Adding Fractions
Learn how to add fractions with the same denominator, related denominators, and how to add mixed numbers by converting to a common denominator.
Adding Fractions With the Same Denominator
When fractions have the same denominator, simply add the numerators. The denominator stays the same — it tells you the size of each part.
Visual: Adding 2/8 + 3/8
2/8 (two eighths)
3/8 (three eighths)
2/8 + 3/8 = 5/8
2/8 + 3/8 = 5/8 — just add the numerators!
Golden Rule
Only add the numerators. Never add the denominators. The denominator tells you what size the pieces are — that does not change!
Adding Fractions With Related Denominators
When denominators are related (one is a multiple of the other), convert the fraction with the smaller denominator to an equivalent fraction using the larger denominator, then add.
Example: 1/2 + 3/8
8 is a multiple of 2, so use 8 as the common denominator.
1/2 = 4/8 (multiply both by 4)
4/8 + 3/8 = 7/8
1/3 + 1/6
1/3 = 2/6
2/6 + 1/6 = 3/6 = 1/2
3/4 + 1/8
3/4 = 6/8
6/8 + 1/8 = 7/8
2/5 + 3/10
2/5 = 4/10
4/10 + 3/10 = 7/10
Adding Mixed Numbers
A mixed number has a whole number part and a fraction part (e.g. 2 3/4). To add mixed numbers, add the whole number parts separately, then add the fraction parts. If the fraction sum is greater than 1, rename it.
Example: 1 2/5 + 2 3/5
Step 1: Add whole numbers: 1 + 2 = 3
Step 2: Add fractions: 2/5 + 3/5 = 5/5 = 1
Step 3: Add together: 3 + 1 = 4
Answer: 1 2/5 + 2 3/5 = 4
Key Vocabulary
Common Denominator
A shared denominator used when adding fractions. E.g. to add 1/4 and 1/8, use 8 as the common denominator.
Mixed Number
A number made up of a whole number and a fraction, such as 2 3/4 or 1 1/2.
Improper Fraction
A fraction where the numerator is larger than the denominator, such as 7/4 or 11/5.
Simplify
To reduce a fraction to its lowest terms by dividing numerator and denominator by their HCF.
Worked Examples
Calculate 3/7 + 2/7
Same denominator — just add numerators.
3 + 2 = 5
Answer: 3/7 + 2/7 = 5/7
Calculate 1/4 + 5/8
Step 1: Common denominator = 8. Convert 1/4: 1/4 = 2/8.
Step 2: 2/8 + 5/8 = 7/8.
Answer: 1/4 + 5/8 = 7/8
Zara runs 2 1/3 km and then 1 2/3 km. How far in total?
Step 1: Add whole numbers: 2 + 1 = 3
Step 2: Add fractions: 1/3 + 2/3 = 3/3 = 1
Step 3: Total: 3 + 1 = 4
Answer: Zara ran 4 km in total.
Knowledge Check
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Key Concepts Summary
- ●When adding fractions with the same denominator, add the numerators and keep the denominator.
- ●When denominators are related, convert to a common denominator before adding.
- ●Never add the denominators — only add the numerators.
- ●For mixed numbers, add the whole parts separately from the fraction parts, then combine.
- ●Always simplify your answer if possible. E.g. 6/8 = 3/4.