A.L.L.
coyura Academy
THE
TEAS
MATH
STUDY GUIDE
+ Practice Questions
A Complete Math Review for the ATI TEAS 7
Every TEAS math topic from whole numbers to statistics — with worked examples,
key formulas, 60 practice questions, full rationales, and a complete answer key.
— What's Inside: — — You Will Master: —
+ Numbers, operations & place value + Perform all four operations precisely
+ Fractions, decimals & percentages + Convert fractions ↔ decimals ↔ %
+ Ratios, proportions & unit conversion + Solve ratio & proportion problems
+ Algebraic expressions & equations + Evaluate and solve algebraic equations
+ Geometry — area, perimeter, volume + Calculate area, perimeter, and volume
+ Statistics, data & measurement + Interpret graphs, mean, median, mode
TEAS Math is not about memorising formulas — it is about applying them accurately under time pressure.
Numbers & Ops Measurement Data & Stats Algebra Geometry
~23% ~23% ~18% ~23% ~13%
Created by ALLcoyura Academy
,A.L.L.
coyura Academy
NUMBERS, OPERATIONS & FRACTIONS
The foundation of TEAS math — master these before moving to any other topic.
WHOLE NUMBERS, ORDER OF OPERATIONS & NUMBER PROPERTIES
Order of Operations — PEMDAS: Number Properties:
Step Example Property Rule
P Parentheses — innermos (3+2)×4 = 5×4 = 20 Commutative a+b=b+a and a×b=b×a
E Exponents (powers/roots) 2³ = 8 Associative (a+b)+c=a+(b+c); (a×b)×c=a×(b×c)
M Multiplication & Division Left to right: 12÷3×2 = 4×2 = 8 Distributive a(b+c)=ab+ac
AS Addition & Subtraction Left to right: 5−2+3 = 3+3 = 6 Identity a+0=a (add) and a×1=a (mult)
Zero Property a×0=0 for all a
FRACTIONS — Operations, Simplifying & Comparing
Fraction Operations: Worked Examples:
Operation Method Problem Solution
Add/Subtract Find LCD → convert → add/subtract numerato 2/3 + 3/4 LCD=12 → 8/12+9/12 = 17/12 = 1 5/12
Multiply Multiply numerators × numerators, denominato 5/6 − 1/4 LCD=12 → 10/12−3/12 = 7/12
Divide Keep the first fraction, Flip the second, Multiply
2/3 × 3/5 = 6/15 = 2/5
Simplify Divide numerator AND denominator by their G
3/4 ÷ 2/3 = 3/4 × 3/2 = 9/8 = 1 1/8
Mixed Numbers Convert to improper fraction: whole×denom+n
Simplify 18/24 GCF=6 → 3/4
Compare Fracs Cross-multiply to compare: 3/4 vs 2/3 → 9 vs 8
Convert 2 3/5 = (2×5+3)/5 = 13/5
DECIMALS — Operations, Place Value & Rounding
Decimal Place Values: Decimal Rules:
Place Value Operation Rule / Method
Thousands 1,000 Adding Line up decimal points → add as whole number
Hundreds 100 Subtracting Line up decimal points → subtract as whole num
Tens 10 Multiplying Ignore decimals → multiply → count total decim
Ones 1 Dividing Move decimal in divisor to make whole number
Tenths 0.1 (1/10) Rounding Look at digit AFTER rounding place: ≥5 round u
Hundredths 0.01 (1/100) Dec→Frac 0.75 = 75/100 = 3/4
Thousandths 0.001 (1/1000) Frac→Dec
Created by ALLcoyura Academy 3/4 → divide 3÷4 = 0.75 Page 2
,A.L.L.
coyura Academy
PERCENTAGES, RATIOS & PROPORTIONS
Core TEAS topics — expect several of these on every exam.
PERCENTAGES — Conversions, Calculations & Applications
Percent Conversions: Percent Problem Types:
Conversion Method & Example Problem Type Formula
% → Decimal Divide by 100: 75% = 0.75 Percent Increase (New−Old)/Old × 100%
Decimal → % Multiply by 100: 0.48 = 48% Percent Decrease (Old−New)/Old × 100%
% → Fraction Write over 100, simplify: 40% = 40/100 = 2/5
Discounts Sale Price = Original × (1 − discount%)
Fraction → % Divide top by bottom × 100: 3/4 = 0.75 = 75%
Tax/Tip Total = Original × (1 + tax% or tip%)
Find % of number Multiply: 30% of 80 = 0.30×80 = 24
Simple Interest I = P×R×T (Principal × Rate × Time)
Find the whole Divide: 24 is 30% of what? → 24÷0.30 = 80
Part/Whole/Percent Part = Whole × Percent (as decimal)
Find the % Is/Of×100: 24 is what % of 80? → 24/80×100
RATIOS & PROPORTIONS — Setting Up and Solving
Ratio Rules & Examples: Proportion Solving:
Concept Explanation Step Method / Example
Ratio Definition Comparison of two quantities: a:b or a/b Set up Write equivalent fractions: a/b = c/d
Equivalent Ratios 2:3 = 4:6 = 6:9 — multiply/divide both by s Cross-multiply a×d = b×c
Part-to-Part 3 red: 5 blue → 3 red out of 8 total
Solve for x Isolate the unknown
Part-to-Whole 3 red out of 8 total = 3/8 are red
Example 1 x/12 = 5/6 → 6x=60 → x=10
Unit Rate 60 miles in 2 hours = 30 miles per hour
Example 2 3/4 = 15/x → 3x=60 → x=20
Scale Factor Map 1:50000 → 2cm = 100,000cm = 1km
Unit conv. 2.5 km × (1000m/1km) = 2500 m
Dosage calc Ordered: 250mg; on hand: 500mg/5mL →
UNIT CONVERSIONS — US Customary & Metric
US Customary Conversions: Metric System (SI) & Conversions:
Measure Conversions Prefix Meaning & Example
Length 12 in=1 ft | 3 ft=1 yd | 5280 ft=1 mile Kilo- (k) ×1000: 1 km = 1000 m
Weight 16 oz=1 lb | 2000 lb=1 ton Hecto- (h) ×100
Volume 8 oz=1 cup | 2 cups=1 pt | 2 pt=1 qt | 4 qt=1 gal Deka- (da) ×10
Time 60 sec=1 min | 60 min=1 hr | 24 hr=1 day Base metre, litre, gram
Created by ALLcoyura Academy Page 3
Deci- (d) ÷10: 1 dm = 0.1 m
Centi- (c) ÷100: 1 cm = 0.01 m
, A.L.L.
coyura Academy
ALGEBRA — EXPRESSIONS, EQUATIONS & INEQUALITIES
TEAS algebra focuses on solving equations, evaluating expressions, and word problems.
ALGEBRAIC EXPRESSIONS & EVALUATING
Key Vocabulary: Evaluating Expressions — Worked Examples:
Term Definition Expression Solution
Variable A letter representing an unknown value (x, y, Evaluate 3x−5 for x=4 3(4)−5 = 12−5 = 7
Constant A fixed number in an expression
Evaluate 2a²+b for a=3,b=1 2(9)+1 = 18+1 = 19
Coefficient Number multiplied by a variable: in 3x, 3 is th
Simplify 4x+2x−x = (4+2−1)x = 5x
Term A single number, variable, or product: 3x², 5,
Simplify 3(2x+4) = 6x+12 (distribute)
Like Terms Same variable and exponent: 3x and 7x; com
Simplify 5x+3−2x+7 = 3x+10 (combine like terms)
Expression Math phrase with no equals sign: 2x + 3
Equation Math statement with equals sign: 2x + 3 = 11 Factor 6x+9 = 3(2x+3)
SOLVING EQUATIONS — One & Two Step
One-Step Equations: Two-Step Equations:
Equation Solution Equation Step-by-Step
x+7=12 Subtract 7: x=5 2x+3=11 Step 1: subtract 3 → 2x=8 | Step 2: divide by 2
x−4=9 Add 4: x=13 3x−7=14 Add 7 → 3x=21 | Divide by 3 → x=7
3x=24 Divide by 3: x=8 x/4+2=6 Subtract 2 → x/4=4 | Multiply by 4 → x=16
x/5=6 Multiply by 5: x=30 5(x−2)=15 Divide by 5 → x−2=3 | Add 2 → x=5
−2x=14 Divide by −2: x=−7 2x+x=18 Combine: 3x=18 | Divide: x=6
INEQUALITIES, WORD PROBLEMS & LINEAR EQUATIONS
Inequalities: Word Problem Strategy:
Concept Rule Step Action
Symbols < less than | > greater than | ≤ less/equal | ≥ greate Step 1 — Read Read entire problem; identify what is being aske
Solve like eq. Solve same as equation: x+3>7 → x>4 Step 2 — Define Assign a variable: 'Let x = the unknown quantity'
Flip the sign Multiply/divide by NEGATIVE → FLIP the inequalit Step 3 — Set up Write an equation based on the relationships de
Example −2x<8 → divide by −2 → x>−4 (sign flipped!) Step 4 — Solve Solve the equation using algebraic methods
Graph Open circle = strict (</>); Closed circle = (≤/≥) Step 5 — Check Substitute answer back; verify it makes sense in
Compound AND means both conditions; OR means either con Key phrases 'more than' = +; 'less than' = −; 'times' = ×; 'of' =
Created by ALLcoyura Academy Page 4
coyura Academy
THE
TEAS
MATH
STUDY GUIDE
+ Practice Questions
A Complete Math Review for the ATI TEAS 7
Every TEAS math topic from whole numbers to statistics — with worked examples,
key formulas, 60 practice questions, full rationales, and a complete answer key.
— What's Inside: — — You Will Master: —
+ Numbers, operations & place value + Perform all four operations precisely
+ Fractions, decimals & percentages + Convert fractions ↔ decimals ↔ %
+ Ratios, proportions & unit conversion + Solve ratio & proportion problems
+ Algebraic expressions & equations + Evaluate and solve algebraic equations
+ Geometry — area, perimeter, volume + Calculate area, perimeter, and volume
+ Statistics, data & measurement + Interpret graphs, mean, median, mode
TEAS Math is not about memorising formulas — it is about applying them accurately under time pressure.
Numbers & Ops Measurement Data & Stats Algebra Geometry
~23% ~23% ~18% ~23% ~13%
Created by ALLcoyura Academy
,A.L.L.
coyura Academy
NUMBERS, OPERATIONS & FRACTIONS
The foundation of TEAS math — master these before moving to any other topic.
WHOLE NUMBERS, ORDER OF OPERATIONS & NUMBER PROPERTIES
Order of Operations — PEMDAS: Number Properties:
Step Example Property Rule
P Parentheses — innermos (3+2)×4 = 5×4 = 20 Commutative a+b=b+a and a×b=b×a
E Exponents (powers/roots) 2³ = 8 Associative (a+b)+c=a+(b+c); (a×b)×c=a×(b×c)
M Multiplication & Division Left to right: 12÷3×2 = 4×2 = 8 Distributive a(b+c)=ab+ac
AS Addition & Subtraction Left to right: 5−2+3 = 3+3 = 6 Identity a+0=a (add) and a×1=a (mult)
Zero Property a×0=0 for all a
FRACTIONS — Operations, Simplifying & Comparing
Fraction Operations: Worked Examples:
Operation Method Problem Solution
Add/Subtract Find LCD → convert → add/subtract numerato 2/3 + 3/4 LCD=12 → 8/12+9/12 = 17/12 = 1 5/12
Multiply Multiply numerators × numerators, denominato 5/6 − 1/4 LCD=12 → 10/12−3/12 = 7/12
Divide Keep the first fraction, Flip the second, Multiply
2/3 × 3/5 = 6/15 = 2/5
Simplify Divide numerator AND denominator by their G
3/4 ÷ 2/3 = 3/4 × 3/2 = 9/8 = 1 1/8
Mixed Numbers Convert to improper fraction: whole×denom+n
Simplify 18/24 GCF=6 → 3/4
Compare Fracs Cross-multiply to compare: 3/4 vs 2/3 → 9 vs 8
Convert 2 3/5 = (2×5+3)/5 = 13/5
DECIMALS — Operations, Place Value & Rounding
Decimal Place Values: Decimal Rules:
Place Value Operation Rule / Method
Thousands 1,000 Adding Line up decimal points → add as whole number
Hundreds 100 Subtracting Line up decimal points → subtract as whole num
Tens 10 Multiplying Ignore decimals → multiply → count total decim
Ones 1 Dividing Move decimal in divisor to make whole number
Tenths 0.1 (1/10) Rounding Look at digit AFTER rounding place: ≥5 round u
Hundredths 0.01 (1/100) Dec→Frac 0.75 = 75/100 = 3/4
Thousandths 0.001 (1/1000) Frac→Dec
Created by ALLcoyura Academy 3/4 → divide 3÷4 = 0.75 Page 2
,A.L.L.
coyura Academy
PERCENTAGES, RATIOS & PROPORTIONS
Core TEAS topics — expect several of these on every exam.
PERCENTAGES — Conversions, Calculations & Applications
Percent Conversions: Percent Problem Types:
Conversion Method & Example Problem Type Formula
% → Decimal Divide by 100: 75% = 0.75 Percent Increase (New−Old)/Old × 100%
Decimal → % Multiply by 100: 0.48 = 48% Percent Decrease (Old−New)/Old × 100%
% → Fraction Write over 100, simplify: 40% = 40/100 = 2/5
Discounts Sale Price = Original × (1 − discount%)
Fraction → % Divide top by bottom × 100: 3/4 = 0.75 = 75%
Tax/Tip Total = Original × (1 + tax% or tip%)
Find % of number Multiply: 30% of 80 = 0.30×80 = 24
Simple Interest I = P×R×T (Principal × Rate × Time)
Find the whole Divide: 24 is 30% of what? → 24÷0.30 = 80
Part/Whole/Percent Part = Whole × Percent (as decimal)
Find the % Is/Of×100: 24 is what % of 80? → 24/80×100
RATIOS & PROPORTIONS — Setting Up and Solving
Ratio Rules & Examples: Proportion Solving:
Concept Explanation Step Method / Example
Ratio Definition Comparison of two quantities: a:b or a/b Set up Write equivalent fractions: a/b = c/d
Equivalent Ratios 2:3 = 4:6 = 6:9 — multiply/divide both by s Cross-multiply a×d = b×c
Part-to-Part 3 red: 5 blue → 3 red out of 8 total
Solve for x Isolate the unknown
Part-to-Whole 3 red out of 8 total = 3/8 are red
Example 1 x/12 = 5/6 → 6x=60 → x=10
Unit Rate 60 miles in 2 hours = 30 miles per hour
Example 2 3/4 = 15/x → 3x=60 → x=20
Scale Factor Map 1:50000 → 2cm = 100,000cm = 1km
Unit conv. 2.5 km × (1000m/1km) = 2500 m
Dosage calc Ordered: 250mg; on hand: 500mg/5mL →
UNIT CONVERSIONS — US Customary & Metric
US Customary Conversions: Metric System (SI) & Conversions:
Measure Conversions Prefix Meaning & Example
Length 12 in=1 ft | 3 ft=1 yd | 5280 ft=1 mile Kilo- (k) ×1000: 1 km = 1000 m
Weight 16 oz=1 lb | 2000 lb=1 ton Hecto- (h) ×100
Volume 8 oz=1 cup | 2 cups=1 pt | 2 pt=1 qt | 4 qt=1 gal Deka- (da) ×10
Time 60 sec=1 min | 60 min=1 hr | 24 hr=1 day Base metre, litre, gram
Created by ALLcoyura Academy Page 3
Deci- (d) ÷10: 1 dm = 0.1 m
Centi- (c) ÷100: 1 cm = 0.01 m
, A.L.L.
coyura Academy
ALGEBRA — EXPRESSIONS, EQUATIONS & INEQUALITIES
TEAS algebra focuses on solving equations, evaluating expressions, and word problems.
ALGEBRAIC EXPRESSIONS & EVALUATING
Key Vocabulary: Evaluating Expressions — Worked Examples:
Term Definition Expression Solution
Variable A letter representing an unknown value (x, y, Evaluate 3x−5 for x=4 3(4)−5 = 12−5 = 7
Constant A fixed number in an expression
Evaluate 2a²+b for a=3,b=1 2(9)+1 = 18+1 = 19
Coefficient Number multiplied by a variable: in 3x, 3 is th
Simplify 4x+2x−x = (4+2−1)x = 5x
Term A single number, variable, or product: 3x², 5,
Simplify 3(2x+4) = 6x+12 (distribute)
Like Terms Same variable and exponent: 3x and 7x; com
Simplify 5x+3−2x+7 = 3x+10 (combine like terms)
Expression Math phrase with no equals sign: 2x + 3
Equation Math statement with equals sign: 2x + 3 = 11 Factor 6x+9 = 3(2x+3)
SOLVING EQUATIONS — One & Two Step
One-Step Equations: Two-Step Equations:
Equation Solution Equation Step-by-Step
x+7=12 Subtract 7: x=5 2x+3=11 Step 1: subtract 3 → 2x=8 | Step 2: divide by 2
x−4=9 Add 4: x=13 3x−7=14 Add 7 → 3x=21 | Divide by 3 → x=7
3x=24 Divide by 3: x=8 x/4+2=6 Subtract 2 → x/4=4 | Multiply by 4 → x=16
x/5=6 Multiply by 5: x=30 5(x−2)=15 Divide by 5 → x−2=3 | Add 2 → x=5
−2x=14 Divide by −2: x=−7 2x+x=18 Combine: 3x=18 | Divide: x=6
INEQUALITIES, WORD PROBLEMS & LINEAR EQUATIONS
Inequalities: Word Problem Strategy:
Concept Rule Step Action
Symbols < less than | > greater than | ≤ less/equal | ≥ greate Step 1 — Read Read entire problem; identify what is being aske
Solve like eq. Solve same as equation: x+3>7 → x>4 Step 2 — Define Assign a variable: 'Let x = the unknown quantity'
Flip the sign Multiply/divide by NEGATIVE → FLIP the inequalit Step 3 — Set up Write an equation based on the relationships de
Example −2x<8 → divide by −2 → x>−4 (sign flipped!) Step 4 — Solve Solve the equation using algebraic methods
Graph Open circle = strict (</>); Closed circle = (≤/≥) Step 5 — Check Substitute answer back; verify it makes sense in
Compound AND means both conditions; OR means either con Key phrases 'more than' = +; 'less than' = −; 'times' = ×; 'of' =
Created by ALLcoyura Academy Page 4
