Your FREE Praxis Core Math Flashcards 2026 – 200+ Cards

A whole number greater than 1 with exactly two distinct factors: 1 and itself (2, 3, 5, 7, 11, 13...).

A whole number greater than 1 that has more than two factors (4, 6, 8, 9, 10...). It is not prime.

No. A prime has exactly two distinct factors; 1 has only one factor (itself), so it is neither prime nor composite.

Yes. 2 is the only even prime number — every other even number is divisible by 2.

A whole number that divides another evenly with no remainder. Factors of 12 are 1, 2, 3, 4, 6, 12.

The product of a number and any whole number. Multiples of 5 are 5, 10, 15, 20, 25...

The largest factor shared by two numbers. GCF of 48 and 60 is 12. Find it by listing factors or using prime factorization.

The smallest multiple shared by two numbers. LCM of 8 and 12 is 24. Useful for adding fractions and 'when do events line up again' problems.

Writing a number as a product of primes. 60 = 2 × 2 × 3 × 5 = 2² × 3 × 5.

Exactly 4. If x and y are distinct primes, xy has factors 1, x, y, and xy.

A whole number and its opposite, including zero: ..., −2, −1, 0, 1, 2, ... No fractions or decimals.

Any number that can be written as a fraction a/b where a and b are integers and b ≠ 0. Includes terminating and repeating decimals.

A number that cannot be written as a fraction; its decimal never ends and never repeats. Examples: √2, π.

The distance of a number from zero on the number line; always nonnegative. |−7| = 7 and |7| = 7.

Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right).

Find a common denominator, rewrite each fraction, add the numerators, keep the denominator, then simplify. 3/4 + 5/6 = 9/12 + 10/12 = 19/12.

Use a common denominator, subtract numerators, keep the denominator, simplify. 11/12 − 1/4 = 11/12 − 3/12 = 8/12 = 2/3.

Multiply numerators and multiply denominators, then simplify. 2/3 × 9/10 = 18/30 = 3/5.

Multiply by the reciprocal of the second fraction (keep–change–flip). 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8.

The multiplicative inverse — flip the fraction. The reciprocal of 2/5 is 5/2; the reciprocal of 4 is 1/4. A number times its reciprocal equals 1.

Divide the numerator and denominator by their GCF. 18/30 ÷ 6/6 = 3/5.

A fraction whose numerator is greater than or equal to its denominator, such as 7/4. It can be written as the mixed number 1¾.

A whole number plus a fraction, such as 2½. Convert to an improper fraction by multiplying the whole number by the denominator and adding the numerator: 2½ = 5/2.

Divide the numerator by the denominator. 3/4 = 3 ÷ 4 = 0.75.

Write the decimal over its place value, then simplify. 0.75 = 75/100 = 3/4.

Divide by 100 (move the decimal two places left). 45% = 0.45.

Multiply by 100 (move the decimal two places right). 0.6 = 60%.

Multiply the number by the percent as a decimal. 20% of 80 = 0.20 × 80 = 16.

Divide the part by the percent as a decimal. If 15 is 25% of a number, the number is 15 ÷ 0.25 = 60.

Change ÷ original × 100. Always divide by the starting value. From 80 to 100: 20 ÷ 80 = 25% increase.

To increase a number by 25%, multiply by 1.25; to decrease by 25%, multiply by 0.75.

A comparison of two quantities, written 3:5, 3 to 5, or 3/5. Reduce ratios like fractions.

An equation stating two ratios are equal, such as 2/3 = x/12. Solve by cross-multiplying: 3x = 24, so x = 8.

For a/b = c/d, multiply diagonally: a × d = b × c. Used to solve proportions.

A rate with a denominator of 1, such as miles per hour or cost per item. Find it by dividing. $12 for 4 lbs = $3 per lb.

The ratio used to enlarge or reduce; multiply each measurement by it. A 1:50 map scale means 1 unit on the map equals 50 real units.

A small number telling how many times to multiply the base by itself. 2³ = 2 × 2 × 2 = 8.

Any nonzero number raised to the 0 power equals 1. 7⁰ = 1.

A negative exponent means take the reciprocal: x⁻ⁿ = 1/xⁿ. So 2⁻³ = 1/8.

When multiplying like bases, add the exponents: xᵐ · xⁿ = xᵐ⁺ⁿ. So 2³ · 2⁴ = 2⁷.

When dividing like bases, subtract the exponents: xᵐ ÷ xⁿ = xᵐ⁻ⁿ. So 2⁵ ÷ 2² = 2³.

Raise a power to a power by multiplying the exponents: (xᵐ)ⁿ = xᵐⁿ. So (2³)² = 2⁶.

A value that, multiplied by itself, gives the number. √36 = 6 because 6 × 6 = 36.

The product of an integer with itself: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100... Their square roots are whole numbers.

A number written as a value between 1 and 10 times a power of 10. 47,000 = 4.7 × 10⁴.

Replace numbers with nearby easy values to check that an answer is reasonable. 19 × 21 ≈ 20 × 20 = 400.

Look at the digit to the right: 5 or more rounds up, 4 or less rounds down. 3.47 to the tenths = 3.5.

A number is divisible by 3 if the sum of its digits is divisible by 3. 132 → 1+3+2 = 6, divisible by 3.

A number is divisible by 9 if the sum of its digits is divisible by 9. 729 → 7+2+9 = 18, divisible by 9.

A number is divisible by 4 if its last two digits form a number divisible by 4. 1,316 → 16 is divisible by 4.

Even numbers are divisible by 2 (end in 0, 2, 4, 6, 8); odd numbers are not. Even × any = even; odd × odd = odd.

Subtract the absolute values and keep the sign of the larger one. −8 + 5 = −3.

Same signs give a positive product; different signs give a negative product. (−4)(−3) = 12; (−4)(3) = −12.

Add the opposite: a − b = a + (−b). 5 − (−3) = 5 + 3 = 8.

Numbers increase from left to right. −5 is less than −2, which is less than 0, which is less than 3.

Use a common denominator or cross-multiply. For 3/4 vs 5/7: 3×7 = 21 vs 5×4 = 20, so 3/4 is larger.

Fractions that name the same value, found by multiplying or dividing top and bottom by the same number. 1/2 = 2/4 = 3/6.

To make 2/3 of a recipe needing 3/4 cup, multiply: 2/3 × 3/4 = 6/12 = 1/2 cup.

The value of a digit based on its position. In 3,482 the 4 means 400 (hundreds place).

Round to the nearest cent (hundredths) by looking at the thousandths digit. $4.567 ≈ $4.57.

The counting numbers plus zero: 0, 1, 2, 3, 4, ... No negatives, fractions, or decimals.

A pair of prime numbers that differ by 2, such as 11 and 13 or 17 and 19.

Exactly two: 1 and the number itself. That is the definition of prime.

Find the perfect squares it falls between. √50 is between √49 = 7 and √64 = 8, so about 7.1.

Multiply or divide by the conversion factor. 3 feet = 36 inches (×12); 250 cm = 2.5 m (÷100).

60 seconds = 1 minute, 60 minutes = 1 hour. 150 minutes = 2 hours 30 minutes.

Multiply by conversion fractions so unwanted units cancel, leaving the desired unit. Lets you convert miles/hour to feet/second, etc.

A percent over 100% means more than the whole. 150% of 40 = 1.5 × 40 = 60.

Markup adds a percent to a price; discount subtracts one. A $50 item at 20% off costs 50 × 0.80 = $40.

I = Prt, where P is principal, r is the annual rate (as a decimal), and t is time in years. $1,000 at 5% for 2 years earns $100.

To split items into identical groups using all of them, find the GCF of the counts. 54 pencils and 72 erasers → GCF 18 kits.

To find when two repeating events coincide, find the LCM of their periods. Laps of 6 and 9 minutes meet again at 18 minutes.

'Of' means multiply. 1/2 of 1/3 = 1/2 × 1/3 = 1/6.

The sum 2a + 4a + ... + 2na is n(n+1)a, since 2a(1 + 2 + ... + n) = 2a · n(n+1)/2.

A decimal with a digit or block that repeats forever, written with a bar. 1/3 = 0.333... = 0.3̄.

A decimal that ends. A fraction terminates when its denominator (in lowest terms) has only 2s and 5s as factors. 3/8 = 0.375.

The number that adds to a given number to make 0. The opposite of 7 is −7.

Multiply the number by itself three times. 4³ = 4 × 4 × 4 = 64.

Multiply the number by itself. 9² = 9 × 9 = 81.

Order does not change a sum or product. a + b = b + a; a × b = b × a.

Grouping does not change a sum or product. (a + b) + c = a + (b + c).

a(b + c) = ab + ac. So 3(x + 4) = 3x + 12.

If one choice has m options and another has n options, the number of combined outcomes is m × n. 3 shirts × 4 pants = 12 outfits.

Use friendly benchmarks. 10% of a number moves the decimal one place left; 50% is half; 25% is a quarter.

Distance = rate × time, so rate = distance ÷ time. 150 miles in 3 hours = 50 mph.

Divide total by quantity to get a per-unit value. 240 copies in 8 minutes = 30 copies per minute.

Each inch is divided into halves, quarters, eighths, sixteenths. A mark halfway between 2 and 3 is 2½ inches.

Compare to 0, ½, or 1. 7/15 is just under ½; 9/10 is near 1.

The power of ten closest to a number. 6,200 is on the order of 10³ (thousands).

Subtracting a negative is the same as adding. 3 − (−5) = 3 + 5 = 8 — a common careless error.

Going from 20% to 25% is a rise of 5 percentage points, but a 25% relative increase (5 ÷ 20). Keep them distinct.

Rational numbers terminate or repeat; irrationals (π, √2) do neither. π ≈ 3.14159... never repeats.

Round each value first to confirm an exact answer is reasonable. If 4.9 × 9.8 ≈ 5 × 10 = 50, then 48.02 is sensible.

Add the ratio parts, divide the total by that sum, then multiply. Share $60 in a 1:2:3 ratio → parts of $10, $20, $30.

'Of' means multiply, 'per' means divide, 'is' means equals. Translate the words into an operation.

Like fractions share the same denominator and can be added directly; unlike fractions need a common denominator first.

Round each factor to a friendly number to predict the size of the answer before computing exactly.

Line up the decimal points and compare digit by digit from the left. 0.4 > 0.38 because 0.40 > 0.38.

10% is the decimal moved one place; 20% is double that. A 20% tip on $30 is about $6.

Total distance ÷ total time, not the average of the speeds. Compute each leg's distance and time first.

Add all the values and divide by how many there are. The mean of 6, 8, 8, 10, 13 is 45 ÷ 5 = 9.

The middle value of an ordered data set. With an even count, average the two middle numbers. Median of 12, 15, 19, 22, 27, 31 is (19+22)/2 = 20.5.

The value that appears most often. In 14, 16, 16, 15, 16, 14, 17 the mode is 16. A set can have no mode or several.

The largest value minus the smallest. For 8, 3, 7, 14, 10, 6, 2, 9 the range is 14 − 2 = 12.

The mean is pulled toward extreme values; the median resists them. For skewed data (incomes, home prices) the median better represents the center.

A measure of how spread out data is around the mean. A larger standard deviation means more spread; a value of 0 means all data points are identical.

Removing a number above the mean lowers the average; removing one below it raises the average. Recompute with the new sum and count.

Multiply each value by its weight (or count), add, then divide by the total weight. A grade with a heavier final counts that score more.

Favorable outcomes ÷ total equally likely outcomes, a value from 0 to 1. Rolling a 4 on a die has probability 1/6.

Multiply the probabilities. P(A and B) = P(A) × P(B). Two events with 0.6 and 0.8 → 0.48.

Add and subtract the overlap. P(A or B) = P(A) + P(B) − P(A and B).

The chance the event does NOT happen: P(not A) = 1 − P(A). If P(rain) = 0.3, P(no rain) = 0.7.

Events where one outcome does not affect the other, like separate coin flips. Their probabilities multiply.

Events where the first outcome changes the second's probability, like drawing cards without replacing them.

Theoretical comes from equally likely outcomes; experimental comes from actual trial results. Over many trials, experimental approaches theoretical.

Uses rectangular bars to compare amounts across categories. Bar length shows the value; read the axis scale carefully.

Shows how a quantity changes over time using points connected by line segments. Good for trends.

Shows parts of a whole as sectors; the whole circle is 100%. A 25% slice is a quarter of the circle (90°).

A bar graph for grouped numerical data; bars touch and each covers an interval (bin). Shows the shape of a distribution.

Plots paired data as points to show the relationship between two variables. A rising pattern suggests a positive correlation.

As one variable increases, the other tends to increase. On a scatterplot the points trend upward to the right.

As one variable increases, the other tends to decrease. On a scatterplot the points trend downward to the right.

Two variables moving together does not prove one causes the other; a third factor may explain both.

A straight line through scatterplot points that summarizes the trend, used to estimate and predict values.

Organizes data by two categories in rows and columns. Read the correct row and column to find a count or a conditional rate.

Data with a long tail to one side. Right-skewed: mean > median; left-skewed: mean < median. The tail points toward the mean.

A distribution with a long right tail caused by a few large values. The mean is greater than the median.

A distribution with a long left tail caused by a few small values. The mean is less than the median.

A distribution where the two halves mirror each other; the mean and median are approximately equal.

A value far from the rest of the data. Outliers strongly affect the mean and the range but barely move the median.

Three values (Q1, Q2/median, Q3) that split ordered data into four equal parts. Q1 is the 25th percentile, Q3 the 75th.

Q3 − Q1, the spread of the middle 50% of the data. It resists outliers.

Displays the five-number summary: minimum, Q1, median, Q3, and maximum. The box spans the IQR.

The percent of data values at or below a given value. Scoring in the 80th percentile means you did as well as or better than 80% of test takers.

A population is the entire group; a sample is the subset actually studied. A good sample is random and representative.

A sample in which every member of the population has an equal chance of being chosen, reducing bias.

A sample that is not representative of the population, giving misleading results. A survey only of volunteers is biased.

The number of times a value or category occurs in a data set. A frequency table lists each value with its count.

A category's count divided by the total, often written as a fraction, decimal, or percent. It estimates probability.

Mean, median, and mode — each describes a 'typical' value differently. The best one depends on the shape of the data.

Range, interquartile range, and standard deviation — they describe how spread out the data is.

Check the axis intervals before estimating values; gridlines may count by 2s, 5s, 10s, etc.

A graph can distort data with a truncated axis, unequal intervals, or 3-D effects. Always read the actual numbers.

Multiply each outcome by its probability and add. The long-run average result of a repeated random process.

Replacing the item keeps each draw independent, so probabilities stay the same and multiply.

Not replacing the item changes the totals, making draws dependent; recompute the probability for each later draw.

A permutation counts ordered arrangements; a combination counts groups where order does not matter. 'Choosing 3' usually means a combination.

Events that cannot happen together; their joint probability is 0, so P(A or B) = P(A) + P(B).

Apply the percent to the relevant total. If 30% of 250 students walk to school, that is 0.30 × 250 = 75 students.

Compare both center (mean/median) and spread (range/standard deviation). Equal means can hide very different spreads.

A running total of frequencies; each entry adds the previous counts. Used to find medians and percentiles.

Splits each value into a stem (leading digits) and a leaf (last digit) to show the distribution while keeping the data.

Probabilities range from 0 (impossible) to 1 (certain). 0.5 means equally likely to happen or not.

The set of all possible outcomes of an experiment. For one die roll the sample space is {1, 2, 3, 4, 5, 6}.

Probability compares favorable outcomes to the total; odds compare favorable to unfavorable. Probability 1/4 is odds of 1 to 3.

Multiply the slice's percent by the total. A 40% slice of a $2,000 budget is 0.40 × 2,000 = $800.

A rising line shows increase, a falling line shows decrease, and a flat line shows no change over the interval.

Multiply each value by its frequency, add those products, and divide by the total frequency.

A data set with two values that tie for most frequent; it has two modes. The distribution shows two peaks.

Read the trend line at the desired x-value to estimate y. Extrapolating far beyond the data is unreliable.

A letter that represents an unknown or changing number, such as x or n in an expression or equation.

A combination of numbers, variables, and operations with no equals sign, such as 3x + 5.

A statement that two expressions are equal, containing an equals sign, such as 2x + 3 = 11.

Terms with the same variable raised to the same power; only like terms can be combined. 3x and 5x combine to 8x.

Undo the operation on both sides. For x + 7 = 12, subtract 7: x = 5.

Undo addition/subtraction first, then multiplication/division. For 4x − 7 = 21: add 7 (4x = 28), divide by 4 (x = 7).

Collect variables on one side and numbers on the other. 3(x + 2) = 5x − 4 → 3x + 6 = 5x − 4 → x = 5.

< less than, > greater than, ≤ less than or equal to, ≥ greater than or equal to.

Solve like an equation, with one rule: flip the inequality sign when you multiply or divide both sides by a negative number.

Multiplying or dividing by a negative reverses the inequality. −3x > 12 → x < −4 (sign flips).

The steepness of a line: rise over run, the change in y divided by the change in x. In y = mx + b, the slope is m.

For points (x₁, y₁) and (x₂, y₂): slope = (y₂ − y₁) ÷ (x₂ − x₁). Through (2, 3) and (6, 11): (11−3)/(6−2) = 2.

y = mx + b, where m is the slope and b is the y-intercept (where the line crosses the y-axis).

The point where a line crosses the y-axis, where x = 0. In y = 2x + 5 the y-intercept is 5.

The point where a line crosses the x-axis, where y = 0. Set y = 0 and solve for x.

A horizontal line has slope 0; a vertical line has an undefined slope.

Lines that never meet; they have equal slopes but different y-intercepts.

Lines that meet at a right angle; their slopes are negative reciprocals (their product is −1).

Two or more equations solved together; the solution is the point satisfying all of them — where the graphs intersect.

Solve one equation for a variable, substitute it into the other, and solve. Good when a variable is already isolated.

Add or subtract the equations to cancel one variable, then solve. Multiply an equation first if needed to match coefficients.

Substitute the given value for the variable and simplify. For 3x + 4 when x = 5: 3(5) + 4 = 19.

'More than' is +, 'less than' is −, 'product' is ×, 'quotient' is ÷. 'Five less than twice a number' is 2x − 5.

A rule that assigns exactly one output to each input. Written f(x); f(3) means evaluate the rule at x = 3.

Use the distributive property to clear parentheses before combining like terms. 2(x + 3) = 10 → 2x + 6 = 10 → x = 2.

The distance around a figure — the sum of all side lengths. A rectangle's perimeter is 2(length + width).

length × width. A 9 cm by 4 cm rectangle has an area of 36 square centimeters.

½ × base × height. A triangle with base 10 and height 6 has area ½ × 10 × 6 = 30 square inches.

π × radius². With radius 5 and π ≈ 3.14, area ≈ 3.14 × 25 ≈ 79 square units.

π × diameter (or 2 × π × radius). A circle with diameter 8 and π ≈ 3.14 has circumference ≈ 25 units.

base × height, where height is the perpendicular distance between the parallel sides.

½ × (base₁ + base₂) × height — the average of the parallel sides times the height between them.

length × width × height. A 5 × 3 × 4 box has a volume of 60 cubic units.

π × radius² × height. A cylinder with radius 3 and height 4 has volume π × 9 × 4 = 36π cubic units.

The total area of all faces of a 3-D figure, measured in square units. Add the areas of each face.

For a right triangle with legs a and b and hypotenuse c: a² + b² = c². A 3-4-5 triangle satisfies it (9 + 16 = 25).

The longest side of a right triangle, opposite the right angle. The Pythagorean theorem finds it from the two legs.

Equilateral (3 equal sides), isosceles (2 equal sides), scalene (no equal sides).

Acute (all angles < 90°), right (one 90° angle), obtuse (one angle > 90°).

Always 180°. If two angles are 50° and 60°, the third is 180° − 110° = 70°.