Adding and Subtracting Mixed Numbers- Worksheet and Practice Tips

What Are Mixed Numbers?

A mixed number combines a whole number and a proper fraction. Think of it as shorthand for an improper fraction you haven't finished converting yet.

Examples:

• 3½ means 3 + ½
• 5¾ means 5 + ¾
• 2⅜ means 2 + ⅜

You need to know how to work with these before you can add or subtract them. Mixed numbers show up constantly in real life — recipes, construction measurements, time calculations.

Adding Mixed Numbers: The Method That Actually Works

Two ways to add mixed numbers exist. One is faster. One is less likely to make you mess up on tests. Use both.

Method 1: Add Parts Separately

Add the whole numbers together. Add the fractions together. Combine the results.

Example: 3½ + 2¼

• 3 + 2 = 5 (whole numbers)
• ½ + ¼ = ¾ (fractions)
• Answer: 5¾

This works fine until the fractions don't share a denominator. Then you need to convert first.

Method 2: Convert to Improper Fractions First

Turn every mixed number into an improper fraction, add them, then convert back.

To convert: Multiply the whole number by the denominator, add the numerator. That becomes your new numerator.

Example: 3½ → (3 × 2) + 1 = 7 → 7/2

This method eliminates the whole-number/fraction separation problem entirely. It's the reliable approach for complex problems.

When Fractions Have Unlike Denominators

You cannot add ½ and ⅓ directly. Find the least common denominator (LCD) first.

For ½ + ⅓: the LCD is 6

• ½ = 3/6
• ⅓ = 2/6
• 3/6 + 2/6 = 5/6

Do this before adding the fractions part of your mixed numbers.

Subtracting Mixed Numbers: The Hard Part

Subtraction gets tricky when the second fraction is larger than the first. You have to borrow from the whole number.

When Borrowing Is Necessary

Example: 5⅓ − 2¾

⅓ is smaller than ¾. You can't subtract ¾ from ⅓ without borrowing.

Here's what you do:

1. Convert 5⅓ to an improper fraction: (5 × 3) + 1 = 16/3
2. Find the LCD of 3 and 4 → 12
3. Convert both: 16/3 = 64/12, and 2¾ = 33/12
4. Subtract: 64/12 − 33/12 = 31/12
5. Convert back: 31/12 = 2 7/12

The borrowing step in traditional column subtraction does the same thing — it just hides the math.

Borrowing in Column Form

If you prefer subtracting vertically:

    5 ⅓
  - 2 ¾
  ------

Borrow 1 (which is 12/12) from the 5. Add it to the ⅓:

    4  (1⅓ = 16/12)
  - 2 ¾
  ------

Now subtract: 16/12 − 9/12 = 7/12. The whole numbers give you 4 − 2 = 2.

Answer: 2 7/12

Quick Reference: Adding vs Subtracting Mixed Numbers

Common Mistakes That Kill Your Answers

• Forgetting to find the LCD — adding ½ + ⅓ = 2/5 is wrong. The denominator changes only when you find common ground.
• Not simplifying at the end — 14/8 looks unfinished. Simplify to 1¾.
• Losing track of whole numbers when converting to improper fractions and back.
• Borrowing incorrectly — when you borrow 1 from the whole number in column subtraction, that 1 equals the denominator of the fraction you're working with.
• Skipping the check — convert your answer back to mixed number form and see if it makes sense.

Practice Worksheet: Adding and Subtracting Mixed Numbers

Solve these without a calculator. Show your work.

Set 1 — Same Denominators:

1. 4⅜ + 2⅛ = ?
2. 7½ − 3¼ = ?
3. 5¾ + 1¾ = ?

Set 2 — Different Denominators:

1. 3½ + 2⅓ = ?
2. 6¾ − 2⅔ = ?
3. 4⅝ + 1⅜ = ?

Set 3 — Requires Borrowing:

1. 5⅓ − 2¾ = ?
2. 8⅛ − 3½ = ?
3. 7⅔ − 4¾ = ?

Set 4 — Multiple Operations:

1. 2½ + 3¾ − 1⅛ = ?
2. 5⅔ − 1½ + 2¼ = ?

Answers

Set 1: 6½ | 4¼ | 7½

Set 2: 5⅚ | 4 1/12 | 6

Set 3: 2 7/12 | 4 5/8 | 2 11/12

Set 4: 5 1/8 | 6 5/12

How to Practice Effectively

Most students practice wrong. They do 20 problems the same way, then wonder why they still get stuck on tests.

What actually works:

• Mix it up — do addition and subtraction problems in the same session. Tests don't label which operation you need.
• Check your work backwards — subtract your answer from the larger number to see if you get the smaller number.
• Time yourself occasionally — speed matters less than accuracy, but if you're spending 10 minutes on one problem, something's wrong with your approach.
• Use the LCD method for everything — it's slower but more reliable. Master it first, then look for shortcuts.
• Identify your weak points — if borrowing consistently trips you up, drill that specifically until it doesn't.

Getting Started

Print the worksheet above. Do Set 1 first. If you get them all right, move to Set 2. If you struggle, go back and review converting between mixed numbers and improper fractions.

Don't move to borrowing problems until adding mixed numbers with different denominators is automatic. Build the foundation before adding complexity.

That's it. There's no secret. Practice the method, not the memory of answers.