### order of operations

the order in which a mathematical expression is evaluated: first grouping symbols, then exponents, then multiplication or division in order from left to right, then addition and subtraction in order from left to right

### different signs

To add two integers with different signs, find the difference of their absolute values. The sum has the sign of the integer with the greatest absolute value.

### same signs

The sum of two positive integers is positive. The sum of two negative integers is negative.

### add the opposite

to change a subtraction problem into an addition problem, change the subtraction to addition and make the next integer its opposite

### guess and test

Make a series of guesses then use the results to get closer and closer until you get the actual answer.

### work backwards

Start with the end result and "undo" operations until you get back to the starting number. Then take the starting number and work through the problem to see if you get the same end result.

### dividing intgers

The quotient of two integers with the same sign is positive.

The quotient of two integers with the different signs is negative.

The quotient of zero and any integer is zero.

### mulitplying intgers

The product of two integers with the same sign is positive.

The product of two integers with the different signs is negative.The product of zero and any integer is zero.

### coffiecnt

number that is multiplied by a variable;

if a variable has no number multiplied by it, the coefficient is understood to be a 1.

### like terms

like terms have identical variables; that is, they have the same variable to the same power. Constants are classified as like terms as well.

### open sentence

an expression that contains at least one unknown quantity and becomes true or false when a test value is substituted for the unknown.

### divison property of equality

If you divide both sides of an equation by the same non-zero number, the two sides remain equal.

### inequality

a mathematical sentence using less than, less than or equal to, greater than, greater than or equal to

### subtraction property of an inequality

you can subtract the same number from each side of an inequality

### multiplication property of an inequality

If you multiply each side of an inequality by a positive number, you leave the inequality symbol unchanged.

If you multiply each side of an inequality by a negative number, you reverse the inequality symbol

### divison property of an inequality

If you divide each side of an inequality by a positive number, you leave the inequality symbol unchanged.

If you divide each side of an inequality by a negative number, you reverse the inequality symbol.

### clustering

If all numbers being added are close to the same value, change them all to the same value and multiply by how many numbers there are.

### compatible numbers

Numbers that are close to the given numbers that make estimation or mental calculation easier.

### front-end estimation

First add the front-end digits then round to estimate the sum of the remaining digits. Combine these estimates.

### rounding

A way to shorten a number to a given place value by looking at the number after that place value—if the next number is five or higher add one to the given place value, but if the next number is less than five keep the given place value the same. Drop all digits after the rounded place value if they are after the decimal point. Fill in all digits after the rounded place value with zeros if it is before the decimal point.

### mean

the sum of the items in a set of data divided by the number of items in the set; also called average

### outlier

a data value that is uncharacteristically high or low compared to the other data values; it can affect the mean of the data

### formula

an equation created to solve a particular type of problem, where each variable always represents the same thing (example: d=rt, where d represents distance, r represents rate of speed, and t represents time)