ATI TEAS Version 7 Mathematics: Numbers and Algebra

Objectives

• Two parts: Numbers and Algebra
• 34 questions total for mathematics, 18 questions for Numbers and Algebra
• Required skills:
  • Converting among non-negative fractions, decimals, and percentages
  • Performing arithmetic operations with rational numbers
  • Comparing and ordering rational numbers
  • Solving equations with one variable
  • Solving real-world problems
  • Applying estimation strategies and rounding rules
  • Using proportions, ratios, rates of change, expressions, equations, and inequalities

Fractions

• Form: A/B where A and B are integers, B ≠ 0
• Numerator: top number
• Denominator: bottom number
• Example: 3/4 (3 is numerator, 4 is denominator)

Percentages

• A ratio expressed as a fraction of 100
• Example: 35% = 0.35 = 35/100
• Calculate by multiplying decimal by 100 or dividing fraction by 100

Place Values

• Each digit in a number has a place value
• Positions: ones, tens, hundreds, thousands, etc.
• Decimal positions: tenths, hundredths, thousandths

Conversion Between Fractions, Decimals, and Percentages

• Fractions to Decimals: Divide numerator by denominator
  • Example: 3/4 = 0.75
• Decimals to Fractions: Divide decimal by the place value
  • Example: 0.75 = 75/100 = 3/4 after simplification
• Percentages to Decimals: Divide by 100
  • Example: 75% = 0.75
• Percentages to Fractions: Write over 100 and simplify

Order of Operations (PEMDAS)

• Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right)
• Example Problems: 3² + 2² = 13, 24 ÷ 12 + 17 - 11 = 8

Rational and Irrational Numbers

• Rational Numbers: Can be expressed as a fraction (A/B)
  • Examples: -1/2, 3/4, 0.125
• Irrational Numbers: Cannot be expressed as a fraction
  • Examples: π, √16, e

Ordering and Comparing Rational Numbers

• Order: Least to greatest by aligning from left (negative) to right (positive)
• Compare: Use number line or symbols such as >, <, ≥, ≤

Solving Equations with One Variable

• Identify Terms: Constants, variables, coefficients
• Inverse Arithmetic Operations: Undo operations to isolate variables
  • Example: x + 18 = 30 ➔ x = 12
• Proportional Relationships: Solve using inverse operations

Real World Problems

• Steps: Identify given information, problem type, solve equation, check work
• Example: Plumber charges $25 + $50 per hour ➔ Cost for 2 hours = $125

Solving Word Problems Using Percentages

• Calculate percentage increase/decrease
• Example: Store discount, population growth

Metric Measurements

• Common Units: Length (meters), Weight (grams), Volume (liters), Temperature (Celsius)
• Area: Square units, Volume: Cubic units

Estimation and Rounding

• Round numbers to nearest whole, tenths, etc.
• Example: 45.678 ➔ 46

Proportions

• Definition: Ratio in fraction form
• Steps: Identify information, draw diagram, solve using equivalent ratios

Direct Proportions and Constant Proportionality

• Directly proportional: Y = kx
• Not directly proportional: Additional constants

Solving with Ratios and Rates of Change

• Rate as a comparison of two units
• Example: 60 miles per hour

Expressions, Equations, and Inequalities

• Expressions: Mathematical phrases with numbers, variables
• Equations: Contain '='
• Inequalities: Contain >, <, ≤, ≥
• Solving inequalities requires reversing signs when multiplying/dividing by negatives
• Example: -2y < -8 ➔ y > 4 after dividing by -2

Summary

• Understanding these mathematical concepts is crucial for success on the TEAS mathematics portion.
• Practice and review are essential to mastering the skills necessary for the exam.