wearing red?
Hint
"One-fourth of" means divide into 4 equal groups and take one group. Same thing as multiplying 1/4 × 24.
Solution
Find 1/4 of 24:
24 ÷ 4 = 6
Answer: 6 students are wearing red shirts.
Problem 7
Addition (Like Denominators)
During art class, Nora used 3/10 of a tube of blue paint and 4/10 of the same tube for green. How much paint did she use altogether?
Hint
"Altogether" means add. Both amounts are in tenths, so the denominators match already.
Solution
Add:
3/10 + 4/10 = 7/10
Answer: Nora used 7/10 of a tube of paint.
Problem 8
Fraction of a Whole Number
A baker made 30 cookies. She decorated 2/5 of them with sprinkles. How many cookies have sprinkles?
Hint
The word "of" is your clue to multiply. Divide 30 into 5 equal groups, then take 2 of those groups.
Solution
Find 2/5 of 30:
30 ÷ 5 = 6 (one-fifth)
6 × 2 = 12 (two-fifths)
Answer: 12 cookies have sprinkles.
Grades 5–6 Grade 5–6 Fraction Word Problems
What types of fraction word problems do 5th and 6th graders solve?
Now things get interesting. The denominators stop matching, mixed numbers show up, and you'll need all four operations. You'll find yourself computing the least common denominator (LCD) for addition and subtraction, and using the Keep-Change-Flip method to divide fractions. These problems pull from Common Core standard 5.NF and cover the kind of scenarios kids actually encounter: cooking, measuring, sharing things with friends.
Problem 9
Addition (Unlike Denominators)
A recipe calls for 1/3 cup of white sugar and 1/4 cup of brown sugar. How much sugar is needed in total?
Hint
Different denominators (3 and 4), so you need equivalent fractions before you can add. The LCD of 3 and 4 is 12.
Solution
Convert to equivalent fractions (LCD = 12):
1/3 = 4/12
1/4 = 3/12
Add:
4/12 + 3/12 = 7/12
Answer: 7/12 cup of sugar in total.
Stuck on unlike denominators? Our adding fractions guide walks through it.
Problem 10
Subtraction (Unlike Denominators)
Ryan ran 3/4 of a mile on Monday and 1/3 of a mile on Tuesday. How much farther did he run on Monday?
Hint
"How much farther" means find the difference. Convert both fractions to equivalent fractions with a common denominator first.
Solution
Common denominator (LCD of 4 and 3 = 12):
3/4 = 9/12
1/3 = 4/12
Subtract:
9/12 − 4/12 = 5/12
Answer: Ryan ran 5/12 of a mile farther on Monday.
More like this: How to Subtract Fractions.
Problem 11
Multiplication
A garden covers 3/5 of an acre. A flower bed takes up 2/3 of the garden. What fraction of an acre is the flower bed?
Hint
A fraction of a fraction. In math, "of" almost always means multiply.
Solution
Multiply straight across:
2/3 × 3/5 = 6/15
Reduce to lowest terms (GCF of 6 and 15 is 3):
6/15 = 2/5
Answer: The flower bed is 2/5 of an acre.
Full breakdown: How to Multiply Fractions.
Problem 12
Division
A ribbon is 3/4 of a yard long. It needs to be cut into pieces that are each 1/8 of a yard. How many pieces can be cut?
Hint
Cutting into equal pieces is division. Use Keep-Change-Flip: keep the first fraction, change division to multiplication, flip the second fraction (use its reciprocal).
Solution
Set up the division:
3/4 ÷ 1/8
Keep-Change-Flip:
3/4 × 8/1 = 24/4 = 6
Answer: 6 pieces can be cut.
See also: How to Divide Fractions.
Problem 13
Mixed Numbers, Addition
On Saturday, Ana walked 1 1/2 miles. On Sunday she walked 2 3/4 miles. How far did she walk over the weekend?
Hint
Add the whole numbers and the fractional parts separately. You'll need a common denominator for 1/2 and 3/4. Quick shortcut: 1/2 is the same as 2/4 (a handy benchmark fraction to memorize).
Solution
Add whole numbers:
1 + 2 = 3
Add fractional parts (LCD of 2 and 4 = 4):
1/2 = 2/4
2/4 + 3/4 = 5/4 = 1 1/4
Combine:
3 + 1 1/4 = 4 1/4
Answer: Ana walked 4 1/4 miles over the weekend.
Problem 14
Multiplication, Fraction of a Whole Number
There are 36 students in a class. Two-thirds passed the fractions quiz on their first try. How many students passed?
Hint
"Two-thirds of 36" means multiply: 2/3 × 36.
Solution
Calculate 2/3 × 36:
36 ÷ 3 = 12
12 × 2 = 24
Answer: 24 students passed on the first try.
Problem 15
Division, Equal Sharing
A bag holds 5/6 of a pound of trail mix. Three friends split it equally. How much does each person get?
Hint
"Split equally" among 3 is division by 3. Dividing by 3 is the same as multiplying by its reciprocal, 1/3.
Solution
Divide:
5/6 ÷ 3 = 5/6 × 1/3 = 5/18
Answer: Each friend gets 5/18 of a pound.
Problem 16
Multi-Step (Addition + Subtraction)
A water tank is completely full. In the morning, 1/4 is drained. In the afternoon, another 1/3 is drained. What fraction of the water remains?
Hint
Start with 1 (the whole tank). Add up the two drained amounts, then subtract the total from 1.
Solution
Total drained (LCD of 4 and 3 = 12):
1/4 = 3/12
1/3 = 4/12
3/12 + 4/12 = 7/12 drained
Subtract from 1 whole:
12/12 − 7/12 = 5/12
Answer: 5/12 of the water remains.
Grade 7+ Grade 7+ Fraction Word Problems
What makes 7th-grade fraction word problems harder?
More steps. You'll convert between mixed numbers and improper fractions, chain two or three operations together, and apply fractions to things like work rates and probability. These fit under Common Core standards 6.NS and 7.NS. If you're losing points on tests, it's probably here, and the fix is almost always the same: slow down and write out every intermediate step. Trying to do too much in your head is where things fall apart.
Problem 17
Multi-Step, Multiplication + Subtraction
A carpenter has a board that is 5 1/2 feet long. He cuts off a piece that is 2/3 of the total length. How long is the remaining piece?
Hint
Two steps here. First find the cut piece (2/3 "of" 5 1/2 means multiply). Then subtract that from the original length. Convert the mixed number to an improper fraction before you start.
Solution
Convert 5 1/2 to an improper fraction:
5 1/2 = 11/2
Find the cut piece (2/3 × 11/2):
2/3 × 11/2 = 22/6 = 11/3 = 3 2/3 ft
Subtract from original (LCD = 6):
11/2 − 11/3 = 33/6 − 22/6 = 11/6 = 1 5/6
Answer: The remaining piece is 1 5/6 feet.
Problem 18
Multi-Step, Scaling a Recipe
A cookie recipe makes 24 cookies and calls for 2 1/4 cups of flour. You only want 8 cookies. How much flour do you need?
Hint
8 is 8/24 = 1/3 of the full batch. Multiply the flour by 1/3.
Solution
Scaling factor:
8 ÷ 24 = 1/3
Convert 2 1/4 to an improper fraction:
2 1/4 = 9/4
Multiply:
1/3 × 9/4 = 9/12 = 3/4
Answer: You need 3/4 cup of flour.
Problem 19
Multi-Step, Combined Work Rate
Maya can paint a wall in 6 hours. Leo can paint the same wall in 4 hours. If they work together, what fraction of the wall do they finish in one hour?
Hint
Find each person's rate as a unit fraction (fraction of the wall per hour), then add them. Classic combined-rate setup.
Solution
Maya's rate:
1/6 of the wall per hour
Leo's rate:
1/4 of the wall per hour
Combined (LCD of 6 and 4 = 12):
1/6 + 1/4 = 2/12 + 3/12 = 5/12
Answer: Together they finish 5/12 of the wall per hour.
Problem 20
Multi-Step, Fraction of a Remainder
A bookstore received 120 books. They sold 3/8 in week one and 1/3 of the remaining books in week two. How many books are left?
Hint
Work in stages. The second fraction applies to the leftovers from week one, not the original 120. This is the #1 trap in multi-step fraction problems, and it catches people every time.
Solution
Week 1: sold 3/8 of 120:
120 × 3/8 = 45 sold
120 − 45 = 75 remaining
Week 2: sold 1/3 of the remaining 75:
75 × 1/3 = 25 sold
75 − 25 = 50 remaining
Answer: 50 books are left after two weeks.
Problem 21
Multi-Step, Distance with Mixed Numbers
A hiker plans to walk 7 1/2 miles to a campsite. After covering 4 2/3 miles, she stops. How much farther does she still need to walk?
Hint
Subtract the distance walked from the total. Convert both mixed numbers to improper fractions and find a common denominator.
Solution
Convert to improper fractions:
7 1/2 = 15/2
4 2/3 = 14/3
Common denominator (LCD = 6):
15/2 = 45/6
14/3 = 28/6
Subtract:
45/6 − 28/6 = 17/6 = 2 5/6
Answer: She still needs to walk 2 5/6 miles.
Problem 22
Multi-Step, Probability
A bag contains 4 red, 6 blue, and 2 green marbles. You draw one at random without replacing it. If the first marble is red, what's the probability the second is also red?
Hint
After pulling out one red marble, recount what's left. How many total? How many red? Probability is just favorable outcomes over total outcomes.
Solution
Total marbles at start:
4 + 6 + 2 = 12
After removing 1 red marble:
Red remaining: 3 Total remaining: 11
Probability:
3/11
Answer: The probability is 3/11 (already in lowest terms since 3 and 11 share no common factor).
How to Solve Fraction Word Problems
There's no single trick. But there is a process that works, and the National Council of Teachers of Mathematics (NCTM) backs this up: problem-solving is about having a toolkit, not memorizing shortcuts. Here's the toolkit.
📖
1. Read It Twice
First pass: just read. Don't pick up a pencil. Second pass: underline the numbers and circle the question. You'd be surprised how many mistakes come from misreading the problem, not from bad math.
🔍
2. Find the Clue Words
Certain words point straight to an operation. "Altogether" means add. "Remaining" means subtract. "Of" means multiply. "Split equally" means divide. The table below has the full list. Memorize it.
✏️
3. Write the Equation First
Turn the story into math before you calculate anything. If you can write down "3/4 ÷ 1/8" from the problem text, you're 80% done. If the equation looks wrong, go back and re-read.
🧩
4. One Step at a Time
Multi-step problems trip people up because they try to do everything at once. Don't. Solve the first operation, write down the result, then move to the next. Keep each piece simple.
📐
5. Reduce Your Answer
Teachers want lowest terms. Divide the numerator and denominator by their greatest common factor (GCF). Convert improper fractions to mixed numbers when the context uses whole amounts.
✅
6. Sanity Check
Does your answer make sense? You added two positive fractions and got something smaller? Something broke. Try sketching a quick number line estimate if you're not sure.
Clue Words Quick-Reference
Print this out or bookmark it. Once you've got these patterns memorized, the hardest part of word problems gets a lot easier.
| Operation |
Clue Words |
Example Phrase |
| Addition |
total, altogether, combined, in all, sum, plus, both |
"How much in total?" |
| Subtraction |
left over, remaining, difference, fewer, less than, how much more |
"How much is left?" |
| Multiplication |
of, times, product, each, per (with groups), area |
"2/3 of the class" |
| Division |
split equally, shared, per (rate), how many fit, cut into |
"Split equally among 4" |
Three Mistakes That Come Up Constantly
These aren't obscure gotchas. They're the same three errors that math teachers see week after week, and both the NCTM and Khan Academy flag them as the most frequent fraction stumbling blocks.
⚠️ Watch for these
1. Adding the denominators. When students see 1/3 + 1/4, some write 2/7. That's wrong. You need equivalent fractions with a matching denominator first. If you're not sure which denominator to use, our LCD Calculator can find it for you.
2. Not reducing. An answer of 6/15 isn't wrong, technically. But on a test it'll probably get marked down because it's not in lowest terms. 6/15 simplifies to 2/5. Always check for a common factor.
3. Wrong operation. "Of" means multiply, not add. "Remaining" means subtract, not divide. The clue-words table above exists for exactly this reason. When in doubt, go look at it before you start calculating.
Frequently Asked Questions
What are fraction word problems?
They're math questions that put fractions into everyday situations instead of just giving you a naked equation. You read a short scenario, figure out which operation to use, then solve. They show up in school from about 3rd grade onward.
How do I know which operation to use?
Clue words. "Total" and "altogether" mean add. "Left over" and "remaining" mean subtract. "Of" means multiply. "Split equally" and "per" mean divide. We built a
reference table above with the full list.
What grade level are these introduced?
Grade 3 under the
Common Core (standard 3.NF), starting with unit fractions and area models. By 5th grade, all four operations are in play. Grades 6 and 7 add multi-step problems and applications like probability.
Why are word problems harder than straight computation?
Because you have to read before you compute. Math education research, including work highlighted by the
NCTM, shows most errors happen in the translation step, not in the math itself. The good news: that reading skill improves fast with practice.
Can I use a calculator to check my work?
What are the most common mistakes?
Adding denominators (writing 1/3 + 1/4 = 2/7), forgetting to reduce to lowest terms, and picking the wrong operation because of a misread clue word. We cover all three in the
mistakes section above.
Accuracy note: Every solution on this page was verified using Python's
fractions library. Problems align with
Common Core State Standards for grades 3 through 7. Last reviewed February 2026.