In this page, we will learn subtracting fractions having

- Same denominators
- Different denominators
- Mixed numbers
- First, (5/6) – (3/4)
- First, subtract the whole numbers and the fractions separately.
- Next,
the differences of the whole numbers and the fractions obtained in the first step*add* - First, convert the mixed fractions into improper fractions
- Next,
the two improper fractions.*subtract* **ALGEBRA 1 HELP****BEGINNING ALGEBRA****COLLEGE ALGEBRA**- ELEMENTRY ALGEBRA
**INTERMEDIATE ALGEBRA****INTRODUCTORY ALGEBRA****COLLEGE MATH****PRE ALGEBRA HELP****PRE CALCULUS**

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: 3 ^{2/3} – 2^{3/4}**

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 3^{2/3} = (3 × 3 + 2)/3 = 11/3, and

The mixed fraction 2^{3/4} = (4 × 2 + 3)/4 = 11/4.

**Step 2: **

Next, ** subtract** the above two improper fractions, for subtracting fractions

3^{2/3} and 2^{3/4}

i.e. 3^{2/3} – 2^{3/4} = (11/3) – (11/4)

= (11× 4)/(3 × 4) – (11 × 3)/(4 × 3)

{converting into equivalent fractions}

= (44/12) – (33/12) = 11/12

3^{2/3} – 2^{3/4}

*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:

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