Summary: Review

Key Concepts

To add numbers with the same sign (both positive or both negative)

  • Add their absolute values (without the + or -).
  • Give the sum the same sign.

To add numbers with different signs (one positive, one negative)

  • Find the difference of their absolute values. (Note that when you find the difference of the absolute values, you always subtract the lesser absolute value from the greater one.)
  • Give the sum the same sign as the number with the greater absolute value.

To subtract signed numbers, change any subtraction of a number to the addition of its negative.

The product or quotient of numbers with different signs (one positive, one negative) is negative.

The product or quotient of numbers with the same sign (both positive or both negative) is positive.

Order of Operations

  • Perform operations within grouping symbols: [latex]\{\}, [], ()[/latex]
  • Evaluate exponents and radicals
  • Multiply and divide, left to right
  • Add and subtract, left to right

Steps for plotting an ordered pair (x, y) in the coordinate plane:

  • Beginning at the origin, move horizontally (the direction of the [latex]x[/latex]-axis) the distance given by the [latex]x[/latex]-coordinate. If the [latex]x[/latex]-coordinate is positive, move to the right; if the [latex]x[/latex]-coordinate is negative, move to the left.
  • Beginning at the [latex]x[/latex]-coordinate, move vertically (the direction of the [latex]y[/latex]-axis) the distance given by the [latex]y[/latex]-coordinate. If the [latex]y[/latex]-coordinate is positive, move up; if the [latex]y[/latex]-coordinate is negative, move down.
  • Draw a point at the ending location. Label the point with the ordered pair.

Glossary

absolute value: a number’s distance from zero; it’s always positive

axis: an element of a coordinate plane. Includes a horizontal axis and a vertical axis, or number lines that intersect at right angles. The horizontal axis is called the [latex]x[/latex]-axis. The vertical axis is called the [latex]y[/latex]-axis.

base: an element of an exponential notation. In [latex]2^{3}, 2[/latex] is the base.

difference: the result of subtraction

exploratory data analysis: a method of creating graphs and numerical summaries based on data gathered from a sample of the population to investigate the answer to a research question

exponent (power): an element of an exponential notation. In [latex]2^{3}, [latex]3[/latex] is the exponent.

exponential notation: a simplified method to represent repeated multiplication

expression: combines numbers and variables with mathematical operations such as addition, subtraction, multiplication, and addition. For example, [latex]2+8 \cdot 5[/latex] is an expression.

integers: counting numbers like 1, 2, 3, etc., including negatives and zero

order of operations / PEMDAS: the order in which a mathematical equation should be solved. The order is parenthesis, exponents, multiplications and divisions, additions, and subtractions, or PEMDAS.

ordered pair: [latex](x,y)[/latex] describes the location of a point relative to the horizontal [latex]x[/latex]-axis (the first value of the ordered pair) and relative to the vertical [latex]y[/latex]−axis (the second value of the ordered pair).

origin: the point at which the two axes intersect on a coordinate plane

product: the result of multiplication

quotient: the result of division

real number: fractions, negative numbers, decimals, integers, and zero are all real numbers

reciprocal: another name for the multiplicative inverse (just as opposite is another name for additive inverse). A number and its reciprocal have the same sign.

sign: this refers to whether a number is positive or negative, + for positive (to the right of zero on the number line) and − for negative (to the left of zero on the number line)

sum: the result of addition