ACCUPLACER Arithmetic key terms

Any of the counting numbers 0, 1, 2, 3, and so on, with no fractional or decimal part. Whole numbers never include negatives or fractions.

A number with no fractional part, drawn from the set of positive counting numbers, their negatives, and zero. On a number line integers appear at evenly spaced marks.

One of the ten symbols 0 through 9 used to write numbers. The position of each digit within a numeral determines the value it contributes.

The value a digit has because of its position in a numeral. In 4,072 the 4 means four thousands while the 7 means seven tens.

A number written in the usual way using digits, such as 3,508. This contrasts with expanded form or word form of the same quantity.

A number rewritten as the sum of the values of each of its digits, for example 3,508 = 3,000 + 500 + 8. It makes place value visible.

Replacing a number with a nearby value that has fewer nonzero digits, chosen by checking the next digit. A digit 5 or greater rounds the target up.

An approximate answer found by rounding or by using compatible numbers instead of exact figures. Estimates are used to check whether a computed answer is reasonable.

Numbers adjusted slightly so they are easy to compute with mentally, such as changing 398 + 205 to 400 + 200. They help produce quick estimates.

The result of adding two or more numbers together. In 7 + 5 = 12, the sum is 12.

The result of subtracting one number from another. In 15 − 8 = 7, the difference is 7.

The result of multiplying two or more numbers. In 6 × 4 = 24, the product is 24.

The result of dividing one number by another. In 36 ÷ 9 = 4, the quotient is 4.

The number being divided in a division problem. In 36 ÷ 9, the dividend is 36.

The number you divide by in a division problem. In 36 ÷ 9, the divisor is 9.

A number that divides another number evenly with no remainder. The factors of 12 are 1, 2, 3, 4, 6, and 12.

The result of multiplying a given number by any whole number. The multiples of 4 include 4, 8, 12, 16, and so on.

The property of one whole number dividing another with zero remainder. Shortcut rules, such as a number ending in 0 or 5 being divisible by 5, let you test this quickly.

The amount left over when one whole number does not divide another evenly. Dividing 17 by 5 gives a quotient of 3 and a remainder of 2.

The agreed sequence for evaluating an expression: grouping symbols first, then exponents, then multiplication and division left to right, then addition and subtraction left to right.

Grouping symbols that tell you to perform the enclosed operation before others. In 3 × (4 + 2), add before multiplying.

A mathematical phrase built from numbers, operation signs, and possibly grouping symbols, with no equals sign. An expression is evaluated rather than solved.

A mathematical statement asserting that two expressions have the same value, indicated by an equals sign. It may be true, false, or true only for certain values.

The top number of a fraction, which counts how many equal parts are being taken. In 3/8 the numerator is 3.

The bottom number of a fraction, which tells how many equal parts make up one whole. In 3/8 the denominator is 8.

A number written as one whole number over another, representing part of a whole or a division. Examples include 1/2, 5/4, and 7/3.

Fractions that name the same amount even though their numerals differ, such as 1/2 and 4/8. Multiplying or dividing numerator and denominator by the same nonzero number creates them.

To rewrite a fraction with the smallest possible whole numbers by dividing numerator and denominator by a shared factor. For example, 6/8 simplifies to 3/4.

The largest whole number that divides two or more given numbers evenly. It is the divisor used to reduce a fraction to lowest terms.

The smallest nonzero number that is a multiple of two or more given numbers. It is used to find a common denominator for fractions.

A single denominator shared by two or more fractions so they can be added or compared. It is usually the least common multiple of the original denominators.

A number written as a whole number plus a proper fraction, such as 2 3/4. It can be rewritten as an improper fraction for computing.

A fraction whose numerator is greater than or equal to its denominator, such as 9/4. Its value is 1 or more and it may be rewritten as a mixed number.

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

The procedure for dividing by a fraction: keep the first fraction, change division to multiplication, and use the reciprocal of the second fraction.

A number written using a decimal point to show place values smaller than one, such as 4.25. Digits to the right of the point represent tenths, hundredths, and so on.

The dot separating the whole-number part of a decimal from its fractional part. Its position determines the size of every digit in the numeral.

A decimal in which one or more digits continue forever in a fixed pattern, such as 0.333... . It can be written with a bar over the repeating block.

A decimal that ends after a finite number of digits, such as 0.75. Fractions whose denominators have only factors of 2 and 5 convert to this form.

A ratio comparing a number to 100, written with the symbol %. For example, 45% means 45 out of every 100, or 45/100.

A comparison of two quantities by division, often written as a to b, a:b, or a/b. It states how much of one quantity exists per unit of another.

A ratio that compares quantities measured in different units, such as miles per hour or dollars per pound. It often describes how one quantity changes with another.

A rate expressed as an amount per single unit of the second quantity, found by dividing. For instance, 12 dollars for 3 pounds gives a unit rate of 4 dollars per pound.

A statement that two ratios are equal, such as 3/4 = 9/12. Proportions are solved by cross multiplying to find an unknown quantity.

A shortcut for solving a proportion by multiplying the numerator of one fraction by the denominator of the other and setting the results equal.

The portion of a whole being described in a percent or ratio problem. In finding 20% of 50, the part is the 10 that results.

The full quantity or base amount that a part is compared to in percent problems. It usually follows the word "of" in a percent sentence.

The amount a value grows, expressed as a percent of its original value. It is found by dividing the increase by the original amount and multiplying by 100.

The amount a value shrinks, expressed as a percent of its original value. It is found by dividing the decrease by the original amount and multiplying by 100.