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Subtracting Fractions
Get ready to become an expert at subtracting fractions & mixed
numbers!
Subtracting with the same denominator.
Subtracting fractions that have the same denominator is simple. You
subtract the numerators and write the difference over the common
denominator. If your answer is an improper fraction, re-write it as a
mixed number.
Example:
56
16
-
46
=23 Solve on your
own. Click for the
answer!
Subtracting fractions with different denominators.Subtracting fractions with different denominators is impossible. In order for fractions to be subtracted from one another, they must have the
same number of parts. The denominator represents the number of parts. Therefore, you must find a
common denominator.
Why?
You have a 5/6 of a pizza left. You eat 1/4 of the pizza that is remaining. How much of leftover pizza
remains now?
A common denominator is necessary so that each piece of pizza is the same size and can be added with the others. What is a common denominator
for 6 and 4?12
- =
What are the steps?
To subtract fractions:
1. Find a common denominator if there isn’t one already. 2. Convert each of your fractions into an equivalent
fraction using the common denominator. 3. Subtract the numerators.4. Write the difference as the numerator in your answer.
The denominator will be your common denominator.5. If your answer is an improper fraction, convert to a
mixed number. Simplify if necessary.
35
47
-
35
Click for the answer!
What is the least common denominator?
3547-
Click for the answer!
How do you re-write the fractions using the common denominator?
35
35
=
=x 5
x 5
x 7
x 721
20
Solve:
35
47
-
135
=
Rewrite using the least common
denominator, then solve on your own.
Click for the answer!
2135
2035
-
What is the least common denominator?
78
15
-
40
Click for the answer!
Solve:
78
15
-
2740
=
Rewrite using the least common
denominator, then solve on your own.
Click for the answer!
3540
840
-
Solve:
56
23
-
16
=
Rewrite using the least common
denominator, then solve on your own.
Click for the answer!
56
46
-
When you subtract multi-digit numbers, do you subtract
from:
Right to left? Left to right?
Right to Left!
For example: 485123
You subtract 5-3 first!-
When we subtract mixed numbers, we do the same
thing!
Right to Left!Subtract the fractions before the whole
numbers
For example: 4 ¾ 1 ¼3
You subtract ¾ - ¼ first!-
24
But Why?
We subtract the fractions before the whole numbers in order to determine if we need to
borrow from the whole number.
Example:
-23
4 14
2
-
2314
=-
8123
12
Click to move through the
problem visually.
512
Example:
-23
4 14
2Click to move through the
problem visually.
512
You already figured out that - is
23
14
512
Next, subtract the whole numbers
4 – 2 = 2
2 + = 2512
512
We subtract the fractions before the whole numbers in order to determine if we need to
borrow from the whole number.
What are the steps?
To subtract mixed numbers:
1. Find a common denominator if there isn’t one already. 2. Convert each of your fractions into an equivalent fraction
using the common denominator. 3. Subtract the numerators.
• If you cannot subtract the numerators because the first numerator is smaller than the second, you need to borrow a whole from the first whole number and add it onto the first fraction.
4. Write the difference as the numerator in your answer. The denominator will be your common denominator.
5. If your answer is an improper fraction, convert to a mixed number.
6. Simplify if necessary.7. Subtract the whole numbers.8. Combine with the fraction difference if necessary.
Solve:
45
12
4 - 2
310
=
Rewrite using the least common
denominator, then solve on your own.
Click for the answer!
810
510
-4 – 2 = 2
310
2 + = 2310
Solve:
34
13
6 - 3
512
=
Rewrite using the least common
denominator, then solve on your own.
Click for the answer!
912
412
-6 - 3 = 3
512
3 + = 3512
Solve:
310
14
7 - 1
120
=
Rewrite using the least common
denominator, then solve on your own.
Click for the answer!
620
520
-7 – 1 = 6
120
6 + = 6120
What If?
4723-
We can’t subtract 14 from 12… So now what?
What if you re-write your fractions using a common denominator, and the first fraction
is larger than the second?
21
21
=
=x 7
x 7
x 3
x 312
14
2
1
4723-
Click to see the steps you take to solve a problem like this!
You need to “borrow” a whole from the whole number part of the first mixed
number.
21
21
=
=x 7
x 7
x 3
x 3 12
14
2
1
1. Borrow 1 from the 2 in the form of a fraction.
2121
2. To make it easy on you, write the fraction as the common denominator over the common denominator.
13. Add your borrowed whole onto the fraction.
4. Now you can subtract!
+3321
=
1921
5. Simplify if necessary.
1234-
You Try!Solve on your own, then click to check your
answer.
4
4
=
=
x 2
x 2 2
3
5
2
2. Borrow 1 from the 4 in the form of a fraction. 4
43. To make it easy on you, write the fraction as the common denominator over the common denominator.
34. Add your borrowed whole onto the fraction.
5. Now you can subtract!
+64
=
34
1. Rewrite with a common denominator
