In this page, we will learn subtracting fractions having
Type 1: Subtracting fractions with same denominators
For subtracting fractions having same denominators, subtract numerators and just write the common denominator in the final difference.
Example:
Subtract 2/5 from 3/5 Or Find 3/5 – 2/5
Solution:
Since denominator 5, is same in both 2/5 and 3/5, therefore:
In the final answer, i.e the difference of the two fractions, write 5 in denominator and 3 – 2 = 1 in numerator.
So, 3/5 – 2/5 = (3 – 2)/5
Note:
To subtract 3/5 from 2/5, i.e. to find 2/5 – 3/5
Follow the same steps
So, 2/5 – 3/5 = (2 – 3)/5 = -1/5
Type 2: Subtracting fractions having different denominators
For subtracting fractions having different denominators, follow the below steps
Step 1: Find LCM of the various denominators in the fractions.
Step 2: Write equivalent fractions of the original fractions with LCM in denominator. (to make denominators same)
Step 3: Add the equivalent fractions.
Example:
Subtract 3/4 from 5/6
Solution:
Step 1:
First, what is the LCM of the denominators 4 and 6?
4 = 2 × 2, and 6 = 2 × 3
So, LCM of 4 and 6 = 2 × 2 × 3 = 12
Step 2:
Now, write equivalent fractions for 3/4 and 5/6 having LCM 12 as the common denominator.
Equivalent fraction for 3/4
Now, 4 × ? = 12, it is
12 ÷ 4 = 3
So, multiply 3 to 1 and 4 in ¼ to get 12 in denominator.
3/4 = (3 × 3)/ (3 × 4) = 9/12
Equivalent fraction for 5/6
6 × ? = 12, it’s
12 ÷ 6 = 2
So, multiply 2 to both 5 and 6 in 5/6 to get 12 in denominator
5/6 = (5 × 2)/ (6 × 2) = 10/12
Step 3:
Finally,
To find the difference: 10/12 – 9/12
Subtract the equivalent fraction 9/12 from 10/12
10/12 – 9/12 = 1/12
Therefore,
(5/6) – (3/4) = 1/12
Short-cut for subtracting fractions having different denominators
To find (a/b) – (c/d)
First, find (a × d – b × c)/(b × d)
Next, reduce the fraction so obtained into simplest term.
Example:
Find (5/6) – (3/4)
= (5 × 4 – 3 × 6)/6 × 4
= (20 – 18)/24
= 2/24
2. Next, reduce 2/24, by cancelling the common factor 2, as below:
2/24 = (2 × 1)/ (2 × 12) = 1/12
Type 3: Subtracting fractions which are mixed numbers
Subtract mixed numbers in two different methods. They are:
1st method:
2nd method:
Example:
Find the difference: 32/3 – 23/4
Below, let us apply both of the above methods for subtracting fractions.
Method 1:
Step 1:
Subtract the whole numbers: 3 – 2 = 1, and
Subtract the fractions: 2/3 – 3/4
Now, lcm of 3 and 4 is 3 × 4 = 12
{If two numbers do not have any common factor, then their LCM is their product}
2/3 = (2 × 4)/ (3 × 4) = 8/12, and
3/4 = (3 × 3)/ (4 × 3) = 9/12
So, 2/3 – 3/4 = (8/12) – (9/12) = -1/12
Step 2:
Next, add the fractions’ difference and the whole numbers’ difference
1 + (-1/12) = 1 – 1/12 = (12/12) – (1/12) = 11/12
Method 2 is
Subtracting fractions by converting them into improper fractions.
The mixed fraction 32/3 = (3 × 3 + 2)/3 = 11/3, and
The mixed fraction 23/4 = (4 × 2 + 3)/4 = 11/4.
Step 2:
Next, subtract the above two improper fractions, for subtracting fractions
32/3 and 23/4
i.e. 32/3 – 23/4 = (11/3) – (11/4)
= (11× 4)/(3 × 4) – (11 × 3)/(4 × 3)
{converting into equivalent fractions}
= (44/12) – (33/12) = 11/12
32/3 – 23/4
Or, using the above short-cut for subtracting fractions, we have
(11/3) – (11/4)
= (11× 4 – 11× 3)/ ( 3 × 4) =
= (44 – 33)/12 = 11/12
RELATED MATH LESSONS:
New! Comments
Have your say about what you just read! Leave me a comment in the box below.