Fractions worksheet, grades 5-6
Adding and Subtracting Fractions
- Unlike denominators and equivalent fractions
- Fraction data table with 3 questions
- Students write 3 of their own word problems
- Answer key, 4-page printable PDF
$4.00
Adding and Subtracting Fractions With Unlike Denominators: A Grade 5 Guide
Math, grades 5-6
Adding and subtracting fractions with unlike denominators is one of the big jobs of grade 5 math. Here is a step-by-step method, the mistakes to watch for and a short practice set to check what students can do.
Short answer: To add or subtract fractions with unlike denominators, find a common denominator, rewrite each fraction as an equivalent fraction with that denominator, then add or subtract the numerators and keep the denominator. Simplify the result. For example, 3/5 - 1/10 becomes 6/10 - 1/10, which is 5/10, or 1/2.
Why do fractions need a common denominator before you add or subtract?
The denominator tells you the size of the pieces. You can only add or subtract pieces of the same size. One half and one quarter are both "one piece", but they are not the same amount, so 1/2 + 1/4 is not 2/6 or 2/4.
Rewriting the fractions with a common denominator cuts both wholes into same-size pieces. Then 1/2 becomes 2/4, and 2/4 + 1/4 = 3/4. This is the idea behind CCSS 5.NF.A.1: replace the fractions with equivalent fractions so they share a denominator, then add or subtract.
If students can explain this step, the procedure has something to hang on. Before any practice, ask them to draw two fraction bars and show why the pieces have to match.
How do you add and subtract fractions with unlike denominators step by step?
- Check the denominators. If they are already the same, go straight to step 4.
- Find a common denominator. Look for the least common multiple. Often one denominator is a multiple of the other: 10 is a multiple of 5, so 10 works for fifths and tenths.
- Rewrite as equivalent fractions. Multiply the numerator and the denominator by the same number. Whatever you do to the bottom, you do to the top.
- Add or subtract the numerators. Keep the denominator the same.
- Simplify and check. Divide the numerator and denominator by their greatest common factor. Then ask whether the answer makes sense.
Worked example from the worksheet: 3/5 - 1/10
- Denominators 5 and 10 are different. 10 is a multiple of 5, so the common denominator is 10.
- 3/5 = 6/10 (multiply top and bottom by 2). 1/10 stays as it is.
- 6/10 - 1/10 = 5/10.
- 5/10 simplifies to 1/2.
- Check: 3/5 is a bit more than a half, and we took away a small piece, so an answer of exactly one half is reasonable.
Worked example from the data table: how much more pizza did Bob eat than Alice?
Bob ate 1/4 and Alice ate 1/6. The least common multiple of 4 and 6 is 12. So 1/4 = 3/12 and 1/6 = 2/12. Then 3/12 - 2/12 = 1/12. Bob ate 1/12 of a pizza more than Alice.
What are the most common mistakes with unlike denominators?
| Mistake | Example | How to address it |
|---|---|---|
| Adding the denominators | 1/2 + 1/4 = 2/6 | Go back to the fraction bars. 2/6 is less than 1/2, so the answer cannot be right. |
| Changing only the denominator | 3/5 = 3/10 | Say it every time: what you do to the bottom, you do to the top. |
| Using a common denominator but not simplifying | Leaving 5/10 instead of 1/2 | Make "simplify and check" a fixed last step. |
| Multiplying denominators when a smaller one works | Using 24 for sixths and quarters instead of 12 | This is not wrong, but it makes simplifying harder. Show the least common multiple as the shortcut. |
| Subtracting in the wrong order | 1/10 - 3/5 in a "how much more" question | Ask which amount is bigger before writing the subtraction. |
What is on the Adding and Subtracting Fractions worksheet?
Adding and Subtracting Fractions by The Learning Edit is a 4-page PDF for grades 5-6: a cover, two pages of tasks and an answer key. It is a short practice set with nine tasks, so think of it as a warm-up, a quick check or homework, not a full unit.
| Task | What students do | The idea behind it |
|---|---|---|
| Part 1: 1/2 + 2/4 | Add halves and quarters | Notice that 2/4 is the same as 1/2. Students who rewrite first find the sum quickly. |
| Part 1: 3/5 - 1/10 | Subtract fifths and tenths | One denominator is a multiple of the other (worked above). |
| Part 1: 1/2 with a denominator of 6 | Write an equivalent fraction | Multiply top and bottom by the same number. The base skill for everything else. |
| Part 2: who ate the most pizza? | Compare 1/6, 1/4, 1/6 and 5/12 | Rewrite all four as twelfths, then compare numerators. |
| Part 2: how much more did Bob eat than Alice? | Subtract 1/6 from 1/4 | Common denominator of 12 (worked above). |
| Part 2: Alice and Charlie combined | Add 1/6 + 1/6 | Same denominators, so add the numerators, then simplify. |
| Part 3: write your own problems | One addition, one subtraction and one comparison word problem | Students show what each operation means in a real situation. Answers vary. |
The answer key on page 4 gives the answers for Parts 1 and 2, including the twelfths working for the Bob and Alice question. Part 3 answers vary, so you check those yourself. For a routine to teach the write-your-own page, see fraction word problems for 5th and 6th grade.
How can you use this fractions practice set in class?
Plan for about 20-30 minutes. It works as a warm-up, a review before a test, homework, a sub plan or a pre-test check before you start teaching unlike denominators. In grade 6, use it as a review of grade 5 work. It matches CCSS 5.NF.A.1 and 5.NF.A.2. The file is A4 and prints on US Letter with fit-to-page. It costs $4.00 from The Learning Edit.
Questions teachers ask
Do students have to use the least common denominator?
No. Any common denominator gives the right answer after simplifying. The least common denominator just keeps the numbers smaller.
What grade learns to add fractions with unlike denominators?
In the Common Core standards it is a grade 5 skill (5.NF.A.1). Grade 6 classes often review it.
How long does the worksheet take?
About 20-30 minutes. It has nine tasks across three parts.
Does the worksheet include mixed numbers?
No. The tasks use fractions without mixed numbers. It focuses on common denominators, equivalent fractions, comparing and word problems.
Is there an answer key?
Yes, on page 4. It covers Parts 1 and 2. Part 3 asks students to write their own problems, so the answers vary.
Can I use it as a pre-test?
Yes. Part 1 shows quickly who can already find a common denominator, and Part 2 shows who can apply it to data.
A quick fractions check, ready to print
Nine tasks on unlike denominators, a fraction data table and an answer key for $4.00.
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Adding and Subtracting Fractions worksheetFraction word problems for grades 5-6All resources by The Learning Edit
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