HESI A2 Math key terms

The top number of a fraction. It tells how many equal parts are being counted or described, as in 3/5 where 3 is the numerator.

The bottom number of a fraction. It names how many equal parts the whole has been split into, as in 3/5 where 5 is the denominator.

A fraction whose numerator is smaller than its denominator, so its value is less than one whole, such as 2/7 or 5/8.

A fraction whose numerator is equal to or larger than its denominator, so its value is one or more, such as 9/4 or 6/6.

A value written as a whole number plus a fraction, such as 2 1/3. It can be rewritten as an improper fraction for multiplying or dividing.

Fractions that name the same amount even though the numbers differ, such as 1/2 and 4/8. Multiplying or dividing top and bottom by the same nonzero number creates them.

Rewriting a fraction with the smallest possible whole numbers by dividing numerator and denominator by their greatest common factor, as 12/18 becomes 2/3.

The smallest number that both denominators divide into evenly. It is used to rewrite fractions with a shared bottom before adding or subtracting them.

Any shared denominator that two or more fractions can be rewritten to use. Fractions must share one before they can be added or subtracted directly.

The fraction flipped upside down, formed by swapping numerator and denominator. The reciprocal of 3/5 is 5/3, and multiplying a fraction by its reciprocal gives 1.

A procedure that keeps the first fraction, changes division to multiplication, and multiplies by the reciprocal of the second fraction. For example, 2/3 ÷ 4/5 becomes 2/3 × 5/4.

A shortcut for multiplying fractions in which a numerator and a denominator sharing a factor are reduced before multiplying, keeping the numbers small and the answer already simplified.

The largest whole number that divides two or more given numbers with no remainder. It is the number used to reduce a fraction to lowest terms.

The smallest nonzero number that is a multiple of two or more given numbers. For 6 and 8 the least common multiple is 24, which also serves as a common denominator.

The value a digit holds based on its position in a number. In 4.276 the 2 means two tenths, the 7 means seven hundredths, and the 6 means six thousandths.

The dot separating the whole-number part of a decimal from its fractional part. Digits to its right represent tenths, hundredths, thousandths, and so on.

Replacing a number with a nearby value of a chosen place. Look at the digit to the right of that place; 5 or more rounds up, 4 or less stays the same.

A decimal in which one digit or block of digits continues forever, such as 0.333... for 1/3. It is often written with a bar over the repeating part.

A decimal that stops after a finite number of digits, such as 0.75 for 3/4 or 0.125 for 1/8. It can be written exactly without rounding.

A ratio comparing a number to 100. The symbol % means per hundred, so 45% equals 45/100 or 0.45.

The relationship part = percent × whole, used to solve for an unknown amount, rate, or base. For instance, 18 is 30% of 60 because 0.30 × 60 = 18.

The amount of increase or decrease stated as a percent of the original value. Find the difference, divide by the original amount, then multiply by 100.

A statement that two ratios are equal, such as 3/4 = 9/12. Cross-multiplying the two ratios produces an equation that can be solved for an unknown.

A comparison of two quantities by division, often written as 3:5 or 3/5. It describes relative size rather than an exact count.

A solving method for proportions in which each numerator is multiplied by the opposite denominator. The two products are set equal to find the missing value.

A rate expressed for exactly one unit of the second quantity, such as 60 miles per 1 hour or $3.25 per 1 pound. It is found by dividing the first quantity by the second.

A reduction from the original price, usually stated as a percent. Multiply the original price by the discount rate to get the savings, then subtract from the original price.

A percentage of a purchase price added to the total by a government. It is computed by multiplying the price by the tax rate and adding that amount.

Money paid for borrowing or earned on a deposit, calculated only on the original principal using interest = principal × rate × time, with time measured in years.

The measurement system used commonly in the United States, including inches, feet, yards, miles, ounces, pounds, cups, pints, quarts, and gallons.

A decimal-based measurement system using prefixes such as kilo-, centi-, and milli- attached to base units like meter, liter, and gram. Conversions move the decimal point.

Changing a measurement from one unit to another by multiplying by a conversion factor equal to 1, such as 12 inches per 1 foot, so the value stays the same.

A fraction that expresses the same quantity in two different units, such as 1,000 milliliters over 1 liter. Because the amounts are equal, the fraction equals 1.

A setup method in which units are written with each number and canceled diagonally, leaving only the desired unit. It helps prevent multiplying by the wrong factor.

A 24-hour clock format that avoids a.m. and p.m. Hours after noon continue past 12, so 2:30 p.m. is written as 1430 and midnight is 0000.

The amount of time that passes between a start and an end point. It is found by subtracting the start time from the end time, regrouping 60 minutes as one hour when needed.

Finding an approximate answer by rounding numbers to convenient values before computing. It is used to check whether an exact answer is reasonable.

The agreed sequence for evaluating expressions: parentheses first, then exponents, then multiplication and division left to right, then addition and subtraction left to right.

A letter-based number system using I, V, X, L, C, D, and M for 1, 5, 10, 50, 100, 500, and 1,000. A smaller symbol before a larger one is subtracted.