Addition and Subtraction
Addition combines amounts while subtraction finds the difference or removes some.
About this topic
Addition combines quantities into a total, while subtraction finds how much is left or how far apart two numbers are. They are inverse operations, meaning one undoes the other: if 47 + 38 = 85, then 85 − 38 = 47. This relationship is the best way to check your work.
Addition is commutative (3 + 5 = 5 + 3) and associative, so you can regroup numbers to make mental maths easier. For example, 38 + 47 + 12 is easier if you add 38 and 12 first to get 50, then add 47 to reach 97. Subtraction has no such freedom, so order matters: 8 − 3 is not 3 − 8. Carrying and borrowing in columns simply apply place value one position at a time, trading ten units for one of the next place or the reverse.
Suppose you have 200 dollars and spend 74 on a jacket. In columns, you borrow from the hundreds so that 200 − 74 becomes 126. Subtraction can be viewed as taking away, as comparing two amounts, or as finding the missing addend, and thinking about which meaning fits a word problem helps you choose the right operation.
These operations are the basis of budgeting, measuring change, keeping score and calculating time differences. A frequent student error is subtracting the smaller digit from the larger in each column regardless of position, which gives wrong answers when borrowing is needed. Estimating first by rounding catches many such slips.
Key ideas
- Addition is commutative so order does not matter
- Subtraction is the inverse of addition
- Check a subtraction by adding the answer back
Quick check
Use cases: where Addition and Subtraction helps
- Homework: review the key idea behind Addition and Subtraction before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Addition and Subtraction without notes.
- Visual learning: play with the interactive lab to see how Addition and Subtraction changes when you adjust its inputs.
- Teaching a friend: explain Addition and Subtraction 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 Addition and Subtraction?
Addition combines amounts while subtraction finds the difference or removes some.
What will I learn in Addition and Subtraction?
Addition is commutative so order does not matter. Subtraction is the inverse of addition. Check a subtraction by adding the answer back.
Is Addition and Subtraction 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 Addition and Subtraction 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 Addition and Subtraction?
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.