How to Add 2 or More Fractions

Adding Fractions

Learn how to perform: adding 2 or more fractions, adding fractions with unlike denominators, addition of fractions with answers and examples, how to add 3 fractions with same or different denominators, adding fractions with whole numbers or mixed Numbers.

Overall Steps to Add Fractions:

1. Find a Common Denominator: Identify the least common multiple (LCM) of the denominators.
2. Convert Fractions: Express each fraction with the common denominator found in step 1.
3. Add Numerators: Add the numerators of the fractions together.
4. Simplify (if necessary): Simplify the resulting fraction, if possible, by finding the greatest common divisor (GCD) of the numerator and denominator and dividing both by it.

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Special Cases to Add Fractions:

• When the Denominators are Already the Same: Simply add the numerators and keep the denominator the same.
• When One Fraction is a Whole Number: Convert the whole number into a fraction with the same denominator as the other fractions before adding.
• When Fractions are Mixed Numbers: Convert mixed numbers into improper fractions before adding.

Example 1: Adding 2 Fractions

Add Given Fractions: 1/4 + 2/3

Step 1: Find LCM of 4 and 3 → LCM(4, 3) = 12

Step 2: Convert fractions: 1/4 becomes 3/12, 2/3 becomes 8/12

Step 3: Add numerators: 3/12 + 8/12 = 11/12

Example 2: Adding 3 Fractions

Add Given Fractions: 1/2 + 1/3 + 1/4

Step 1: Find LCM of 2, 3, and 4 → LCM(2, 3, 4) = 12

Step 2: Convert fractions: 1/2 becomes 6/12, 1/3 becomes 4/12, 1/4 becomes 3/12

Step 3: Add numerators: 6/12 + 4/12 + 3/12 = 13/12

Step 4: Simplify if necessary → 13/12 cannot be simplified

Example 3: Adding 4 Fractions

Add Given Fractions: 1/5 + 2/3 + 3/4 + 1/8

Step 1: Find LCM of 5, 3, 4, and 8 → LCM(5, 3, 4, 8) = 120

Step 2: Convert fractions: 1/5 becomes 24/120, 2/3 becomes 40/120, 3/4 becomes 90/120, 1/8 becomes 15/120

Step 3: Add numerators: 24/120 + 40/120 + 90/120 + 15/120 = 169/120

Step 4: Simplify if necessary → 169/120 cannot be simplified

Example 4: Adding Fractions with Common Denominators

Add Given Fractions: 1/4 + 3/4

Step 1: Denominators are already the same

Step 2: Add numerators: 1/4 + 3/4 = 4/4

Step 3: Simplify if necessary → 4/4 = 1 (Whole Number)

Example 5: Adding a Whole Number and a Fraction

Add Given Fractions: 2 + 1/3

Step 1: Convert whole number to fraction with the same denominator as the fraction: 2 = 6/3

Step 2: Add numerators: 6/3 + 1/3 = 7/3

Example 6: Adding Mixed Numbers

Add Given Fractions: 1 1/4 + 2 1/2

Step 1: Convert mixed numbers to improper fractions: 1 1/4 = 5/4, 2 1/2 = 5/2

Step 2: Find LCM of 4 and 2 → LCM(4, 2) = 4

Step 3: Convert fractions: 5/4 becomes 5/4, 5/2 becomes 10/4

Step 4: Add numerators: 5/4 + 10/4 = 15/4