Basic Arithmetic- Fundamental Math Operations Explained

What Basic Arithmetic Actually Is

Basic arithmetic is the foundation of all mathematics. It covers four operations: addition, subtraction, multiplication, and division. That's it. Nothing fancy.

Most people learned this before age 10. But if you're refreshing your math skills or helping a kid with homework, this guide cuts through the noise.

Addition: Putting Numbers Together

Addition combines numbers into a larger total. Use the + symbol.

Examples:

• 3 + 5 = 8
• 12 + 7 = 19
• 45 + 33 = 78

The numbers you're adding are called addends. The result is the sum.

Adding Larger Numbers

When adding multi-digit numbers, align them by place value (ones under ones, tens under tens). Add from right to left, carrying over when needed.

Example:

   47
+  58
-----
  105

7 + 8 = 15. Write 5, carry 1. Then 4 + 5 + 1 = 10. Done.

Subtraction: Taking Away

Subtraction removes one number from another. Use the − symbol.

Examples:

• 9 − 4 = 5
• 15 − 8 = 7
• 100 − 37 = 63

The starting number is the minuend. The number being subtracted is the subtrahend. The result is the difference.

When Subtraction Gets Tricky

Sometimes you need to borrow. When the top digit is smaller than the bottom digit, take from the next column.

   52
-  27
-----
   25

2 − 7 doesn't work, so borrow 1 from the 5 (making it 4), turning the 2 into 12. Now 12 − 7 = 5.

Multiplication: Speed-Add

Multiplication is repeated addition. Instead of 3 + 3 + 3, write 3 × 3. Use ×, ·, or *.

Examples:

• 4 × 6 = 24
• 7 × 8 = 56
• 12 × 5 = 60

The numbers multiplied are factors. The result is the product.

Memorizing Multiplication Tables

You need to know your times tables up to 12 × 12. Here's a quick reference for the trickier ones:

Most people struggle with 7s, 8s, and 12s. Drill these until they're automatic.

Division: Splitting Into Equal Parts

Division splits a number into equal groups. Use ÷, /, or the division symbol.

Examples:

• 20 ÷ 4 = 5
• 56 ÷ 7 = 8
• 144 ÷ 12 = 12

The number being divided is the dividend. The number doing the dividing is the divisor. The result is the quotient.

Division With Remainders

Not all division works out evenly. When that happens, you get a remainder.

   17 ÷ 5 = 3 remainder 2
   or
   17 ÷ 5 = 3.4

3 groups of 5 fit into 17, with 2 left over.

Order of Operations: PEMDAS

When an expression has multiple operations, you need rules. Otherwise 2 + 3 × 4 could mean 20 or 14.

PEMDAS tells you the order:

1. Parentheses first
2. Exponents (powers and roots)
3. Multiplication and Division (left to right)
4. Addition and Subtraction (left to right)

Example: 2 + 3 × 4

Multiply first. 3 × 4 = 12. Then add. 2 + 12 = 14. Not 20.

Example: (2 + 3) × 4

Parentheses first. 2 + 3 = 5. Then multiply. 5 × 4 = 20.

How to Practice Basic Arithmetic

You don't need expensive courses. Here's what actually works:

• Flash cards — shuffle a deck, flip, answer fast. Time yourself.
• Mental math drills — calculate your grocery total without a calculator.
• Online tools — Khan Academy, IXL, or simple quiz websites.
• Daily use — tip calculations, splitting bills, measuring ingredients.

Do 10-15 minutes daily. You'll see results within a week.

Quick Reference: Operations Summary

Getting Started: Your First Practice Set

Try these without a calculator:

1. 47 + 38 = ?
2. 93 − 27 = ?
3. 8 × 7 = ?
4. 72 ÷ 9 = ?
5. 3 + 4 × 5 = ?

Answers: 85 | 66 | 56 | 8 | 23 (remember: multiply first)

If you missed any, re-read the relevant section above. That's all there is to it.