Subtracting fractions is easy when the denominators match, but most real problems do not come that way. The trick is to rewrite both fractions with the same denominator first, then subtract. You can check your work with the free tools on Calc Solver.
What Unlike Denominators Mean
The denominator tells you how many equal parts the whole is split into. In 5/6 and 1/4, the wholes are split into 6 parts and 4 parts, so the pieces are different sizes. You cannot subtract different-sized pieces directly, which is why a common denominator comes first.
Step 1: Find the Lowest Common Multiple
Find the smallest number both denominators divide into. For 6 and 4, the multiples of 6 are 6, 12, 18, and the multiples of 4 are 4, 8, 12, so the lowest common multiple is 12. That number becomes the new denominator for both fractions.
Step 2: Make Equivalent Fractions
Convert each fraction to twelfths without changing its value. Multiply the top and bottom of 5/6 by 2 to get 10/12, and multiply the top and bottom of 1/4 by 3 to get 3/12. Both fractions now describe the same size pieces.
Step 3: Subtract the Numerators
Subtract the top numbers and keep the denominator: 10/12 minus 3/12 is 7/12. The denominator never changes during subtraction, because it only names the size of the pieces.
Step 4: Simplify the Answer
Check whether the result can be reduced. The numbers 7 and 12 share no common factor except 1, so 7/12 is already in simplest form and the problem is done.
Common Mistakes to Avoid
First, subtracting the denominators as well as the numerators, which gives a wrong answer. Second, forgetting to multiply the numerator when you change the denominator. Third, skipping the final simplification step. A quick check is to estimate: 5/6 is close to 1 and 1/4 is small, so an answer near 7/12 makes sense.
Practice Problems to Try
Solve 7/8 – 1/3, then 5/9 – 1/6, then 11/12 – 3/8. For each one, find the lowest common multiple, convert, subtract, and simplify.