TEAS BUNDLE

The Numbers & Algebra domain is the largest slice of the TEAS Math section. This guide covers the three highest-yield skills: working with rational numbers, solving percent problems, and solving equations. Learn each rule, study the worked example, then test yourself.

How to use this guide

Each area below gives the core rules and formulas, a worked example, and two practice questions. The answers follow each practice set, so cover them and try the questions first. A 10-question mixed set at the end blends all three areas like the real exam, with a full answer key.

Areas covered: Rational Numbers · Percentages · Solving Equations · 16 practice questions

1. Rational Numbers

fractions · decimals · integers · ordering & operations

Key concepts

• A rational number is any number you can write as a fraction a/b (with b ≠ 0) — that includes integers, terminating decimals, and repeating decimals.

• To compare or order rational numbers, put them in one common form — usually convert everything to decimals.

• Add/subtract fractions with a common denominator; multiply straight across; divide by multiplying by the reciprocal (flip).

• Mind the signs: negative ÷ negative = positive; negative + negative = more negative.

Formulas & rules

• Add/subtract: find a common denominator, then combine the numerators.

• Multiply: top × top, bottom × bottom. Divide: keep, flip, multiply.

• Fraction → decimal: divide the numerator by the denominator.

Worked example

Order these from least to greatest: 3/4, 0.7, 5/8.

1. Convert each to a decimal: 3/4 = 0.75, 0.7 = 0.70, 5/8 = 0.625.

2. Compare the decimals: 0.625 < 0.70 < 0.75.

Least to greatest: 5/8, 0.7, 3/4.

💡 Memory hook: KFC: Keep–Flip–Change. To divide fractions, Keep the first, Flip the second, and Change ÷ to ×. And to compare messy numbers, turn them all into decimals first.

Practice: Rational Numbers

1. Which of the following is the greatest value?

• A. 2/3

• B. 0.6

• C. 5/8

• D. 0.72

2. What is 3/4 − 1/6?

• A. 7/12

• B. 1/2

• C. 2/10

• D. 5/6

Answers and working

• 1 → D. As decimals: 2/3 ≈ 0.667, 0.6, 5/8 = 0.625, and 0.72. The greatest is 0.72.

• 2 → A. Common denominator 12: 9/12 − 2/12 = 7/12.

2. Percentages

percent of a number · percent change · discounts

Key concepts

• A percent means “per hundred.” Convert a percent to a decimal by dividing by 100 (25% = 0.25).

• Part = percent × whole. Rearranged: percent = part ÷ whole, and whole = part ÷ percent.

• Percent change = (new − old) ÷ old × 100. A positive result is an increase; a negative one is a decrease.

• For a discount, sale price = original × (1 − discount rate).

Formulas & rules

• part = % × whole | % = part ÷ whole

• Percent change = (new − old) ÷ old × 100

• Proportion form: is / of = % / 100, then cross-multiply.

Worked example

After a 20% discount, a jacket costs $80. What was the original price?

1. A 20% discount means you pay 80% of the original: 0.80 × original = 80.

2. Divide: original = 80 ÷ 0.80 = 100.

Original price: $100.

💡 Memory hook: “IS over OF = % over 100.” Set up the percent proportion — the is number over the of number equals the percent over 100 — then cross-multiply.

Practice: Percentages

1. What is 15% of 240?

• A. 24

• B. 36

• C. 40

• D. 360

2. A quantity increases from 40 to 50. What is the percent increase?

• A. 10%

• B. 20%

• C. 25%

• D. 50%

Answers and working

• 1 → B. 0.15 × 240 = 36.

• 2 → C. (50 − 40) ÷ 40 = 10/40 = 0.25 = 25%.

3. Solving Equations

one- & two-step · distributing · proportions

Key concepts

• Solving an equation means isolating the variable by undoing each operation in reverse order.

• Keep it balanced: whatever you do to one side, do to the other (like a scale).

• Use the distributive property to clear parentheses: a(b + c) = ab + ac.

• A proportion (two equal ratios) is solved by cross-multiplying.

Formulas & rules

• Undo in reverse: deal with + / − first, then × / ÷.

• Do the same operation to both sides to stay balanced.

• Proportion a/b = c/d → a × d = b × c.

Worked example

Solve for x: 3x + 6 = 18.

1. Subtract 6 from both sides: 3x = 12.

2. Divide both sides by 3: x = 4.

x = 4.

💡 Memory hook: PEMDAS backwards = SADMEP. To undo an equation, reverse the order of operations — handle + and − first, then × and ÷ — and whatever you do to one side, do to the other.

Practice: Solving Equations

1. Solve for x: 5x − 7 = 28.

• A. 5

• B. 7

• C. 9

• D. 21

2. Solve for x: 2(x + 3) = 20.

• A. 7

• B. 10

• C. 13

• D. 17

Answers and working

• 1 → B. Add 7 to both sides: 5x = 35. Divide by 5: x = 7.

• 2 → A. Distribute: 2x + 6 = 20. Subtract 6: 2x = 14. Divide by 2: x = 7.

★ Mixed practice: 10 TEAS-style questions

All three areas, like the real exam. Answer every question before checking the key below.

1. Order these from least to greatest: 1/2, 0.45, 3/5. (Rational)

• A. 1/2, 0.45, 3/5

• B. 3/5, 1/2, 0.45

• C. 0.45, 3/5, 1/2

• D. 0.45, 1/2, 3/5

2. A laptop that cost $600 increases in price by 25%. What is the new price? (Percent)

• A. $625

• B. $700

• C. $750

• D. $800

3. Solve for x: 4x + 9 = 33. (Equations)

• A. 6

• B. 7

• C. 8

• D. 11

4. What is 2/5 + 1/3? (Rational)

• A. 3/8

• B. 3/15

• C. 2/15

• D. 11/15

5. 30 is what percent of 120? (Percent)

• A. 20%

• B. 25%

• C. 30%

• D. 40%

6. Solve for x: 3(x − 2) = 15. (Equations)

• A. 3

• B. 5

• C. 7

• D. 9

7. Which decimal is equivalent to 7/8? (Rational)

• A. 0.875

• B. 0.78

• C. 0.85

• D. 0.70

8. A shirt is 20% off and now costs $90. What was the original price? (Percent)

• A. $108

• B. $110

• C. $112.50

• D. $120

9. Solve the proportion: 3/4 = x/20. (Equations)

• A. 12

• B. 15

• C. 16

• D. 18

10. A 2.5 L bottle has 1,500 mL poured out. What fraction of the bottle remains? (Rational)

• A. 1/5

• B. 3/5

• C. 1/2

• D. 2/5

Answer key and explanations

Test yourself: free Math quiz

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