Pre-Algebra · course sample
Pre-Algebra Foundations
Build a foundation with integers, fractions, ratios, expressions, and equations. Revisit the ideas that make later algebra easier to follow.
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The full sample outline
Start with the foundations, then build on one idea at a time.
Chapter 1
Integers
Use a number line to make sense of positive and negative quantities.
- 1
Order and absolute value
Compare signed numbers and interpret distance from zero.
- 2
Add and subtract integers
Explain a signed-number calculation using movement on a number line.
- 3
Multiply and divide integers
Apply sign rules and check whether an answer is reasonable.
- 1
Chapter 2
Fractions, decimals, and percents
Represent the same quantity in different forms and choose a useful one.
- 1
Equivalent fractions
Find equivalent fractions and use common denominators to add or subtract.
- 2
Convert between forms
Write a fraction as a decimal and a percent.
- 3
Percent of a quantity
Calculate a simple discount while distinguishing the saving from the final price.
- 1
Chapter 3
Ratios and proportions
Compare quantities using consistent units and multiplicative reasoning.
- 1
Describe a ratio
Distinguish part-to-part and part-to-whole comparisons.
- 2
Unit rates
Find a per-unit quantity and state its units.
- 3
Solve a proportion
Scale equivalent ratios and check a solution in context.
- 1
Chapter 4
Expressions
Translate a situation into mathematical language without adding an equals sign unnecessarily.
- 1
Variables and terms
Identify a variable, coefficient, and constant in an expression.
- 2
Evaluate expressions
Substitute a value and use the order of operations.
- 3
Equivalent expressions
Distribute and combine like terms without changing an expression's value.
- 1
Chapter 5
Equations
Keep an equation balanced while finding an unknown value.
- 1
One-step equations
Use an inverse operation on both sides of an equation.
- 2
Two-step equations
Undo operations in a sensible order and show each step.
- 3
Check a solution
Substitute the answer into the original equation and interpret it in context.
- 1
Let's work through an example
A percent is a part of the whole
In a hypothetical shop, a $40 item is discounted by 25%. What is the price before any tax?
- 1
Convert 25% to 25/100 = 0.25. This is the fraction of the original price being taken off, not the fraction you pay.
- 2
Find the discount: 0.25 × $40 = $10. One quarter of forty dollars is ten dollars.
- 3
Subtract the discount from the original price: $40 − $10 = $30. Tax is not included in this example.
The idea to keep: Label the quantity you calculate. A $10 discount and a $30 final price answer different questions.
Check your thinking · read-only quiz
What is 3/4 written as a percent?
Choose an answer in your head, then open the explanation. Nothing is submitted, graded, or saved.
- A.25%
- B.34%
- C.75%
- D.300%
Reveal answer and explanation
Answer C: 75%
Divide 3 by 4 to get 0.75, then multiply by 100 to express it as a percent. So 3/4 = 75%, meaning 75 out of every 100 equal parts.