Level 177
Level 179

#### 35 words 0 ignored

Ready to learn
Ready to review

## Ignore words

Check the boxes below to ignore/unignore words, then click save at the bottom. Ignored words will never appear in any learning session.

**Ignore?**

(+)(+) = (+)

These rules apply to both multiplication and division.

When multiplying and even number of negative factors, the product is positive.

When multiplying an odd number of negative factors, the product is negative.

b/a is the reciprocal of a/b

The reciprocal is also called the "multiplicative inverse" of a number

invert, or flip, the fraction

To find the reciprocal of a fraction...

-2/5 = -2/5 = 2/-5

A negative fraction can be written in three different, but equivalent ways:

Division

process of breaking a quantity into equal parts

quotient

the answer to a division problem

Dividend

the number that is being divided

divisor

the number that divides another number.

To Divide Signed Numbers

divide the absolute values or numerical parts, and determine the sign of the quotient.

the quotient is positive.

If the dividend and the divisor have the same sign

the quotient is negative.

If the dividend and the divisor have different signs

To divide by a fraction

find the reciprocal of the divisor, find the any common factors, and multiply.

To divide by a mixed number

rewrite as an improper fraction, find the reciprocal of the divisor and multiply.

exponent

A mathematical notation indicating the number of times a quantity is multiplied by itself

The base is the number being multiplied

The exponent is the number of times the base is used as a factor

2 to the fourth power or 2⁴

The exponential form of 2 x 2 x 2 x 2 is

Sign Rule for Exponents

When the base is negative, be especially careful in determining the sign of the answer.

A negative base raised to an even power is positive

A negative base raised to an odd power is negative

X² = squared

X³ = cubed

Exponent Expressions with Negative Signs

Be careful how you read expressions with exponents and negative signs.

(-2)⁴ means (-2)(-2)(-2)(-2) = 16

When the negative sign is inside the parentheses, the negative applies to all the bases

-2⁴ means (-2)(2)(2)(2) = -16

When there are no parentheses, the negative only applies to the first base

Special Cases with Exponents

Any non-zero number raised to the zero power is equal to 1 x⁰ = 1 (b ≠ 0)

The Distributive Property

For all real numbers a, b, and c, a(b + c) = ab + ac

The Distributive Property is most useful when it does not conflict with the order of operations.

That is, it is mostly used when you cannot perform the operations inside the parentheses. The Distributive Property can be used to remove the parentheses.

commutative property of multiplication

If the order of factors changes, the product stays the same.

associative property of multiplication

When the grouping of factors changes, the products stays the same.

identity property of multiplication

The product of 1 and any number is that number.

algebraic expression

An expression consisting of one or more numbers and variables along with one or more arithmetic operations

term

An element or number in a sequence.

Like Terms

expressions that contain the same variables to the same power

Combining like terms

If an expression has several terms, you might find it helpful to rearrange the terms so that like terms are together.

Use the Distributive Property to remove the parentheses.

Many expressions in algebra use grouping symbols such as (parentheses), {braces}, or [brackets].

the opposite of what is inside the parentheses.

A negative sign in front of the parentheses means