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We learn how to add two or more fractions with the same or different denominators through the addition of fractions. Fraction addition is dependent on two main factors:
- Same denominators
- Different denominators
If the denominators of two fractions are the same, the fractions can be combined directly since they are considered to be similar fractions. However, if the denominators differ (these fractions are known as unlike fractions), we must first make the denominators equal before adding the fractions. Learn more about like and unlike fractions on here.
Addition of Fractions With Same Denominators
If the denominators of two or more fractions are identical, we can simply add the numerators while maintaining the equality of the denominators.
To add fractions with the same denominator, use these steps:
- Add the numerators together while maintaining the common denominator.
- Create the fraction in a more straightforward form.
For example: Add the fractions: 5/6 and 7/6.
Since the denominators are identical, therefore we can add the numerators directly.
(5/6) + (7/6) = (5 + 7)/6 = 12/6
Simplify the fraction
12/6 = 2
Hence, the sum of ⅚ and 7/6 is 2.
Fraction Addition With Different Numerators
We cannot determine the numerators directly when two or more fractions with various denominators are combined.
To add fractions with different denominators, follow these steps:
- Check the denominators of the fractions.
- By calculating the LCM of the denominators and rationalizing them, make the fraction denominators the same.
- Keeping the denominator constant, multiply the fractions’ numerators.
- To obtain the total, simplify the fraction.
Just an example: Add 3/12 + 5/2
Solution: Both the fractions 3/12 and 5/2 have different denominators.
We can write 3/12 = ¼, in a simplified fraction.
Now, ¼ and 5/2 are two fractions.
LCM of 2 and 4 = 4
Multiply 5/2 by 2/2.
5/2 x 2/2 = 10/4
Now add ¼ and 10/4
¼ + 10/4 = (1+10)/4 = 11/4
Hence, the sum of 3/12 and 5/2 is 11/4.
Adding Fractions With Whole Numbers
Three easy steps will add the fraction and the whole number:
- In the form of a fraction, write the given full number (for instance, 3/1)
- Add the fractions after matching the denominators.
- Simplify the fraction
Just an example: Add 7/2 + 4
Here, 7/2 is a fraction and 4 is a whole number.
We can write 4 as 4/1.
Now making the denominators same, we get;
7/2 and 4/1 x (2/2) = 8/2
Add 7/2 and 8/2
7/2 + 8/2 = 15/2
Hence, the sum of 7/2 and 4 is 15/2.
Adding Fractions with Co-prime Denominators
Co-prime denominators: The denominators that share only one other common factor are those.
Let’s use the following steps to learn how to add fractions with co-prime denominators:
- Verify whether the denominators are co-prime.
- Multiply the first fraction’s numerator and denominator by the other fraction’s denominator, then multiply the second fraction’s numerator and denominator by the first fraction’s denominator.
- Add the resulting fractions and simplify
Just an example, the addition of fractions 9/7 and 3/4 can be done as follows.
The denominators 7 and 4 are coprime since they have only one highest common factor 1.
So, (9/7) + (3/4) = [(9 × 4) + (3 × 7)]/ (7 × 4)
= (36 + 21)/28
= 57/28
Adding Mixed Fractions
Combining a whole number and a fraction results in a mixed fraction. Two mixed fractions must first be transformed into improper fractions before being added together.
Follow the below steps to add mixed numbers:
- Create incorrect fractions from the provided mixed fraction.
- Verify whether the denominators are identical or different.
- If there are distinct denominators, then explain them.
- Fractions are added, then simplified.
Let’s use the following example to clarify how to combine mixed fractions:
Example: Add : 3 ⅓ + 1 ¾
Solution:
Step1: Convert the given mixed fractions to improper fractions.
3 ⅓ = 10/3
1 ¾ = 7/4
Step 2: Make the denominators same by taking the LCM and multiplying the suitables fractions for both.
LCM of 3 and 4 is 12.
So, 10/3 = (10/3) × (4/4) = 40/12
7/4 = (7/4) × (3/3) = 21/12
Step 3: Take the denominator as common and add numerators. Then, write the final answer.
(40/12) + (21/12) = (40 + 21)/12 = 61/12
Therefore, 3 ⅓ + 1 ¾ = 61/12 = 5 1/12
Subtraction of Fractions
Mathematical procedures like addition and subtraction are comparable, as we all know. Additionally, addition involves adding two or more numbers, and subtraction involves taking a number away from another. As a result, fraction subtraction likewise adheres to the same rule as fraction addition.
For given fractions, if the denominators are the same, we can simply remove the numerator while maintaining the original denominator.
If a fraction has a different denominator, we must first rationalize it before we may subtract.
Some examples are:
Example 1: Subtract ⅓ from 8/3.
Solution: We need to find,
8/3 – ⅓ = ?
We may immediately subtract the two fractions 13 and 8/3 because their common denominator is 13.
8/3 – ⅓ = (8-1)/3 = 7/3
Example 2: Subtract ½ from ¾.
Solution: We need to subtract ½ from ¾, i.e.,
¾ – ½ = ?
We must rationalize the two fractions by using the LCM because the denominators of the two fractions differ.
LCM (4,2) = 4
Now multiply the ½ by 2/2, to get 2/4
Therefore,
¾ – 2/4 = (3-2)/4 = ¼
Hence, ¾ – ½ = ¼
Solved Examples
Let’s work through some fraction addition-based challenges.
Q. 1: Add 1/2 and 7/2.
Solution: Given fractions: 1/2 and 7/2
Since the denominators are identical, we can simply add the numerators in this case while leaving the denominator alone.
Therefore,
1/2 + 7/2
= (1+7)/2
= 8/2
=4
Q. 2: Add 3/5 and 4.
Solution: We can write 4 as 4/1
Now, 3/5 and 4/1 are the two fractions to be added.
We must first simplify the denominators because they are different in this case before adding the fractions.
Hence,
3/5 + 4/1
Taking LCM of 5 and 1, we get;
LCM(5,1) = 5
In order to find the second fraction, 4/1, we must multiply it by 5 in both the numerator and denominator.
(4×5)/((1×5) = 20/5
Now 3/5 and 20/5 have a common denominator, i.e. 5, therefore, adding the fractions now;
3/5 + 20/5
= 23/5
Addition of Fraction Worksheet
One of the key concepts in grades 6, 7, and 8 are fraction addition. Here, a worksheet for adding fractions is available. You’ll be able to quickly and simply solve fraction addition sums after practicing the questions on this worksheet. Practice using the fraction addition worksheet provided on this site to succeed in tests.
Practice Questions
- ⅜ + ⅝ =
- 1(⅓) + 3(5/2) =
- 2(¾) + ___ = 7
- ⅖ + ⅔ =
- 3/7 + 2 + 4/3 = ?
Visit Knowledge Glow to learn much more mathematical topics in an interesting way.
Frequently Asked Questions – FAQs
How Do You Combine Two Fractions With Various Denominators?
To add two fractions with distinct denominators, we must remove the LCM from the denominators and change them to the same value. The fractions’ numerators should then be added while maintaining the common denominator. For instance, ½ + ⅗
LCM of 2 and 5 = 10
= (5/5) x (½) + (⅗) x (2/2)
= (5+6)/10
= 11/10
What Guidelines Apply While Adding and Subtracting Fractions?
To add and subtract fractions, use two straightforward rules. We can add and subtract fractions directly if the denominators match. However, if the denominators differ, we must rationalize the denominators by determining the LCM of the two, and then we must add the fractions.
How Do You Add Fractions and Whole Numbers?
If we add a whole number and a fraction, then we need to first write the whole number in the form of a fraction. For example, by adding 3 and ½ we get,
3+½ = 3x(2/2) + ½ = 6/2 + ½ = 7/2
How Do You Add Big Fractions?
Let us take two fractions: 11/24 and 9/60
LCM of 24 and 60 = 120
Therefore,
= (11/24)x(5/5) + (9/60)x(2/2)
= (55+18)/120
= 73/120
How May Fractions With Similar Denominators Be Added?
Let us say, ⅗ and 7/5 are two fractions. Since ⅗ and 7/5 are two like fractions, having the same denominator, we can add the numerators directly.
Therefore,
⅗ + 7/5 = (3+7)/5 = 10/5 = 2
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