How Can Students Subtract Fractions Step-By-Step?

Quick cheat I use when I'm in a rush: 1) get a common denominator, 2) convert both fractions, 3) subtract numerators, 4) simplify. It sounds obvious, but saying it out loud helps me avoid accidental slips.

If mixed numbers show up, I either turn everything into improper fractions first or I borrow from the whole number like I would with ordinary subtraction—whichever feels cleaner for that problem. For example, for 2 1/8 - 1 3/4 I convert: 17/8 - 7/4 → 17/8 - 14/8 = 3/8. I also like to reduce fractions before subtracting when possible because smaller numbers are easier to manage.

A couple of little habits keep me from getting stuck: write the steps vertically so you can see the conversion, and test your final answer by estimating with decimals. It’s a tiny routine, but it saves time and makes the whole thing feel less like a puzzle and more like a neat trick I can use anytime.

Grab a pencil and your favorite eraser—subtracting fractions becomes way less scary when you chop it into tiny, consistent steps.

First, if the fractions have the same denominator, it’s straightforward: subtract the numerators and keep the denominator. For example, 5/12 - 2/12 = 3/12, then simplify to 1/4. If the denominators are different, find the least common denominator (LCD). Convert each fraction so they share that denominator. Say you want to do 3/4 - 1/6: the LCD is 12, so 3/4 becomes 9/12 and 1/6 becomes 2/12. Then subtract the numerators: 9/12 - 2/12 = 7/12. Reduce if possible.

Mixed numbers just need a tiny conversion trick. Either convert mixed numbers to improper fractions first, or subtract whole parts and fractional parts separately (borrowing when necessary). For instance, 2 1/3 - 1 5/6: change to improper fractions: 7/3 - 11/6. LCD is 6, so 14/6 - 11/6 = 3/6 = 1/2. If borrowing is easier for you, turn 2 1/3 into 1 + 4/3 and subtract stepwise. Always simplify your result and check with a quick decimal estimate in your head to make sure the answer has the right sign and magnitude.

A few practical tips I use: reduce fractions early if you can, use prime factors or the LCM trick to get the LCD faster, and keep a scrap of paper for converting mixed numbers to improper ones. Visualizing with a number line or drawing pie slices helps when you hit that awkward moment of borrowing. It’s satisfying when a messy pair of fractions collapses neatly into a simple result—keeps me reaching for my pencil again.

Picture a pizza Cut into different slices; that’s how I picture unequal denominators when subtracting fractions, and it makes the process feel intuitive instead of abstract.

Step 1: If fractions already share a denominator, subtract the top numbers and leave the bottom. If not, find the least common denominator—the smallest number both denominators divide into. Use prime factors or just list multiples if the numbers are small. Step 2: Convert both fractions to equivalents with that common denominator by multiplying numerator and denominator by the same number. Step 3: Subtract the new numerators. Step 4: Simplify the result by dividing numerator and denominator by their greatest common factor. If you end up with a mixed number from an improper fraction, convert it back to a mixed number by dividing the numerator by the denominator.

When mixed numbers are involved, I sometimes subtract whole parts first and then fractional parts; if the fractional part of the minuend (the first number) is smaller than the subtractor’s fractional part, borrow 1 from the whole part and convert it into an equivalent fraction with the same denominator. For example, 1 1/4 minus 3/8: convert to common denominator 8, giving 5/4 - 3/8 → 10/8 - 3/8 = 7/8. A simple mental check I always do is convert the final fraction to a decimal to make sure the size feels right.