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L.2 Subtract fractions with unlike denominators

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What does it mean to subtract fractions with unlike denominators?

Subtracting fractions with unlike denominators means finding the difference between two fractions that have different bottom numbers (denominators). To subtract them, you first need to make the denominators the same.

Example:
  • 3412
  • Both denominators are different (4 and 2), so we must find a common denominator before subtracting.
Note

The denominator shows how many equal parts make up a whole. You can only subtract fractions when the parts are the same size.

How to find a common denominator

To subtract fractions with different denominators, find a common denominator—usually the least common multiple (LCM) of the denominators. Then, make equivalent fractions that share that denominator.

Steps:
  • Step 1: List the denominators. Example: 4 and 2.
  • Step 2: Find the least common multiple (LCM) of 4 and 2 → 4.
  • Step 3: Rewrite each fraction with the denominator 4:
    • 12 = 24
Note

Always make sure both fractions are written with the same denominator before subtracting. The numerator changes, but the denominator stays the same.

How to subtract after finding a common denominator

Once the fractions have the same denominator, subtract the numerators (top numbers) and keep the denominator the same.

Example:
  • Rewrite: 3424
  • Subtract the numerators: 3 − 2 = 1
  • Result: 14
Note

Only subtract the numerators. The denominator tells how many total equal parts make up the whole and does not change.

Subtracting mixed numbers with unlike denominators

When mixed numbers have unlike denominators, convert them into fractions with a common denominator before subtracting. You may need to regroup if the top fraction is smaller than the one you are subtracting.

Example:
  • 23 from 312
  • Find the common denominator (6):
  • 312 = 336 and 23 = 46
  • Subtract: 33646 = 256
Note

If you cannot subtract because the top fraction is smaller, borrow 1 from the whole number and change it into a fraction with the same denominator before subtracting.

Check your answer

After subtracting, always check that your answer is in simplest form. Simplify the fraction if both numerator and denominator can be divided by the same number.

Example:
  • 26 can be simplified because both 2 and 6 can be divided by 2.
  • Simplified result: 13
Note

Fractions should always be written in simplest form unless the problem asks you to show all steps. Simplifying makes your final answer easier to understand.