Class 5 - Addition of Fractions: Step by Step Guide with Solved Examples

Addition of fractions is an important math skill. A fraction represents a part of a whole number. When we add fractions, we combine parts to make a larger part.

For example: if you eat 1/4 of a pizza and your friend eats 1/4 of the same pizza, together you have eaten 2/4 or 1/2 of the pizza14+14=24=12.

• Numerator: The top number in a fraction

• Denominator: The bottom number in a fraction

• Fraction: A part of a whole number written as numerator/denominator

Table of Contents

• Addition of Fractions with the Same Denominators
• Addition of Fractions with Different Denominators
• Addition of Fraction and a Whole Number
• Adding Fractions with Variables
• Solved Examples on Addition of Fractions
• Practice Questions on Addition of Fractions

Addition of Fractions with the Same Denominators

If the fractions that have the same denominator. We can add directly the numerators by keeping the denominator common.

When denominators are the same, follow this simple rule:

• Add only the numerators

• Keep the denominator the same

• Simplify if possible

Formula: a/b + c/b = (a + c)/b

Example 1: Simple Addition of Like Fractions

Problem: 2/7 + 3/7 = ?

Solution:

• Numerators: 2 + 3 = 5

• Denominator: 7 (stays the same)

• Answer: 5/7

Step by step:

1. Check denominators: Both are 7

2. Add numerators: 2 + 3 = 5

3. Write answer: 5/7

4. Check if we can simplify: No, 5/7 is in simplest form

Example 2: Addition with Simplification

Problem: 3/8 + 5/8 = ?

Solution:

• Step 1: Add numerators: 3 + 5 = 8

• Step 2: Keep denominator: 8

• Step 3: Write fraction: 8/8

• Step 4: Simplify: 8/8 = 1

Answer: 1 (or 8/8)

Addition of Fractions with Different Denominators

When Two or more fractions with different denominators. Adding unlike fractions is more complex than adding like fractions.

To add fractions with different denominators, we must first make the denominators the same. We do this by finding the Least Common Denominator (LCD).

Steps to Follow:

1. Find the Least Common Denominator (LCD)

2. Convert each fraction to an equivalent fraction with the LCD

3. Add the numerators

4. Keep the new denominator

5. Simplify if needed

How to Find the LCD

The LCD is the smallest number that both denominators can divide into equally.

Example: For 1/4 and 1/6

• Multiples of 4: 4, 8, 12, 16, 20...

• Multiples of 6: 6, 12, 18, 24...

• LCD = 12 (smallest common multiple)

Example 1: Adding Unlike Fractions

Problem: 1/3 + 1/4 = ?

Solution:

Step 1: Find LCD

• Multiples of 3: 3, 6, 9, 12...

• Multiples of 4: 4, 8, 12...

• LCD = 12

Step 2: Convert to equivalent fractions

• 1/3=1×4/3×4=4/12

• 1/4=1×3/4×3=3/12

Step 3: Add the fractions

• 4/12+3/12=7/12

Answer: 7/12

Example 2: Adding Unlike Fractions with Larger Numbers

Problem: 2/5 + 3/7 = ?

Solution:

Step 1: Find LCD

• Multiples of 5: 5, 10, 15, 20, 25, 30, 35...

• Multiples of 7: 7, 14, 21, 28, 35...

• LCD = 35

Step 2: Convert fractions

• 2/5=2×7/5×7=14/35

• 3/7=3×5/7×5=15/35

Step 3: Add

• 14/35+15/35=29/35

Step 4: Simplify

• 29 and 35 have no common factors

• Answer remains 29/35

Answer: 29/35.

Addition of Fraction and a Whole Number

Any whole number can be written as a fraction with 1 as the denominator.

Examples:

• 2 = 2/1

• 5 = 5/1

• 10 = 10/1

Rule for Adding Fractions and Whole Numbers

1. Convert the whole number to a fraction (denominator = 1)

2. Find the LCD if needed

3. Add like you normally would

4. Simplify the answer

Example 1: Adding a Fraction to a Whole Number

Problem: 2 + 3/4 = ?

Solution:

Method 1 (Mixed Number):

• Keep the whole number separate

•   234

•  

  =(2×4)+34

•  

  =8+34

• =114

Method 2 (Improper Fraction):

• Convert 2 to a fraction: 2 = 8/4

• Add:  8/4+3/4=11/4

• Convert back to mixed number: 114=234

Answer:  234=114

Example 2: Multiple Whole Numbers and Fractions

Problem: 3 + 5/6 = ?

Solution:

Step 1: Convert whole number

• 3+56

Step 2: Add

• =186+56

Step 3: Convert to mixed number

• =236

Answer:=356

Example 3: Adding Multiple Fractions and Whole Numbers

Problem: 4 + 1/2 + 3/4 = ?

Solution:

Step 1: Convert whole number to fraction

• 4 = 4/1

Step 2: Find LCD for 1, 2, and 4

• LCD = 4

Step 3: Convert all fractions

• 4/1 = 16/4

• 1/2 = 2/4

• 3/4 = 3/4

Step 4: Add

• 16/4 + 2/4 + 3/4 = 21/4

Step 5: Convert to mixed number

•  214

• 214=514

•  =5 remainder 1
  
  

• =514

Answer:=514

Adding Fractions with Variables

Variables are letters (like x, y, a, b) that represent unknown numbers. When adding fractions with variables, the same rules apply.

• Like fractions with variables: Add numerators, keep denominator
• Unlike fractions with variables: Find LCD, convert, then add
• Treat variables as you would regular numbers

Example 1: Like Fractions with Variables

Problem: x/5 + 2/5 = ?

Solution:

Step 1: Check denominators

• Both have denominator 5

Step 2: Add numerators

• x + 2 = x + 2

Step 3: Write answer

• (x + 2)/5

Answer: (x + 2)/5

Example 2: Unlike Fractions with Variables

Problem: x/3 + y/4 = ?

Solution:

Step 1: Find LCD

• LCD of 3 and 4 = 12

Step 2: Convert fractions

• x/3 = 4x/12

• y/4 = 3y/12

Step 3: Add

• 4x/12 + 3y/12 = (4x + 3y)/12

Answer: (4x + 3y)/12

Example 3: Simplifying Variable Expressions

Problem: 2a/6 + 3a/6 = ?

Solution:

Step 1: Add numerators

• 2a + 3a = 5a

Step 2: Keep denominator

• 5a/6

Step 3: Simplify if possible

• 5a and 6 have no common factors

• Answer: 5a/6

Answer: 5a/6

Example 4: Mixed Variable and Number Fractions

Problem: (x + 1)/4 + 3/4 = ?

Solution:

Step 1: Check denominators

• Both are 4 

Step 2: Add numerators

• (x + 1) + 3 = x + 1 + 3 = x + 4

Step 3: Write answer

• (x + 4)/4

Answer: (x + 4)/4

Solved Examples on Addition of Fractions

Example 1: Complex Unlike Fractions

Problem: 3/8 + 5/12 = ?

Solution:

Step 1: Find LCD

• Multiples of 8: 8, 16, 24, 32...

• Multiples of 12: 12, 24, 36...

• LCD = 24

Step 2: Convert to equivalent fractions

• 3/8 = 3×3/8×3 = 9/24

• 5/12 = 5×2/12×2 = 10/24

Step 3: Add

• 9/24 + 10/24 = 19/24

Step 4: Check if simplified

• GCD(19, 24) = 1, so it's already simplified

Answer: 19/24

Example 2: Three Fractions with Different Denominators

Problem: 1/2 + 1/3 + 1/6 = ?

Solution:

Step 1: Find LCD

• Multiples of 2: 2, 4, 6, 8...

• Multiples of 3: 3, 6, 9...

• Multiples of 6: 6, 12...

• LCD = 6

Step 2: Convert fractions

• 1/2 = 3/6

• 1/3 = 2/6

• 1/6 = 1/6

Step 3: Add all numerators

• 3/6 + 2/6 + 1/6 = 6/6

Step 4: Simplify

• 6/6 = 1

Answer: 1

Example 3: Mixed Numbers

Problem: 2 1/4 + 3 1/2 = ?

Solution:

Step 1: Convert mixed numbers to improper fractions

• 2 1/4 = 9/4

• 3 1/2 = 7/2

Step 2: Find LCD

• LCD of 4 and 2 = 4

Step 3: Convert to equivalent fractions

• 9/4 = 9/4

• 7/2 = 14/4

Step 4: Add

• 9/4 + 14/4 = 23/4

Step 5: Convert back to mixed number

• 23/4 = 5 3/4

Answer: 5 3/4

Example 5: Word Problem

Problem: Sarah drinks 1/3 of a glass of milk in the morning and 1/4 of a glass in the evening. How much milk does she drink in total?

Solution:

Step 1: Identify what we need to add

• Morning: 1/3

• Evening: 1/4

• Total: 1/3 + 1/4

Step 2: Find LCD

• LCD of 3 and 4 = 12

Step 3: Convert

• 1/3 = 4/12

• 1/4 = 3/12

Step 4: Add

• 4/12 + 3/12 = 7/12

Answer: Sarah drinks 7/12 of a glass of milk in total.

Practice Questions on Addition of Fractions

1: Like Fractions (Same Denominator)

1. 2/5 + 1/5 = ?

2. 3/8 + 2/8 = ?

3. 4/9 + 3/9 = ?

4. 1/6 + 2/6 + 1/6 = ?

5. 5/10 + 3/10 = ?

2: Unlike Fractions (Different Denominators)

1. 1/2 + 1/3 = ?

2. 2/3 + 1/6 = ?

3. 3/4 + 1/8 = ?

4. 1/5 + 1/10 = ?

5. 2/5 + 3/7 = ?

3: Whole Numbers and Fractions

1. 2 + 1/4 = ?

2. 3 + 2/5 = ?

3. 5 + 3/8 = ?

4. 1 + 1/2 + 1/4 = ?

5. 4 + 1/3 + 1/6 = ?

4: Mixed Numbers

1. 1 1/2 + 2 1/4 = ?

2. 2 2/3 + 1 1/3 = ?

3. 3 1/4 + 2 3/8 = ?

4. 4 1/5 + 2 2/5 = ?

5. 1 1/6 + 2 1/3 + 1 1/2 = ?

5: Variables and Algebraic Fractions

1. x/4 + 2/4 = ?

2. a/3 + b/3 = ?

3. 2x/5 + 3x/5 = ?

4. (x + 1)/6 + 2/6 = ?

5. x/2 + x/3 = ?

6: Word Problems

1. Cooking: A recipe needs 1/2 cup of flour and 1/4 cup of sugar. How much total dry ingredients do you need?

2. Distance: John walked 1/3 of a mile in the morning and 2/5 of a mile in the afternoon. How far did he walk in total?

3. Painting: Maya painted 3/8 of a wall on Monday and 1/4 of the wall on Tuesday. How much of the wall did she paint?

4. Time: It takes 1/4 hour to drive to the store and 1/3 hour to shop. How much time did Maria spend?

5. Money: Tom has 2 1/2 dollars and his friend gives him 1 3/4 dollars. How much money does he have now?