Free TEAS 7 Math Exam Flashcards

Divide the numerator by the denominator: 5/8 becomes 5 divided by 8, or 0.625. The four-function calculator makes this trivial, so the real risk is setting the division up backward as 8 divided by 5, which gives 1.6.

Move the decimal point two places right and add the percent sign (0.045 = 4.5%); reverse the move to go from percent to decimal (103% = 1.03). On fill-in-the-blank numeric items, enter the value in exactly the form the question requests instead of adding extra digits such as 1.030.

1/8 = 0.125 = 12.5%, 1/4 = 0.25 = 25%, 1/3 = 0.333... = 33.3%, 1/2 = 0.5 = 50%, 2/3 = 0.666... = 66.7%, 3/4 = 0.75 = 75%. Recognizing these instantly saves calculator keystrokes in a section that averages only about 1.5 minutes per question.

Parentheses, then Exponents, then Multiplication and Division left to right, then Addition and Subtraction left to right. Multiplication does not outrank division and addition does not outrank subtraction, so 12 divided by 3 times 2 equals 8, not 2.

Rewrite both fractions over a common denominator, then combine only the numerators: 1/3 + 1/4 = 4/12 + 3/12 = 7/12. Denominators are never added, so 1/3 + 1/4 is not 2/7.

Multiply by the reciprocal of the divisor: 3/4 divided by 2/5 equals 3/4 times 5/2, or 15/8. Dividing by a value less than 1 makes the result larger, which is a fast sanity check on your answer.

Convert every value to a decimal first, then compare digit by digit from the left. Comparing raw fractions by eye invites the classic error of assuming 3/8 is larger than 2/5, when 0.375 is actually less than 0.4.

On a number line the value farther left is smaller, so -7 is less than -3 even though 7 is greater than 3. The same reversal applies to fractions: -1/2 is less than -1/4.

Undo the operations in reverse order of operations, applying the same step to both sides until the variable stands alone. Substituting your answer back into the original equation takes seconds and catches most sign and transposition errors.

Multiplying or dividing both sides by a negative number reverses the direction of the inequality, so -2x > 6 becomes x < -3. Adding or subtracting a negative number never flips the sign.

a(b + c) = ab + ac, so 3(x - 5) = 3x - 15. The most common slip is distributing to the first term only and writing 3x - 5, which changes the value of the expression.

Substitute the value for each variable, then follow the order of operations. Wrap substituted negatives in parentheses: if x = -4, then x squared is (-4)(-4) = 16, not -16.

Sum or increased by means add, difference or less than means subtract, product or of means multiply, quotient or per means divide, and is means equals. Order matters: five less than x is x - 5, not 5 - x.

Identify exactly what is being asked, list the given quantities with their units, choose the operations, compute, then re-read the question before selecting. Many wrong answer choices are correct intermediate values, such as total spent when the question asked for the amount remaining.

Convert every quantity to a common unit before combining them, since 3 feet plus 8 inches cannot be added as written. Converting at the start rather than at the end stops a single unit error from propagating through every later step.

part over whole equals percent over 100. Solving for whichever piece is missing handles all three question shapes: what is 30% of 60, what percent of 60 is 18, and 18 is 30% of what number.

Percent change equals (new value minus original value) divided by the original value, times 100. The denominator is always the ORIGINAL value; dividing by the new value is the single most common percent-change error.

An amount that rises 20% and then falls 20% does not return to its starting value: 100 becomes 120, then 96. Each percent must be applied to the running amount, not to the original.

Look only at the digit immediately to the right of the place you are rounding to: 5 or more rounds up, 4 or less rounds down. Digits farther right do not chain upward, so 4.449 rounds to 4.4 at the tenths place, not 4.5.

Estimate when the answer choices are far apart or the item says approximately, because rounding to friendly numbers can eliminate three options in seconds. Compute exactly only when two choices survive the estimate.

Write two equal ratios with matching units in matching positions, then cross-multiply: 3/4 = x/20 gives 4x = 60, so x = 15. If the units sit in different positions on each side, such as miles over hours set equal to hours over miles, the algebra still produces a number, but it is the wrong one.

Corresponding sides of similar figures are proportional, so a scale of 1 inch to 8 feet makes a 3.5-inch drawing represent 28 feet. Keep the drawing unit in the numerator on both sides of the proportion so the units cancel correctly.

In a direct proportion both quantities rise together and the quotient y divided by x stays constant; in an inverse proportion one rises as the other falls and the product xy stays constant. Doubling hours doubles pay (direct), but doubling workers halves the time (inverse).

A 3:2 ratio of nurses to aides means 3 parts out of 5 total parts are nurses, so nurses are 3/5, or 60%, of the staff. Reading 3:2 as three out of two, or as 3/2 of the whole, is the standard trap.

A unit rate expresses a comparison per one unit of the second quantity, so 240 miles in 4 hours is 60 miles per hour. Reducing to unit rates is what makes better-buy comparisons between different package sizes possible.

Rate of change equals the change in the output divided by the change in the input, the same computation as slope. A negative rate of change simply means the quantity is decreasing; it is not a sign that the arithmetic went wrong.

If an axis is labeled in thousands, a bar of height 6 represents 6,000. Skipping the label produces an answer that is the right shape but off by a factor of 1,000, and such values usually appear among the distractors.

A bar graph compares separate categories and its bars are drawn with gaps; a histogram shows how often values fall within continuous numeric intervals and its bars touch. Reordering bars is harmless on a bar graph but destroys the meaning of a histogram.

A circle chart shows each category's share of a whole that totals 100%, so it answers proportion questions directly. It cannot give raw counts unless a total is stated, and it cannot show change over time.

A line graph connects points to show how a quantity changes across an ordered variable such as time; a scatterplot plots paired values to reveal a relationship without implying any order. Connecting scatterplot points would falsely suggest a sequence that the data do not have.

Row totals, column totals, and the grand total must agree, so any single missing cell can be recovered by subtraction. Note carefully whether the item wants a raw count, a percentage of the row, or a percentage of the grand total, because the three answers differ.

Add every value and divide by the number of values. The mean is pulled toward extreme values, so one unusually large data point raises the mean even though the middle of the data has not moved.

Order the values from least to greatest and take the middle one; with an even count, average the two middle values. Because the median ignores how far out the extremes lie, it describes a skewed data set more fairly than the mean.

The value that occurs most often in a data set. A set can have no mode, one mode, or several modes, and the mode is the only one of the three centers that also works for non-numeric categories.

Range equals the largest value minus the smallest value, a one-number measure of spread. Because it uses only the two extremes, two data sets with the same range can be shaped completely differently.

Standard deviation describes how far values typically sit from the mean: a small value means the data cluster tightly, a large value means they scatter widely. It answers how spread out the data are, a question mean, median, and mode cannot address.

The independent variable is the one that is changed or selected and is plotted on the horizontal x-axis; the dependent variable responds to it and is plotted on the vertical y-axis. Swapping them mislabels which quantity is being explained by the other.

In a positive correlation both variables move in the same direction; in a negative correlation one rises as the other falls; no correlation shows no consistent pattern. Direction and strength are separate ideas, so a weak relationship can still be clearly positive.

Two variables can move together because of a third factor or pure coincidence, so even a strong correlation never proves that one causes the other. Expect a causal conclusion to appear as a tempting distractor on data-relationship items.

In y = mx + b, m is the slope, the change in y for each one-unit change in x, and b is the y-intercept, the value of y when x equals 0. A negative m means the line falls from left to right, matching a negative relationship between the variables.

Perimeter is the distance around a two-dimensional shape (plain units), area is the surface it covers (square units), and volume is the space a solid holds (cubic units). Matching the unit in the answer choices to the quantity requested eliminates wrong options immediately.

Rectangle: A = lw. Triangle: A = one-half times base times height. Circle: A = pi times r squared. The triangle's height is the perpendicular height, not the slanted side, and the circle formula uses the radius, never the diameter.

C = 2 times pi times r, which is the same as pi times the diameter since d = 2r. A circle with a radius of 4 has a circumference of 8 pi, about 25.1; squaring the radius instead of doubling it would give the area formula by mistake.

Rectangular prism: V = lwh. Cylinder: V = pi times r squared times h. Both are simply the area of the base multiplied by the height, so identifying the base shape first tells you which formula applies.

In a right triangle, a squared plus b squared equals c squared, where c is the hypotenuse opposite the right angle. Solving for a leg requires subtraction (a squared = c squared minus b squared), so adding in that case gives a value that is too large.

Multiply by conversion fractions arranged so the unwanted unit cancels: 5 ft times (12 in / 1 ft) equals 60 in. If the unit you want does not end up in the numerator, the conversion fraction is upside down.

kilo- (1,000), hecto- (100), deka- (10), the base unit, deci- (0.1), centi- (0.01), milli- (0.001). Each rung is a factor of 10, so converting within the metric system only moves the decimal point.

12 in = 1 ft, 3 ft = 1 yd, 5,280 ft = 1 mile, 16 oz = 1 lb, 8 fluid oz = 1 cup, 2 cups = 1 pint, 2 pints = 1 quart, 4 quarts = 1 gallon. The TEAS provides no conversion reference chart in either the online or paper format, so these common equivalents must be recalled from memory.

1 in = 2.54 cm exactly, 1 kg is about 2.2 lb, 1 L is about 1.06 quarts, and 1 mL equals 1 cubic centimeter. Predicting whether the number should get larger or smaller tells you whether to multiply or divide.

The linear conversion factor must be raised to the same power as the unit: because 1 ft = 12 in, 1 square foot equals 144 square inches and 1 cubic foot equals 1,728 cubic inches. Multiplying an area by 12 instead of 144 produces an error of more than tenfold.