TEAS 7 Mathematics Study Guide

Fractions and decimals

Adding and subtracting fractions needs a common denominator; multiplying does not. To compare fractions quickly, cross-multiply rather than converting both to decimals.

Always simplify the final answer. Unsimplified results are frequently offered as distractors.

Multiply and divide fractions

Multiply straight across, numerator by numerator and denominator by denominator. To divide, invert the second fraction and multiply — the rule usually remembered as "keep, change, flip".

Cancel common factors before multiplying. It is faster and it avoids simplifying a large fraction at the end.

Converting fractions into decimals

Divide the numerator by the denominator. Knowing the common conversions on sight — 1/2, 1/3, 1/4, 1/5, 1/8 and their multiples — saves time you will need elsewhere.

Percent and decimals

A percentage is a fraction of 100, so 45% is 0.45. To find a percentage of a number, multiply; to find what percentage one number is of another, divide the part by the whole and multiply by 100.

Percentage increase and decrease use the original value as the denominator, never the new one.

Proportions

A proportion sets two ratios equal and is solved by cross-multiplying. This is the single most useful skill on the section, because dosage, scale and unit problems are all proportions in disguise.

Write the units into your setup. If they do not cancel to leave the unit you want, the proportion is arranged wrongly.

Absolute change and relative change

Absolute change is the raw difference between two values. Relative change expresses that difference as a percentage of the starting value, which is why a small absolute change can be a large relative one.

Variables and equations

Solve by isolating the variable, doing the same operation to both sides and undoing operations in reverse order. Substitute your answer back into the original equation to check.

Dependent and independent variables

The independent variable is the one that is changed or controlled; the dependent variable is the one measured in response. On a graph the independent variable goes on the x-axis.

Phrase it as "the dependent variable depends on the independent one" and the pair is hard to mix up.

Application of slope

Slope is rise over run: the change in y divided by the change in x. In a word problem it is a rate — cost per item, distance per hour, dose per kilogram.

A positive slope rises left to right, a negative slope falls, and a horizontal line has a slope of zero.

Money management

Budgeting questions cover income against expenses, unit price comparison, discounts, tax, tips and simple interest. They are multi-step arithmetic problems presented in a real context.

Apply a discount before tax unless the question says otherwise, and read carefully whether it asks for the amount saved or the amount paid.

Measurements and units

You need household and metric conversions and the relationships between them: 1 kg is about 2.2 lb, 1 inch is 2.54 cm, 1 L is about 1.06 quarts. Convert in single, checkable steps.

Divide pounds by 2.2 to reach kilograms. Multiplying instead is the most common error on the whole section.

Identifying appropriate units of measurement

Choosing a sensible unit is its own skill: millilitres for medication, litres for fluid intake, grams for a dressing, kilograms for a patient. The answer is the unit that gives a manageable number.

Visualizing data

Bar charts compare categories, line graphs show change over time, pie charts show parts of a whole, and scatter plots show relationships between two variables. Match the display to the question being asked.

Statistics

Mean is the average, median the middle value of an ordered list, mode the most frequent, and range the highest minus the lowest. Median resists outliers where mean does not.

With an even number of values, the median is the mean of the middle two.

Probability

Probability is favourable outcomes over total outcomes, expressed as a fraction, decimal or percentage between 0 and 1. For independent events happening together, multiply the separate probabilities.

Area of geometric figures

Rectangle is length × width, triangle is half base × height, parallelogram is base × height. Composite shapes are solved by splitting them into these and adding.

Area answers carry squared units. An answer given in plain centimetres is wrong before you check the arithmetic.

Circumference and area of a circle

Circumference is 2πr and area is πr². The commonest slip is being given a diameter and using it as the radius, which doubles or quadruples the answer.

Sides of a right-triangle

The Pythagorean theorem, a² + b² = c², relates the two shorter sides to the hypotenuse. The hypotenuse is always the longest side and always opposite the right angle.