Adding and Subtracting Fractions
Fractions need a common denominator before combining.
About this topic
You can only add or subtract fractions directly when they share a denominator, because then you are counting pieces of the same size. Then you add or subtract the numerators and keep the denominator unchanged: 2/7 + 3/7 = 5/7.
When denominators differ, find a common denominator, ideally the LCM, rewrite each fraction as an equivalent one, then combine. Always simplify the result. For 1/3 + 1/4, the LCM of 3 and 4 is 12, so we write 4/12 + 3/12 = 7/12. For subtraction, 5/6 − 1/4 becomes 10/12 − 3/12 = 7/12. With mixed numbers, convert to improper fractions or add whole parts and fractional parts separately, borrowing when needed.
Imagine eating 1/3 of a pizza at lunch and 1/4 at dinner. Together that is 7/12 of the pizza, a little over half. The same skill is used in carpentry measurements, such as adding 3/8 inch and 1/2 inch, and in combining shares of a budget.
The common mistake of adding denominators too, giving 1/3 + 1/4 = 2/7, is easy to avoid by remembering that the pieces' size does not change when you combine them. Sense-check with estimation: the answer 2/7 is smaller than 1/3 alone, which cannot be right when you are adding.
Key ideas
- Find the LCM of denominators
- Convert then add numerators only
- Simplify the result
Quick check
Use cases: where Adding and Subtracting Fractions helps
- Homework: review the key idea behind Adding and Subtracting Fractions before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Adding and Subtracting Fractions without notes.
- Visual learning: play with the interactive lab to see how Adding and Subtracting Fractions changes when you adjust its inputs.
- Teaching a friend: explain Adding and Subtracting Fractions in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Adding and Subtracting Fractions?
Fractions need a common denominator before combining.
What will I learn in Adding and Subtracting Fractions?
Find the LCM of denominators. Convert then add numerators only. Simplify the result.
Is Adding and Subtracting Fractions part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Adding and Subtracting Fractions lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Adding and Subtracting Fractions?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.