Adding Fractions with Unlike Denominators Worksheets (original) (raw)

Last Updated : 23 Jul, 2025

Welcome to our Adding Fractions with Unlike Denominators Worksheet! When adding fractions, it's easy when the denominators (bottom numbers) are the same. However, when they're different, we need to find a common denominator first. This worksheet will help you practice this important skill.

Remember, to add fractions with unlike denominators, follow these steps:

**Step 1: Find the least common multiple (LCM) of the denominators.

**Step 2: Convert each fraction to an equivalent fraction with the LCM as the denominator.

**Step 3: Add the numerators of the equivalent fractions.

**Step 4: Simplify the result if possible.

What is Adding Fractions with Unlike Denominators?

Adding fractions with different denominators means that you need to add fractions with different denominators. In this case, you convert the given fractions into similar fractions to get a common denominator and make the addition easier.

This is done by finding the least common multiple (kgV) of the given denominators. Convert each fraction to get a common denominator and then add the numerators to get the sum.

Solved Examples on Adding Fractions with Unlike Denominators

**Problem 1: 1/3 + 1/4

**Solution:

Using the formula: a/b + c/d = (ad + bc) / bd

1/3 + 1/4 = (1×4 + 1×3) / (3×4) = (4 + 3) / 12 = 7/12

Explanation: We cross-multiply 1 with 4 and 1 with 3 for the numerator, then multiply the denominators. This gives us a common denominator of 12. The final step is to add the numerators.

**Problem 2: 2/5 + 3/7

**Solution:

2/5 + 3/7 = (2×7 + 3×5) / (5×7) = (14 + 15) / 35 = 29/35

Explanation: We cross-multiply 2 with 7 and 3 with 5 for the numerator, then multiply 5 and 7 for the denominator. This gives us 29/35, which cannot be simplified further.

**Problem 3: 5/6 - 1/4

**Solution:

5/6 - 1/4 = (5×4 - 1×6) / (6×4) = (20 - 6) / 24 = 14/24 = 7/12

Explanation: We treat subtraction the same as addition, but with a negative sign. After cross-multiplying and subtracting, we get 14/24, which can be simplified by dividing both numerator and denominator by 2.

**Problem 4: 3/8 + 5/12

**Solution:

3/8 + 5/12 = (3×12 + 5×8) / (8×12) = (36 + 40) / 96 = 76/96 = 19/24

Explanation: After cross-multiplying and adding, we get 76/96. This can be simplified by dividing both numerator and denominator by 4.

**Problem 5: 2/3 + 3/4

**Solution:

2/3 + 3/4 = (2×4 + 3×3) / (3×4) = (8 + 9) / 12 = 17/12 = 1 5/12

Explanation: The result 17/12 is an improper fraction. We can convert it to a mixed number by dividing 17 by 12: 17 ÷ 12 = 1 remainder 5, so 17/12 = 1 5/12.

**Problem 6: 1/2 + 2/3 + 3/4

**Solution:

We'll do this step by step:

1/2 + 2/3 = (1×3 + 2×2) / (2×3) = (3 + 4) / 6 = 7/6

Now we add this result to 3/4:

7/6 + 3/4 = (7×4 + 3×6) / (6×4) = (28 + 18) / 24 = 46/24 = 23/12 = 1 11/12

Explanation: We first add the first two fractions, then add the result to the third fraction. The final step is simplifying 46/24 to 23/12 and converting to a mixed number.

**Problem 7: 5/8 - 1/3

**Solution:

5/8 - 1/3 = (5×3 - 1×8) / (8×3) = (15 - 8) / 24 = 7/24

Explanation: We treat subtraction as adding a negative fraction. After cross-multiplying and subtracting, we get 7/24, which cannot be simplified further.

**Problem 8: 3/5 + 7/10

**Solution:

3/5 + 7/10 = (3×10 + 7×5) / (5×10) = (30 + 35) / 50 = 65/50 = 13/10 = 1 3/10

Explanation: After cross-multiplying and adding, we get 65/50. This can be simplified by dividing both numerator and denominator by 5, giving 13/10, which can be written as a mixed number.

**Problem 9: 2/9 + 5/6

**Solution:

2/9 + 5/6 = (2×6 + 5×9) / (9×6) = (12 + 45) / 54 = 57/54 = 19/18 = 1 1/18

Explanation: After cross-multiplying and adding, we get 57/54. This can be simplified by dividing both numerator and denominator by 3, giving 19/18, which can be written as a mixed number.

**Problem 10: 4/7 - 2/5 + 1/3

**Solution:

We'll do this step by step:

4/7 - 2/5 = (4×5 - 2×7) / (7×5) = (20 - 14) / 35 = 6/35

Now we add this result to 1/3:

6/35 + 1/3 = (6×3 + 1×35) / (35×3) = (18 + 35) / 105 = 53/105

Practice Questions:

Instructions: Add the following fractions given below:

Q 1: 1/3 + 1/4 = ____

Q 2: 2/5 + 3/8 = ____

Q 3:3/4 + 1/6 = ____

Q 4: 1/2 + 2/3 = ____

Q 5:3/8 + 5/6 = ____

Q 6:2/3 + 3/5 = ____

Q 7:1/4 + 3/10 = ____

Q 8: 5/6 + 1/3 = ____

Q 9: 2/7 + 3/14 = ____

Q 10: 3/5 + 1/4 = ____

Summary

This worksheet on adding fractions with unlike denominators provides students with practice in finding common denominators and performing fraction addition. It includes 10 practice questions and 10 solved examples that demonstrate the step-by-step process of converting fractions to equivalent forms with a common denominator, adding the numerators, and simplifying the results when possible. This skill is crucial for more advanced mathematical concepts and real-world applications involving fractions.