ATI TEAS - Mathematics

Writing decimals in words

0.07: seven hundredths 0.7: seven tenths 7.0: seven 0.009 nine thousandths 0.113 one hundred thirteen thousandths 0.901 nine hundred one thousandths

Decimal point

A symbol that used to separate the ones place from the tenths place in decimals or dollars from cents in currency.

Operations with Decimals - Adding and Subtracting Decimals

Adding and Subtracting Decimals - When adding and subtracting decimals, the decimal points must always be aligned. Adding decimals is just like adding regular whole numbers Example: 4.5 + 2 = 6.5

Operations with Fractions - Adding and Subtracting Fractions

Adding and Subtracting Fractions -

Operations with Positive and Negative Numbers - Addition

Addition - When adding signed numbers if the signs are the same simply add the absolute values of the addends and apply the original sign of the sum Example: (+4) + (-8) = -4 and (-4) + (+8) = +4

Operations - Addition

Addition increases the value of one quanitity by the value of another quantity. The result is called a sum

Even number

Any integer that can be divided by 2 without leaving a remainder. For example: 2,4,6,8 and so on.

Odd Number

Any integer that can not be divided evenly by 2. For example: 3,5,7,9 and so on.

Decimal Number

Any number that uses a decimal point to show the part of the number that is less than one Example: 1.234

Integer

Any positive or negative whole number, including zero. Integers do not include fractions, decimals, or mixed numbers.

Composite Number

Any whole number greater than 1 that has more than two different factors; in other words, any whole number that is not a prime number. For example: The composite number 8 has the factors of 1,2,4, and 8

Prime number

Any whole number greater than 1 that has only two factors, itself and 1; that is, a number that can be divided evenly only by 1 and itself.

Percentages

fractions that are based on a whole of 100; that is, one whole is equal to 100%. The word percent means "per hundred" fractions can be expressed as percents by finding equivalent fractions with a denomination of 100.

mixed number

is a number that contains both an integer and a fraction. Any improper fraction can be rewritten as a mixed number.

Fractions

is a number that is expressed as one integer written above another integer, with a dividing line between them

prime factor

is a prime number factors of 12 are 2 and 3

Numerator

top number of a fraction

Common denominator

two fractions are manipulated so that they have the same denominator

equivalent fractions

two fractions that have the same value but are expressed differently Example: 2/10, 3/15, 4/2, and 5/25 = (1/5)

Writing number in word form

write each number(s) in word form 29: twenty-nine 478: four hundred seventy-eight 9,435: nine thousand four hundred and thirty-five 98, 542: ninty-eight thousand five hundred and fourty-two 302,876: three hundred two thousand and eight hundred seventy-six

Two places to the right

Convert Decimal to a percent move the decimal two places to the right

Operations with Decimals - Dividing Decimals

Dividing Decimals - Every division problem has a divisor and a dividend. The dividend is the number that is being divided. In the problem 14 / 7, 14 is the dividend and 7 is the divisor. In a problem with decimals the divisor must be converted into a whole number. Begin by moving the decimal in the same number of spaces to the right.

Operations with Fractions - Dividing Fractions

Dividing Fractions -

Operations with Positive and Negative Numbers - Division

Division - The rules for dividing signed numbers are similar to multiplying signed numbers. If the dividend the divisor have the same sign, the quotient is positive. If the dividend and divisor have opposite signs, the quotient is negative. Example: (-4) / (+8) = -0.5

Rational numbers

Includes all integers, decimals and fractions. Any terminating or repeating decimal number is a rational number.

Order of Operations (PEMDAS)

Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction

Rational

Means the number that can be expressed as a ratio or fraction. Set of rational numbers include integers and decimals.

Operations with Positive and Negative Numbers - Multiplication

Multiplication - If the signs are the same the product is positive when multiplying signed numbers. Example: (+4) x (+8) = +32 and (-4) x (-8) = -32. When more than two factors are multiplied together, the sign of the product is determined by how many negative factors are present. If there are an odd number of negative factors then the product is negative whereas an even number of negative factors indicates a positive product. Example: (+4) x (-8) x (-2) = +64 (-4) x (-8) x (-2) = -64

Operations with Decimals - Multiplying Decimals

Multiplying Decimals - A simple multiplication problem has two components: a multiplicand and a multiplier. When multiplying decimals, work as though the numbers were whole rather than decimals. Once the final product is calculated, count the number of places to the right of the decimal in both the multiplicand and the multiplier. Then, count the number of places from the right of the product and place the decimal in that position.

Operations with Fractions - Multiplying Fractions

Multiplying Fractions -

Quotient

Of the two numbers "x divided by y" It can also be thought as x out of y equal parts

decimals

Portions of integers expressed as numbers following a decimal point

Operations with Positive and Negative Numbers - Subtraction

Subtraction - For subtracting signed numbers, change the sign of the number after the minus symbol and follow the same rules for addition. Example: (+4) - (+8) = (+4) + (-8) = -4

Operations - Subtraction

Subtraction is the opposite operation to addition, it decreases the value of one quantity by the value of another quantity The result is called the difference

Two places to the left

To convert from a percent to a decimal move it two places to the left

Place value

Write the place value of each digit in the following number 14,059.826 1: ten thousands 4: thousands 0: hundreds 5: tens 9: ones 8: tenths 2: hundredths 6: thousandths

Numbers

are the basic building blocks of mathematics. Specific features of numbers are identified by the following terms.

Real numbers

are the set of all rational and irrational numbers

denominator

bottom number of a fraction

Operations - Multiplication

can be thought of as repeated addition. One number tells how many times to add the other number to itself.

Irrational numbers

cannot be written as a fraction or decimals because the number of decimal places is infinite and there is no recurring patter of digits within the number. For example, pi begins with 3.141502 and continues without terminating or repeating, so pi is an irrational number.

Operations - Division

is the opposite operation to multiplication one number tells us how many parts to divide the other numbers into

greatest common factor

largest number that is a factor of two or more numbers

least common multiple

number chosen to be that common denominator should be least common multiple of the two original denominator

common factor

number that divides exactly into two or more other numbers Example: factors of 12 are 1,2,3,4

The decimal

or base 10, system is a number system that uses ten different digits (0,1,2,3,4,5,6,7,8,9). An example of a number system that uses something other than ten digits is the binary, or base 2, number system, used by computers which only the numbers 0 and 1. It is thought that the decimal system originated because people had only their ten fingers for counting.

reducing

simplifying the fraction