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ExplainerMathGrades 3–5

Subtracting Fractions with Unlike Denominators

What Is This?

Subtracting fractions with unlike denominators follows exactly the same process as adding them — you must find a common denominator before you can subtract. The only difference is that in Step 3 you subtract the numerators instead of adding them. If you already understand how to add fractions with unlike denominators, you are most of the way there.

Why Does It Matter?

Fraction subtraction is essential for measuring differences and finding remainders in real life. If a container is 3/4 full and you use 1/3 of it, how much is left? If a project is 5/6 complete and yesterday it was only 1/2 complete, how much progress was made? These everyday questions require subtracting fractions with unlike denominators.

How It Works

The process follows the same four steps as fraction addition — only Step 3 changes.

Step 1: Find the Least Common Denominator (LCD)

List the multiples of each denominator until you find the smallest number they share.

Step 2: Rewrite each fraction using the LCD

Multiply the numerator and denominator of each fraction by whatever number makes the denominator equal to the LCD.

Step 3: Subtract the numerators

Once both fractions have the same denominator, subtract the top numbers. The denominator stays the same.

Step 4: Simplify if possible

Divide both numerator and denominator by their greatest common factor (GCF).

Worked Example 1: 3/4 − 1/3

Step 1 — Find the LCD of 4 and 3:

  • Multiples of 4: 4, 8, 12, 16...
  • Multiples of 3: 3, 6, 9, 12...
  • LCD = 12

Step 2 — Rewrite both fractions with denominator 12:

  • 3/4 → multiply top and bottom by 3 → 9/12
  • 1/3 → multiply top and bottom by 4 → 4/12

Step 3 — Subtract the numerators:

  • 9/12 − 4/12 = 5/12

Step 4 — Can we simplify 5/12?

  • 5 and 12 share no common factor other than 1
  • Answer: 5/12

Worked Example 2: 5/6 − 3/8

Step 1 — Find the LCD of 6 and 8:

  • Multiples of 6: 6, 12, 18, 24...
  • Multiples of 8: 8, 16, 24...
  • LCD = 24

Step 2 — Rewrite both fractions:

  • 5/6 → multiply by 4/4 → 20/24
  • 3/8 → multiply by 3/3 → 9/24

Step 3 — Subtract:

  • 20/24 − 9/24 = 11/24

Step 4 — Simplify:

  • 11 is prime, so 11/24 cannot be simplified
  • Answer: 11/24

Worked Example 3: A Real-World Problem

A water tank was 7/8 full in the morning. By afternoon it was only 1/3 full. What fraction of the tank was used?

We need to find: 7/8 − 1/3

Step 1 — LCD of 8 and 3:

  • Multiples of 8: 8, 16, 24...
  • Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24...
  • LCD = 24

Step 2 — Rewrite:

  • 7/8 → multiply by 3/3 → 21/24
  • 1/3 → multiply by 8/8 → 8/24

Step 3 — Subtract:

  • 21/24 − 8/24 = 13/24

Step 4 — Simplify:

  • 13 is prime, so 13/24 cannot be simplified
  • Answer: 13/24 of the tank was used

Subtracting Mixed Numbers

When subtracting mixed numbers, subtract the whole number parts and the fraction parts separately. Sometimes you need to borrow from the whole number when the fraction you are subtracting is larger than the fraction you are subtracting from.

Example without borrowing: 3 and 5/6 − 1 and 1/4

  • LCD of 6 and 4 is 12
  • 5/6 = 10/12, 1/4 = 3/12
  • Subtract fractions: 10/12 − 3/12 = 7/12
  • Subtract whole numbers: 3 − 1 = 2
  • Answer: 2 and 7/12

Example with borrowing: 4 and 1/4 − 1 and 3/4

  • Same denominator (4) so no LCD needed
  • 1/4 − 3/4 is impossible (top number too small)
  • Borrow 1 from the whole number: 4 becomes 3, and 1/4 becomes 1 and 1/4 = 5/4
  • Subtract fractions: 5/4 − 3/4 = 2/4 = 1/2
  • Subtract whole numbers: 3 − 1 = 2
  • Answer: 2 and 1/2

Common Mistakes

Mistake 1: Subtracting the denominators

Just as with addition, the denominator is never subtracted. The denominator is matched using the LCD, and only the numerators are subtracted. 3/4 − 1/3 does not equal 2/1.

Mistake 2: Subtracting before finding the LCD

You must convert both fractions to the same denominator BEFORE subtracting. Subtracting 3/4 − 1/3 as 3−1 over 4−3 = 2/1 is completely wrong on two counts — you are both subtracting denominators and skipping the conversion step.

Mistake 3: Subtracting in the wrong order

Always subtract the smaller fraction from the larger one unless you are working with mixed numbers where borrowing handles the order automatically. 3/4 − 5/6 requires care — convert first to 9/12 − 10/12, and since 9 < 10 the answer is negative: −1/12. For Grade 3–5, most problems are set up so the result is positive.

Mistake 4: Forgetting to simplify

An answer of 4/8 is technically correct but incomplete. Always divide numerator and denominator by their GCF. 4/8 simplifies to 1/2.

Key Takeaways

  • Subtracting fractions with unlike denominators uses exactly the same LCD method as addition — only the operation in Step 3 changes
  • Find the LCD, rewrite both fractions, subtract only the numerators, simplify
  • Never subtract the denominators — only match them
  • For mixed numbers: subtract whole number parts and fraction parts separately
  • If the fraction part of the first number is smaller than the fraction part of the second, borrow 1 from the whole number
  • Always simplify your final answer

Practice and Resources

Ready to practise? Try our Grade 3–5 Subtracting Fractions Worksheet with a range of problems from straightforward subtraction to challenging word problems. Test yourself with our Grade 5 Math Practice Test. For extra fraction practice, try the Fraction Builder game.

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