ACCUPLACER Arithmetic flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Order of operations

Evaluate parentheses first, then exponents, then multiplication and division from left to right, then addition and subtraction from left to right.

Divisibility rule for 3

A whole number is divisible by 3 if the sum of its digits is divisible by 3, for example 471 since 4+7+1=12.

Prime number

A whole number greater than 1 whose only positive divisors are 1 and itself; 2, 3, 5, 7, and 11 are examples.

Remainder formula

Dividend equals divisor times quotient plus remainder, and the remainder is always less than the divisor.

Rounding whole numbers

Find the place being rounded, then increase it by one if the digit to its right is 5 or more; otherwise leave it unchanged.

Commutative property

Addition and multiplication can be reordered without changing the result: a+b=b+a and a×b=b×a. Subtraction and division do not have this property.

Distributive property

Multiplying a sum by a number gives the same result as multiplying each addend separately: a×(b+c)=a×b+a×c.

Place value order

Reading left from the decimal, whole-number places are ones, tens, hundreds, thousands, ten-thousands, hundred-thousands, then millions.

Adding fractions

Rewrite the fractions with a common denominator, add the numerators, and keep that denominator, then simplify the result.

Dividing fractions

To divide by a fraction, multiply by its reciprocal, so a/b ÷ c/d becomes a/b × d/c.

Multiplying fractions

Multiply the numerators together and the denominators together, then simplify; simplifying before multiplying keeps numbers smaller.

Improper fraction conversion

Convert a mixed number by multiplying the whole number by the denominator, adding the numerator, and placing the result over the denominator.

Simplifying fractions

Divide the numerator and denominator by their greatest common factor to write the fraction in lowest terms.

Comparing fractions

For positive denominators, a/b is greater than c/d exactly when a×d is greater than b×c, found by cross-multiplying.

Equivalent fractions

Multiplying or dividing both numerator and denominator by the same nonzero number produces a fraction with the same value.

Reciprocal

The reciprocal of a fraction a/b is b/a, found by swapping numerator and denominator; the product of a fraction and its reciprocal is 1.

Fraction size test

A fraction a/b is less than 1 when a<b, equal to 1 when a=b, and greater than 1 when a>b.

Adding decimals

Line up the decimal points vertically, add or subtract as with whole numbers, and place the decimal point in the answer directly below.

Multiplying decimals

Multiply as with whole numbers, then give the answer as many decimal places as the two factors have combined.

Dividing decimals

Move the divisor's decimal point to make it a whole number, move the dividend's point the same number of places, then divide.

Multiplying by powers of ten

Multiplying by 10, 100, or 1000 moves the decimal point 1, 2, or 3 places to the right; dividing moves it left the same number of places.

Comparing decimals

Line up place values and compare digits from left to right, adding trailing zeros as needed so 0.5 and 0.50 are equal.

Decimal place values

The places to the right of the decimal point are tenths, hundredths, thousandths, and ten-thousandths, in that order.

Fraction to decimal

Divide the numerator by the denominator to convert a fraction to a decimal, for example 3/4 becomes 0.75.

Rounding decimals

Locate the place being rounded and increase it by one if the digit immediately to its right is 5 or more.

Percent definition

Percent means per hundred, so p% equals p/100; for example 45% equals 0.45 or the fraction 9/20.

Percent equation

Part equals percent times whole, written P = r × W, where r is the percent expressed as a decimal.

Percent change formula

Percent change equals the new value minus the old value, divided by the old value, times 100; positive means increase.

Solving proportions

Set the two ratios equal as a/b = c/d and cross-multiply to get ad = bc, then solve for the missing term.

Ratio notation

A ratio compares two quantities and may be written with a colon a:b, with the word to, or as the fraction a/b.

Decimal to percent

Multiply the decimal by 100 and attach a percent sign; for example 0.35 becomes 35%.

Unit rate

A ratio with a denominator of 1, found by dividing the first quantity by the second, such as miles per hour.