Algebra Basics: Start Here

Your gentle introduction to algebraic thinking - no prior experience needed!

Welcome to Algebra!

Don't worry if math has always seemed difficult or confusing. Algebra is about finding patterns and solving puzzles. We'll start with the very basics and build your confidence step by step.

Remember:

  • Everyone starts as a beginner
  • Mistakes help you learn
  • Algebra is like learning a new language
  • Take your time - understanding is more important than speed

What You'll Learn

  • What algebra is and why it matters
  • Basic mathematical operations
  • Understanding patterns and relationships
  • Simple problem-solving strategies
  • Building confidence with numbers

1. What is Algebra?

Algebra is About Patterns

Algebra is the study of patterns and relationships. Instead of working with specific numbers, we use letters and symbols to represent general situations.

Everyday Patterns:

Shopping

If apples cost $2 each, how much for x apples?

Cost = 2 × x

Growing Plants

Each week a plant grows 3 inches. After w weeks?

Height = 3 × w

Temperature

Convert Celsius to Fahrenheit: multiply by 9/5 and add 32

°F = \frac{9}{5} × °C + 32

Find the Pattern

Look at these numbers: 2, 4, 6, 8, ?

What comes next?

Pattern: Add 2 each time

Algebraically: Each number is 2 times its position

n^{th} number = 2n

2. Numbers and Basic Operations

Types of Numbers

Natural Numbers

Counting numbers: 1, 2, 3, 4, ...

Whole Numbers

Natural numbers plus zero: 0, 1, 2, 3, ...

Integers

Whole numbers and negatives: ..., -2, -1, 0, 1, 2, ...

Rational Numbers

Fractions and decimals: 1/2, 0.5, 3.14, ...

Number Line Explorer

-5 -4 -3 -2 -1 0 1 2 3 4 5
0
Basic Operations Practice

8 + 5 =

12 - 7 =

6 × 4 =

20 ÷ 5 =

Understanding Fraction Division

When dividing fractions, remember: \frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}

Example:

Solve: \frac{1}{2} \div \frac{1}{4} = \, ?

Multiply by the reciprocal: \frac{1}{2} \times \frac{4}{1}

Multiply numerators and denominators: \frac{1 \times 4}{2 \times 1} = \frac{4}{2}

Simplify: \frac{4}{2} = 2

Visual: One half divided by one quarter = 2

3. Introducing Variables

What are Variables?

Variables are letters that represent unknown or changing values. Think of them as empty boxes waiting to be filled with numbers.

Example:

If you have some number and add 3, you get 8.

What is the number? We can write: x + 3 = 8

Here, x is the unknown number we're trying to find.

Variable Stories

Apple Story

You have some apples. You give away 2 apples and have 5 left.

How many did you start with?

x - 2 = 5

Candy Story

You buy candy for $3 and have $2 left from $10.

How much did the candy cost? (Wait, that's not right...)

10 - x = 2

4. Solving Simple Equations

The Goal

The goal is to get the variable alone on one side of the equation. Whatever you do to one side, you must do to the other side.

Balance Scale Method

x + 3
=
8
Simple Equation Practice

Solve: x + 5 = 12

x =

Solve: y - 3 = 9

y =

Solve: 2z = 16

z =

5. Word Problems

Translating Words to Math

Word problems can seem tricky, but they're just stories that need to be turned into equations.

Key Phrases:

  • "is" or "equals" → =
  • "more than" or "plus" → +
  • "less than" or "minus" → -
  • "times" or "of" → ×
  • "divided by" → ÷
Word Problem Practice

Problem 1: Sarah has some stickers. She gives 4 to her friend and has 9 left. How many did she start with?

Equation: x - 4 = 9

x =

Problem 2: A movie ticket costs $8. You have $20. How much change will you get?

Equation: 20 - 8 = x

x =

How Are You Doing?

Before moving on, make sure you understand:

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