Addition and Subtraction of Fractions Explained — Step by Step (JAMB/WAEC Mathematics)
Adding and subtracting fractions requires finding a common denominator before combining the numerators, since fractions with different denominators cannot be added or subtracted directly.
This is one of the most fundamental skills in JAMB and WAEC Mathematics, underpinning many later topics involving algebraic fractions and equations. This lesson walks through the process step by step, with practical worked examples.
Quick takeaways
- Fractions can only be added or subtracted directly when they share the same denominator.
- If denominators differ, you must first find a common denominator, usually the Lowest Common Multiple (LCM) of the two denominators.
- Once denominators match, add or subtract the numerators only, keeping the denominator unchanged.
- Mixed numbers should generally be converted to improper fractions before adding or subtracting, especially when subtraction would otherwise require “borrowing.”
- Always simplify (reduce) your final answer to its lowest terms, since exams often expect fractions in simplest form.
Timestamps
- 0:00 Introduction
- 0:31 Adding Fractions
- 1:01 Worked Example 1
- 3:35 Worked Example 2
- 5:27 Worked Example 3
Why do fractions need a common denominator before adding or subtracting?
A fraction’s denominator represents how many equal parts a whole has been divided into, so fractions with different denominators represent parts of differently sized wholes. Just as you can’t directly add “3 of one size of slice” to “2 of a different size of slice” without first converting them to the same size, fractions must share a common denominator before their numerators can be meaningfully combined.
How do you add or subtract fractions with the same denominator?
When fractions already share the same denominator, simply add or subtract the numerators, keeping the denominator unchanged:
a/c + b/c = (a + b)/c
For example, 2/7 + 3/7 = 5/7. This is the simplest case, since no conversion is needed before combining the fractions.
How do you add or subtract fractions with different denominators?
When denominators differ, follow these steps:
- Find the Lowest Common Multiple (LCM) of the two denominators — this becomes your common denominator
- Convert each fraction to an equivalent fraction with this common denominator
- Add or subtract the numerators, keeping the common denominator unchanged
- Simplify the resulting fraction if possible
For example, to add 1/3 + 1/4: the LCM of 3 and 4 is 12, so 1/3 becomes 4/12 and 1/4 becomes 3/12, giving 4/12 + 3/12 = 7/12.
How do you add or subtract mixed numbers?
Mixed numbers (like 2½) combine a whole number with a fraction, and the most reliable approach is to convert them into improper fractions first, before applying the same steps as above:
- Convert each mixed number to an improper fraction
- Find a common denominator if needed
- Add or subtract the numerators
- Convert the result back to a mixed number if required, and simplify
Converting to improper fractions first is especially important for subtraction, since working directly with mixed numbers can require “borrowing” from the whole number part, which is a common source of errors if done carelessly.
Common mistakes students make with adding and subtracting fractions
- Adding or subtracting denominators directly, instead of only combining numerators once denominators match
- Using an incorrect common denominator that isn’t actually a multiple of both original denominators
- Forgetting to convert mixed numbers to improper fractions before subtracting, leading to borrowing errors
- Forgetting to simplify the final answer to its lowest terms
Frequently asked questions
Q: Why can’t you add fractions with different denominators directly? Because the denominator represents how many equal parts a whole has been divided into, so fractions with different denominators represent differently sized parts, which must be converted to a common size (denominator) before their numerators can be combined.
Q: How do you find a common denominator for two fractions? The most reliable method is to find the Lowest Common Multiple (LCM) of the two denominators, then convert each fraction to an equivalent fraction using that common denominator.
Q: Should you convert mixed numbers before subtracting them? Yes, converting mixed numbers to improper fractions first is generally the most reliable approach, since it avoids the borrowing errors that can occur when subtracting mixed numbers directly.
Q: Why is it important to simplify a fraction after adding or subtracting? Exams typically expect answers in their simplest form, so failing to simplify a correct but unreduced fraction can result in lost marks even when the underlying calculation was correct.
Want to build on this with more advanced algebra? Read our lesson on changing the subject of a formula →
This is one topic from our full JAMB & WAEC Maths course — see everything covered →
