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📚 Arithmetic Academy

Learn mathematics one step at a time!

Welcome to Arithmetic Academy!

Arithmetic is the branch of mathematics that deals with numbers and basic operations.

In this course, you will learn five important topics:

  • Addition – combining numbers.
  • Subtraction – finding the difference.
  • Multiplication – repeated addition.
  • Division – splitting numbers into equal groups.
  • PEMDAS – the order in which operations are performed.

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1. Addition (+)

Addition combines two or more numbers to find their total.

5 + 3 = 8

How does it work?

Imagine you have 5 apples and receive 3 more.

You now have 8 apples!

Important properties

  • Commutative: 3 + 5 = 5 + 3
  • Associative: (2 + 3) + 4 = 2 + (3 + 4)
  • Identity: Adding zero changes nothing.
12 + 18 = 30

2. Subtraction (−)

Subtraction removes an amount from a number or finds the difference between two numbers.

10 − 4 = 6

How does it work?

If you have 10 apples and give away 4, you have 6 remaining.

Important properties

  • Subtraction is not commutative: 8 − 3 ≠ 3 − 8.
  • Subtracting zero changes nothing.
  • A number minus itself equals zero.
25 − 13 = 12

3. Multiplication (×)

Multiplication is repeated addition.

4 × 3 = 12

How does it work?

4 × 3 means adding 4 three times:

4 + 4 + 4 = 12

Important properties

  • Commutative: 3 × 4 = 4 × 3
  • Associative: (2 × 3) × 4 = 2 × (3 × 4)
  • Identity: Any number multiplied by 1 stays the same.
  • Zero: Any number multiplied by 0 equals 0.
12 × 8 = 96

4. Division (÷)

Division splits a number into equal groups.

20 ÷ 4 = 5

How does it work?

If you have 20 apples and divide them equally between 4 people, each person gets 5 apples.

Important properties

  • Division is not commutative.
  • Dividing by 1 leaves the number unchanged.
  • A nonzero number divided by itself equals 1.
  • Division by zero is undefined.
144 ÷ 12 = 12

5. Order of Operations (PEMDAS)

When an expression contains multiple operations, you must follow a specific order.

PEMDAS stands for:

  1. P – Parentheses
  2. E – Exponents
  3. MD – Multiplication and Division (left to right)
  4. AS – Addition and Subtraction (left to right)

Example

3 + 4 × 2

Step 1: Multiply first.

3 + 8

Step 2: Add.

11

Answer: 11

Another example

(5 + 3) × 2²

Parentheses: 8 × 2²

Exponents: 8 × 4

Multiplication: 32

Answer: 32

📝 Arithmetic Practice

Test your knowledge with randomly generated questions!

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