Algebra 1

Front 1

Symbols of Inclusion

Back 1

Parentheses, ( ), or brackets, [ ]. Used to tell which operation to do first.

Front 2

Vinculum

Back 2

The bar used in fractions.

Front 3

Expression

Back 3

A collection of numbers, operation signs, and symbols of inclusion. Ex: 36 ÷ 3 × 4 + 2

Front 4

Evaluating the expression

Back 4

Finding the value of an expression.

Front 5

Arithmetic operations

Back 5

Addition, subtraction, multiplication, division.

Front 6

Variable

Back 6

A letter that represents a number. It can represent different numbers at different times, but it represents the same number each place it appears in an expression.

Front 7

Substitute

Back 7

To replace a variable with a constant.

Front 8

Terms

Back 8

Numbers that are added to each other or subtracted from each other.

Front 9

Factors

Back 9

Numbers that are multiplied together.

Front 10

Base

Back 10

x^y ... x is the base.

Front 11

Exponent

Back 11

x^y... y is the exponent

Front 12

Power

Back 12

x^y ... the entire expression is the power.

Front 13

Order of operations

Back 13

Parentheses first, then any powers, then multiply and divide from left to right in order, and last add and subtract in order from left to right.

Front 14

Equation

Back 14

A sentence (such as x + 3 = 5) which says that one expression is equal to another expressin.

Front 15

Solution

Back 15

A solutiin of an equation is a number you can substitute for the variable that makes the sentence true. For instance, 2 is a solution of x + 3 = 5 because 2 + 3 equals 5.

Front 16

Transforming an equation

Back 16

To transform an equation means to do the same operation to each member of the equation.

Front 17

Perimeter

Back 17

The distance around a figure.

Front 18

Area

Back 18

Measure of the "space" inside a figure.

Front 19

Additive inverses, or opposites

Back 19

Two numbers are additive inverses, or opposites, of each other if their sum equals zero. (For instance, -5 and 5 are additive inverses because -5 + 5 = 0.)

Front 20

Absolute value

Back 20

The absolute value of a number, written |number|, is its distance from the origin on a number line. (For example, |-5|= 5, and |5|= 5. Both are five numbers from zero.)

Front 21

To add signed numbers

Back 21

1. If two numbers have opposite signs: subtract absolute values. The answer has the sign of the term with the greater absolute value.

2. If the two numbers have have the same sign: add the absolute values. Use the sign of the two numbers for the answer.

Front 22

Positive numbers

Back 22

Greater than zero.

Front 23

Negative numbers

Back 23

Less than zero.

Front 24

Integers

Back 24

All whole numbers, positive or negative. No fractions.

Front 25

Real numbers

Back 25

All numbers on the number line, positive, negative, and zero. They include fractions, decimals, etc., and fill the entire number line, leaving no gaps.

Front 26

Subtraction

Back 26

Subracting a number means adding its opposite. That is, x - y = x + (-y).

Front 27

Multiplication by -1

Back 27

-1 times a number equals the opposite of that number; that is, for any real number x.

Front 28

Sign of a product

Back 28

The sign of a product will be:

Negative, if it has an odd number of negative factors.

Positive, if it has an even number of negative factors.

Front 29

Sign of a power of a negative number

Back 29

(Negative number)^even exponent is positive.

(Negative number)^odd exponent is negative.

Note: an expression like -3^4 is NOT a power of a negative number, since taking the power is done before taking the opposite.

Front 30

Multiplicative inverse, or reciprocal

Back 30

Two nonzero numbers are multiplicative inverses, or reciprocals, of each other if their product equals 1. For instance, 2/3 and 3/2 are reciprocals since 2/3 × 3/2 = 1.

Front 31

Division

Back 31

Dividing a number means multiplying by its reciprocal. That is, for any real numbers x and y does not equal zero, x/y = x × 1/y.

Front 32

Commute

Back 32

To commute two numbers in an expression means to interchange their positions.

Since you can commute two terms in a sum without changing the answer, addition is said to be a commutative operation. So is multiplication.

Front 33

Associate

Back 33

To associate two of the numbers in an expression means to group them with parentheses (without changing their positions) so that the operation between them is done first.

Since you can associate any two terms in a sum without changing the answer addition is said to be an associative operation. Multiplication is also an associative operation.

Front 34

Distance formula

Back 34

Distance = (rate)(time), or d=rt