How to Subtract Fractions

Visual subtraction tool

See how fraction parts become ready to subtract

Make the parts match, regroup one whole when you need more pieces, then take away the second amount.

Type the full expression

Examples: 3/4 - 1/6, 2 - 3/4, or 2 1/4 - 1 2/3.

Visual explanation

Notice the part sizes

notice

The fractions name different-sized pieces, so they are not ready to subtract yet.

First amount9/4

2 wholes

Amount to take away5/3

1 whole

1/4 part

1/3 part

These pieces are not the same size yet.

How fraction subtraction works

Subtract only parts that are the same size

Subtracting fractions is about taking away one shared unit. The denominator tells you the size of that unit; the numerator tells you how many of those units are left.

Same denominators

Seventh-pieces already match, so 5/7 - 2/7 means three seventh-pieces remain.

Unlike denominators

Fourth-pieces and sixth-pieces need to be redrawn as one shared unit before one amount can be taken away from the other.

Start the problem

Choose the right first move for the problem

Check the denominators and the fractional parts before you calculate. That prevents the two common mistakes: taking away unlike parts and trying to subtract more parts than the first amount has.

The denominators already match

Subtract the counted parts and keep the denominator.

5/7 - 2/7 = 3/7

Both fractions count sevenths, so the size of every piece stays the same while the number of pieces decreases.

The denominators are different

Rewrite both fractions as one shared part size.

3/4 - 1/6 uses twelfths

Fourths and sixths are different-sized parts. Rewrite them as twelfths before taking any parts away.

A whole number is being reduced

Regroup one whole into fractional parts when you need pieces to subtract.

3 - 1 2/3 = 2 3/3 - 1 2/3

One whole becomes three thirds, so there are enough third-pieces to take away the mixed-number fraction.

A mixed number does not have enough fractional parts

Regroup one whole before subtracting the fractional parts.

2 1/4 - 1 2/3 becomes 1 15/12 - 1 8/12

After the parts match, regroup one whole into twelfths so the first amount has enough twelfths to subtract.

Learn each case

Once you know the first move, keep the model visible. These examples show what needs to be rewritten, when a whole needs to regroup, and what remains after the subtraction.

Like denominators

Subtract fractions with the same denominator

5/7 - 2/7 = 3/7

Take away two seventh-pieces from five seventh-pieces and keep the shared unit, sevenths.

For parents: Say: "We are taking away some sevenths, so the pieces are still sevenths."

Unlike denominators

Subtract fractions with different denominators

3/4 - 1/6 = 9/12 - 2/12 = 7/12

Rewrite fourths and sixths as twelfths before subtracting.

For parents: Say: "We cannot take sixth-pieces from fourth-pieces until they name the same-sized parts."

Whole number

Subtract a mixed number from a whole number

3 - 1 2/3 = 2 3/3 - 1 2/3 = 1 1/3

Regroup one whole into thirds, then take away the mixed-number fractional part.

For parents: Say: "One whole can become three thirds, so we have third-pieces to take away."

Mixed numbers

Subtract mixed numbers by regrouping

2 1/4 - 1 2/3 = 7/12

Make twelfths first, then regroup one whole so fifteen twelfths can take away eight twelfths.

For parents: Say: "The whole is still there; we only changed it into twelfths."

Common mistakes

Avoid changing the size or amount of the parts

Subtracting denominators instead of keeping the shared unit size the same.
Rewriting only one fraction when the denominators are different.
Trying to take away more fractional parts than the first mixed number has.
Regrouping one whole but forgetting to add those new parts to the first fraction.
Stopping before reducing the remaining fraction.

Practice order

Predict the first move before you open the answer. Then enter one expression into the visual tool and compare your prediction with the bars and the solution path.

1.Same denominator: 5/7 - 2/7
2.Unlike denominators: 3/4 - 1/6
3.Whole minus mixed number: 3 - 1 2/3
4.Mixed numbers: 2 1/4 - 1 2/3

Explain it out loud

"I can subtract the top numbers once both fractions name the same-sized parts."

"If I need more parts, I regroup one whole." When a child is stuck, ask one question and wait for the model to do some of the explaining.

What size is one piece in each fraction before we subtract?
Do both fractions name the same-sized parts yet?
Do we have enough fractional parts to take away the second amount?
If not, how can one whole become more of those same-sized parts?

Common questions

Subtracting Fractions FAQ

The denominator tells the size of each part. Taking away parts changes how many parts remain, not the size of every part.