The concept of fractional addition is one of the most fundamental topics taught in elementary and secondary schools. Students can easily understand a variety of addition of fractions questions with detailed explanations by using the resources below. These questions can be used by students to acquire a quick overview of the topics. Examine the detailed explanations for each question to double-check your answers. Click here for more information about the addition of fractions.

Addition of Fractions

Because fractions include a numerator and a denominator separated by a bar, adding fractions would be a little different than adding numbers. Making the denominators equal adjusts fractions for addition. Unlike fractions are changed to like fractions to enable addition easier.

Also, read: Fractions.

Addition of Fractions Questions with Solutions

Addition of Fractions with Same Denominators

Step 1: Make sure the fractions’ denominators are the same. If so, move on to step 2.

Step 2: Add the numerators and divide by the common denominator to get the total.

Step 3: If necessary, simplify the fraction to its simplest form.

1. Add the fraction: 5/7 + 2/7.

Solution:

Given: 5/7 + 2/7

Here, the denominators of both fractions are the same, i.e. 7.

Hence, we can add the numerators and divide them by the common denominator.

5/7 + 2/7 = (5+2)/7

5/7 + 2/7 = 7/7

Further, the fractions can be simplified as follows:

5/7 + 2/7 = 1/1.

2. Find the sum: 10/2 + 5/2.

Solution:

Given: 10/2 + 5/2.

Since the denominators of the given fractions are equal, we can add the numerators.

Hence, we get

10/2 + 5/2 = (10 + 5)/2

10/2 + 5/2 = 15/2

Now, the fraction 15/2 cannot be simplified further.

Therefore, 10/2 + 5/2 is 15/2.

3. Add the fractions: 71/9 + 19/9.

Solution:

Given: 71/9 + 19/9.

Here, the denominators of the given two fractions are the same.

71/9 + 19/9 = (71+19)/9

71/9 + 19/9 = 90/9

Thus, it can be further simplified as:

71/9 + 19/9 = 10/1

4. Find the sum of 12/3 and 3/3.

Solution:

Given two fractions are 12/3 and 3/3.

Here, both fractions have the same denominator, i.e. 3.

Hence, we can directly add the numerator and keep the common denominator as 3.

i.e.,

12/3 + 3/3 = (12+3)/3

12/3 + 3/3 = 15/3

Now, the simplified form is:

12/3 + 3/3 = 5/1.

Therefore, the sum of 12/3 and 3/3 is 5/1.

Addition of Fractions with Different Denominators

Step 1: Check the fractions’ denominators. If the fractions’ denominators are different, move on to step 2.

Step 2: Find the LCM of the denominators and rationalise them to make the denominators of the fractions the same.

Step 3: Add the fractions’ numerators while keeping the denominator the same.

Step 4: To get the final sum, simplify the fraction.

5. Add the fraction: 2/3 + ½.

Solution:

Given fractions are 2/3 and 1/2.

Here, the denominators of the fractions are different. So, take the LCM of 2 and 3 to make denominators the same.

Thus, LCM of 2 and 3 is 6.

Therefore,

2/3 + 1/2 = 4/6 + 3/6

Now, the denominator of both fractions are the same, i.e. 6

2/3 + 1/2 = (4 + 3)/6

2/3 + 1/2 = 7/6, which cannot be simplified further.

Hence, 2/3 + 1/2 is 7/6.

Also, read: Like and Unlike Fractions.

6. Find the sum of the fractions 4/3 and 3/5.

Solution:

Given fractions: 4/3 and 3/5.

Since the denominators are different, take the LCM of 3 and 5.

Thus, the LCM of 3 and 5 is 15.

Hence, 4/3 + 3/5 = 20/15 + 9/15

4/3 + 3/5 = (20 + 9)/15

4/3 + 3/5 = 29/15.

Now, the fraction 29/15 cannot be simplified further.

Hence, the sum of 4/3 and 3/5 is 29/15.

7. 2/7 + 5/4 = _____.

Solution:

Given: 2/7 + 5/4

Take the LCM of 7 and 4 since the denominators are different.

As we know, the LCM of 4 and 7 is 28.

Therefore, 2/7 + 5/4 = 8/28 + 35/28

Now, add the numerators, we get

2/7 + 5/4 = (8 + 35) / 28

2/7 + 5/4 = 43/28

Hence, 2/7 + 5/4 = 43/28.

8. The sum of 8/3 and 4/9 is ____.

Solution:

Here, the two fractions are 8/3 and 4/9.

Now, the LCM of 3 and 9 is 9.

Hence, 8/3 + 4/9 = 24/9 + 4/9

8/3 + 4/9 = (24 + 4) / 9

8/3 + 4/9 = 28/9

Therefore, the sum of 8/3 and 4/9 is 28/9.

Addition of Fractions with Whole Numbers

Step 1: Substitute a fraction for the specified whole number. For example, 5 can be written as 5/1.

Step 2: Equalise the denominators and perform the addition of fractions.

Step 3: If necessary, simplify the fraction.

9. Add: 7 + 2/3.

Solution:

Given: 7 + 2/3.

Now, write 7 in the form of a fraction.

i.e ., 7 = 7/1

Hence, 7 + 2/3 = 7/1 + 2/3

Take, LCM of 1 and 3, which is equal to 3.

Hence, 7 + 2/3 = 21/3 + 2/3

7 + 2/3 = (21 + 2) / 3

7 + 2/3 = 23/3.

Therefore, the sum of 7 + 2/3 is 23/3.

10. The sum of 12 and 4/5 is ____.

Solution:

Given: 12 + 4/5.

Thus, 12 + 4/5 = 12/1 + 4/5

Now, the LCM of 1 and 5 is 5.

Hence, 12 + 4/5 = 60/5 + 4/5

12 + 4/5 = (60 + 4)/5

12 + 4/5 = 64/5.

Hence, the sum of 12 and 4/5 is 64/5.

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Practice Questions

Answer the following questions:

  1. Find the sum of 26/5 and 12/5.
  2. The sum of 17/9 and 14/7 is ____.
  3. 12 + 16/9 = ____.

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