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Pre-Algebra and Elementary Algebra

Master basic operations, fractions, decimals, and simple equations for ACT

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📂 Subtopics in Pre-Algebra and Elementary Algebra

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Pre-Algebra Basics

Number properties, fractions, percents, ratios, exponents and basic statistics.

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Pre-Algebra and Elementary Algebra (ACT)

Number Operations

Order of Operations (PEMDAS)

Example: 3+4×223 + 4 \times 2^2

  1. Exponents: 22=42^2 = 4
  2. Multiply: 4×4=164 \times 4 = 16
  3. Add: 3+16=193 + 16 = 19

Fractions and Decimals

  • Adding fractions: Find common denominator
  • Converting: 0.25=140.25 = \frac{1}{4}
  • Percent to decimal: 15%=0.1515\% = 0.15

Simple Equations

One-step: x+7=12⇒x=5x + 7 = 12 \quad \Rightarrow \quad x = 5

Two-step: 3x−5=10⇒3x=15⇒x=53x - 5 = 10 \quad \Rightarrow \quad 3x = 15 \quad \Rightarrow \quad x = 5

Word Problems

Strategy:

  1. Identify the unknown (let xx = ...)
  2. Write an equation
  3. Solve
  4. Check if answer makes sense

Example: "Five more than twice a number is 17" 2x+5=17⇒x=62x + 5 = 17 \quad \Rightarrow \quad x = 6

ACT Tips

  • Calculator allowed! Use it for complex arithmetic
  • Work backwards: Plug answer choices into equations
  • Estimate: Eliminate unreasonable answers

📚 Practice Problems

1Problem 1easy

❓ Question:

What is 23+16\frac{2}{3} + \frac{1}{6}?

💡 Show Solution

Solution:

Find common denominator (6): 23=46\frac{2}{3} = \frac{4}{6}

Add: 46+16=56\frac{4}{6} + \frac{1}{6} = \frac{5}{6}

Answer: 56\frac{5}{6}

2Problem 2easy

❓ Question:

What is 23+16\frac{2}{3} + \frac{1}{6}?

💡 Show Solution

Solution:

Find common denominator (6): 23=46\frac{2}{3} = \frac{4}{6}

Add: 46+16=56\frac{4}{6} + \frac{1}{6} = \frac{5}{6}

Answer: 56\frac{5}{6}

3Problem 3medium

❓ Question:

If 5x−3=225x - 3 = 22, what is xx?

💡 Show Solution

Solution:

Add 3 to both sides: 5x=255x = 25

Divide by 5: x=5x = 5

Answer: x=5x = 5

ACT Tip: Always check: 5(5)−3=25−3=225(5) - 3 = 25 - 3 = 22 ✓

4Problem 4medium

❓ Question:

If 5x−3=225x - 3 = 22, what is xx?

💡 Show Solution

Solution:

Add 3 to both sides: 5x=255x = 25

Divide by 5: x=5x = 5

Answer: x=5x = 5

ACT Tip: Always check: 5(5)−3=25−3=225(5) - 3 = 25 - 3 = 22 ✓

5Problem 5hard

❓ Question:

A shirt originally costs \40$. It is on sale for 25% off. What is the sale price?

💡 Show Solution

Solution:

Calculate discount: 0.25×40=100.25 \times 40 = 10

Subtract from original: 40−10=3040 - 10 = 30

Or use multiplier: 40×(1−0.25)=40×0.75=3040 \times (1 - 0.25) = 40 \times 0.75 = 30

Answer: \30$

6Problem 6hard

❓ Question:

A shirt originally costs \40$. It is on sale for 25% off. What is the sale price?

💡 Show Solution

Solution:

Calculate discount: 0.25×40=100.25 \times 40 = 10

Subtract from original: 40−10=3040 - 10 = 30

Or use multiplier: 40×(1−0.25)=40×0.75=3040 \times (1 - 0.25) = 40 \times 0.75 = 30

Answer: \30$

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📌 Related Topics in ACT Math

ACT Algebra and FunctionsACT Geometry and TrigonometryIntermediate Algebra and Coordinate GeometryACT Statistics and ProbabilityPlane Geometry and TrigonometryPre-Algebra Basics

❓ Frequently Asked Questions

What is Pre-Algebra and Elementary Algebra?▾
Master basic operations, fractions, decimals, and simple equations for ACT
How can I study Pre-Algebra and Elementary Algebra effectively?▾
Start by reading the study notes and working through the examples on this page. Then use the flashcards to test your recall. Practice with the 6 problems provided, checking solutions as you go. Regular review and active practice are key to retention.
Is this Pre-Algebra and Elementary Algebra study guide free?▾
Yes — all study notes, flashcards, and practice problems for Pre-Algebra and Elementary Algebra on Study Mondo are free to access. No account is needed.
What course covers Pre-Algebra and Elementary Algebra?▾
Pre-Algebra and Elementary Algebra is part of the ACT Prep course on Study Mondo, specifically in the ACT Math section. You can explore the full course for more related topics and practice resources.
Are there practice problems for Pre-Algebra and Elementary Algebra?▾
Yes, this page includes 6 practice problems with detailed solutions. Each problem includes a step-by-step explanation to help you understand the approach.