If you're preparing for the SAT, ACT, or any standardized math exam, mastering basic algebra is essential. These foundational concepts appear frequently on standardized tests and often make the difference between an average score and a top score.
In this guide, you'll learn:
- Basic algebra keywords
- Solving algebraic expressions
- Combining like terms
- Fraction busting
- Cross multiplying
- Practice quizzes for each topic
Basic Algebra Keywords You Must Know
Understanding math keywords is critical for solving word problems correctly.
Two of the most important keywords are:
- of = multiply
- per = divide
Examples
- 50% of 80
- = 0.50 × 80
- 60 miles per hour
- = 60 ÷ 1 hour
These keywords appear frequently on SAT Math and ACT Math questions.
Practice quiz: All Exams | The School of Mathematics
Solving Basic Algebraic Expressions
Solving algebraic equations means getting the variable alone.
To do this, use the reverse order of operations (PEMDAS).
Example
Solve:
3x² + 4 = 79
Step 1: Subtract 4
3x² = 75
Step 2: Divide by 3
x² = 25
Step 3: Take the square root
x = ±5
Fractions in Algebra
Fractions can make equations look harder than they really are.
Example
(3/4)x = 15
You can solve this in two ways:
Method 1: Divide by the fraction
x = 15 ÷ (3/4)
Method 2: Multiply by the reciprocal
Multiply both sides by 4/3:
x = 20
In many cases, multiplying by the reciprocal is faster and cleaner.
Practice quiz: All Exams | The School of Mathematics
Combining Like Terms
Combining like terms is one of the most common algebra skills tested on standardized exams.
Key rule
You can combine terms only if they have the same variables and exponents.
Example
5x²y + 12xy² − 6xy − 7x²y + xy² + 5xy
Group like terms:
- (5x²y − 7x²y)
- (12xy² + xy²)
- (−6xy + 5xy)
Final answer:
−2x²y + 13xy² − xy
Practice quiz: All Exams | The School of Mathematics
Fraction Busting
Fraction busting means multiplying all terms by the common denominator to eliminate fractions.
This method makes many algebra problems much easier to solve.
Example
x/2 + (x + 3)/3 = 5/x
The common denominator is 6x.
Multiply every term by 6x to eliminate all fractions, then solve the simplified equation.
Fraction busting is especially useful when equations contain multiple fractions.
Practice quiz: All Exams | The School of Mathematics
Cross Multiplying
Cross multiplying is used when one fraction equals another fraction.
Example
x/4 = (x + 2)/6
Cross multiply:
6x = 4(x + 2)
Solve:
6x = 4x + 8
2x = 8
x = 4
Important tip
All numbers can be written as fractions.
For example:
7 = 21/(x − 4)
You can rewrite this as:
7/1 = 21/(x − 4)
Now cross multiply:
7(x − 4) = 21
Solve:
7x − 28 = 21
7x = 49
x = 7
Practice quiz: All Exams | The School of Mathematics
Why Basic Algebra Matters for SAT and ACT
Basic algebra shows up in:
- SAT Math
- ACT Math
- PSAT
- College placement tests
- High school math exams
When you master these concepts, you can solve problems faster, avoid common mistakes, and build a stronger foundation for advanced math.
Practice Basic Algebra With Free Quizzes
Practice is one of the fastest ways to improve your math score.
Take our free quizzes:
All Exams | The School of Mathematics
Final Thoughts
Basic algebra is one of the most important topics in standardized test math. Once you understand keywords, equations, fractions, like terms, and cross multiplying, you'll be in a much better position to improve your score on the SAT and ACT.
Start practicing today with our free quizzes on The School of Mathematics.
Start here: All Exams | The School of Mathematics