Math term index (choose one):

• Absolute value
  The absolute value of a number is the positive value of that number. For a positive number, it is just the number. For a negative number it is it's positive value. So, the absolute value of 5 is 5, and the absolute value of -5 is 5 also. Absolute value is written like this:
  | - 5 | = 5 with vertical bars around the number.
  You can think of absolute value as the distance from zero to your number. Now, here's a problem for you:
  What is | - 8 |?
  
  
• Acute
  An acute angle is less than 90 degrees. A 90-degree angle is called a right angle
  
  
  
• Algebraic Expression
  An algebraic expression is a mathematical phrase that can contain ordinary numbers, variables (like x or y) and operators (like add,subtract,multiply, and divide).
  Here are some algebraic expressions:
  
  a + 1
  
  a - b
  
  3x
  
  x - a / b
  
  In the above expression the "/" means divide. The "3x" means multiply the variable x by 3.
  
  Many english phrases translate directly into algebraic expressions, as shown in the following table (where x stands for "a number"):
  
  

  English expression	Algebraic expression
  A number plus eight	x + 8
  four less than a number	x - 4
  half of a number	x / 2

  
  
  If you set an algebraic expression equal to something, with an equal sign, you now have an equation, like: X - 4 = 10
  To learn more about expressions, see the notes on expressions.
  
  
• Angle
  An angle is formed when 2 lines meet or cross each other:
  Angles are measured in degrees. The angle shown above is approximately 40 degrees.
  A right angle: is 90 degrees.
  If you want to learn more about angles, see the angle notes.
  
  
• Adjacent
  Adjacent means "next to each other". Adjacent sides of a polygon are the sides that are next to each other.
  
  
• Area
  The area of a flat, or plane figure is the number of unit squares that can be contained within it. The unit square is usually some standard unit, like a square meter, a square foot, or a square inch. So, if you are trying to find the area of a sheet of paper that is 9 inches by 11 inches, and the unit square you want is the square inch, then there are 9 X 11 = 99 square inches in that sheet of paper. In this 4 inch by 3 inch rectangle,
  each little square is a square inch. Count the little one-inch squares and find the total area. Is it the same as multiplying the width of the rectangle by the height?
  
  
• Arithmetic Sequence
  An arithmetic sequence is one in which the same number is added or subtracted from each element to get the next element in the sequence.
  2, 4, 6, 8, 10, ... is an arithmetic sequence.
  
  
• Circumference
  The circumference of a circle is the distance around the circle. It is the circle's perimeter. The formula for circumference is:
  C = d
  where d is the circle's diameter and is 3.14 (approximately).
  .
  
  
• Complementary angles
  Two angles are said to be complementary if their sum is 90^o. This makes them add up to a right angle. In a right triangle, the 2 angles other than the right angle are complementary because they add up to 90 degrees. (All the angles of a triangle add up to 180^o).
  Here's a problem for you:
  What is the measure of the missing angle in this right triangle?
  The missing angle and the 45 degree angle are complementary.
  
  
• Concentric
  Concentric means having the same center. Two circles which have the same center are concentric:
  
  
  
• Congruent
  Two figures are congruent if they are the same size and shape. They can be mirror images of each other, or turned in any direction relative to each other.
  
  
  
• Consecutive
  Consecutive means "one after another", or "in a row". So ...
  The first 4 consecutive numbers are 1,2,3, and 4.
  The first 4 consecutive odd numbers are 1,3,5, and 7.
  Now here is a problem for you:
  What are the first 4 consecutive even numbers?
  
  
• Cylinder
  A cylinder is a solid with circular ends and straight sides. A pipe is a cylinder. The formula for the volume of a cylinder is:
  V = L R²
  where R is the radius of the end of the cylinder and L is it's length.
  
  
  
• Decimal
  A decimal number is a number with a decimal point in it, like these:

       1.5      .6     3.14
  

  The number to the left of the decimal is an ordinary whole number. The first number to the right of the decimal is the number of tenths (1/10's). The second is the number of hundredths (1/100's) and so on. So, for the number 1.5, this is a shorthand way of writing the mixed number 1 5/10.
  3.14 is a shorthand way of writing 3 + 1/10 + 4/100.
  Now, here is a problem for you:
  Can you write the decimal for 3 3/10?
  
  A decimal can be converted to either a fraction or a percent. The following table shows you how to convert between fractions, decimals and percents:

  	... to a fraction	... to a decimal	... to a percent
  From a fraction ...		Divide the numerator of the fraction by the denominator Example 3/4: divide 3 by 4 to get .75	Convert to a decimal, then multiply by 100 Example: 3/4 is the decimal .75 .75 X 100 = 75%
  From a decimal ...	If the decimal has 1 number past the decimal ===> Multiply by 10 to get the numerator and make the denominator 10 Example: .7 X 10 = 7 Fraction is 7/10 If the decimal has 2 numbers past the decimal ===> Multiply by 100 to get the numerator and make the denominator 100 Example: .72 X 100 = 72 Fraction is 72/100 If the decimal has 3 numbers past the decimal ===> Multiply by 1000 to get the numerator and make the denominator 1000 Example: .725 X 1000 = 725 Fraction is 725/1000		Multiply the decimal by 100 Example: .38 X 100 = 38%
  From a percent ...	Make a fraction by making the percent the numerator with a denominator of 100 Example: 38% = 38/100	Divide the percent by 100 Example: 38%: divide 38 by 100 to get .38

  
  
  
• Denominator
  The denominator is the bottom part of a fraction. For example, in the fraction 3/4, the denominator is 4.
  
  The number on the top is called the numerator. The denominator is the number of parts that you cut something into. For example, if you cut a pizza into 4 pieces (the denominator), and you get 3 pieces (the numerator), then you got 3/4 of the pizza.
  Now, here's a question for you:
  In the fraction 7/13, what is the denominator?
  
  
  
• Percent
  A percent is the number of parts out of 100 of something. For example, a quarter (25 cents) is 25 percent of a dollar (100 cents). It is the numerator of a fraction whose denominator is 100. So, the fraction 25/100 is 25 percent, sometimes written as 25%. If you have a decimal number, like .72 and you want to convert it to a percent, you just multiply it by 100. So the decimal .72 becomes (100 X .72) = 72 percent. The following table shows you how to convert between fractions, decimals and percents:

  	... to a fraction	... to a decimal	... to a percent
  From a fraction ...		Divide the numerator of the fraction by the denominator Example 3/4: divide 3 by 4 to get .75	Convert to a decimal, then multiply by 100 Example: 3/4 is the decimal .75 .75 X 100 = 75%
  From a decimal ...	If the decimal has 1 number past the decimal ===> Multiply by 10 to get the numerator and make the denominator 10 Example: .7 X 10 = 7 Fraction is 7/10 If the decimal has 2 numbers past the decimal ===> Multiply by 100 to get the numerator and make the denominator 100 Example: .72 X 100 = 72 Fraction is 72/100 If the decimal has 3 numbers past the decimal ===> Multiply by 1000 to get the numerator and make the denominator 1000 Example: .725 X 1000 = 725 Fraction is 725/1000		Multiply the decimal by 100 Example: .38 X 100 = 38%
  From a percent ...	Make a fraction by making the percent the numerator with a denominator of 100 Example: 38% = 38/100	Divide the percent by 100 Example: 38%: divide 38 by 100 to get .38

  
  
  
• Diagonal
  A straight line connecting two corners (or vertices) of a polygon that are not next to each other.
  
  
  
• Diameter
  The diameter of a circle is the distance across the circle, through it's center. It is the circle's width and is usually represented by the letter d. It is twice the circle's radius.
  
  
  
• Digit
  A digit is a single whole number (0 to 9) in a number 10 or larger. For example, the number 432 has 3 digits. Each digit has a place value. In the number 432, the 2 is the number of ones in the number.
  
  The 3 is the number of 10's in the number, and the 4 is the number of 100's in the number. So you can add them up, like this:
  

  4 X 100 =	400
  3 X 10 =	30
  2 X 1 =	2
  	---
  	432

  
  
  Now here's a problem for you: What is the 10's digit in the number 5678?
  
  
  
• Discount
  A discount is a percentage that is subtracted from a number. For example, a 10% discount of $30 is $3 (10% converted to a decimal is .10 and .10 x 30 is 3). So an item that sells for $30 and is being offered at a 10% discount can be bought for $27. ($30 - $3).
  Now here's a problem for you:
  If that item that sells for $30 were offered at a 20% discount, how much would you have to pay for it?
  
  
• Distributive Property
  The distributive property of algebra is about grouping terms. It states that for any real numbers a,b, and c, that :
  
  

  ac + bc = (a + b)c or ...

  ac -  bc = (a - b)c

  So, using a = 4 and b = 5:
  

  4c + 5c = (4 + 5)c = (4 + 5)c or ...

  4c -  5c = (4 -  5)c = - c

  The opposite is also true:
  
  (a + b)c = ac + bc
  
  Basically what this property means is that if two or more terms involve the same variable (say "c"), and they are either added or subtracted, then you can group the other terms together inside parentheses and multiply the whole term in the parentheses times c. This often lets you simplify an expression by combining the terms inside the parentheses. Here's an example:
  1. Start with: 4ac - 2bc + 3ac + 5bc
  2. All terms involve c, so we have :(4a - 2b + 3a + 5b)c
  3. We can group the a and b terms also:((4 + 3)a + (-2 + 5)b)c
  4. Now simplify:( 7a + 3b )c
  
  
  
• Equation
  An equation is a math sentence that says that 2 things are equal. An equation always has an equal (=) sign. The thing or things that are on the left side of the equal sign are equal to the things on the right side of the equal sign. Here are a few equations:

      X = Y + 5
      A = B - 4
      Z = 3 A
      C =  D  (circumference of a circle)
      A = W H  (area of a rectangle with width W and height H)
      E = M C2 (Einstein's famous equation)
  

  In the first equation, if Y is 2, then X must be 2 + 5 or 7 to make the equation true. In the second equation, if B is 10, then A must be 6 to make the equation true. In the third equation, the number next to the letter means multiply the value of the variable represented by "A" by 3. So if A is 4, then Z must be 12 to make the third equation true.
  
  Now here's a problem for you:
  
  In the first equation, if Y were 10, what would X be?
  
  
• Equilateral triangle
  An equilateral triangle is one that has all 3 sides the same length:
  All the angles of the triangle are the same too. They are all 60 degrees.
  
  
  
• Exponent
  An exponent is a small number written with another big number that tells how many times to multiply the big number by itself. It looks like this:
  3² and this means 3 x 3 which equals 9.
  The little 2 is the exponent
  It DOES NOT mean to multiply the 3 by 2. It means to multiply the 3 times itself. Here's another one: 4³ = 4 x 4 x 4 = 64.
  The little 3 tells how many 4's to multiply together.
  Now, can you tell me what 5² is?
  
  
• Factor
  To factor a number means to break it up into numbers that can be multiplied together to get the original number.
  
  EXAMPLES:
  

     6 = 3 x 2  so, factors of 6 are 3 and 2
     9 = 3 x 3  so, factors of 9 are 3 and 3
  

  Sometimes, numbers can be factored into different combinations. For example,

     8 = 4 x 2 = 2 x 2 x 2
    18 = 9 x 2 = 6 x 3 = 3 x 2 x 3
  

  
  Now, here's a problem for you:
  What are the factors of 12?
  For more practice factoring see the Math Pak Factor drills.
  
  
• Factorial
  A number factorial means to multiply that number by all the whole numbers below it. It is written with a exclamation (!) mark after it, like this: 5!, and means:
  5! = 5 x 4 x 3 x 2 x 1 = 120
  6! = 6 x 5 x 4 x 3 x 2 x 1 = 720
  Now here is a question for you:
  What is 4!?
  
  
  
• Fraction
  A fraction is a number between zero and 1 and is expressed as one number over another number, like this: The number on top is called the numerator and the number on the bottom is called the denominator. It means that if you cut up a whole into 2 parts (the denominator), then the fraction is 1 of those 2 parts, or a half. When you think of a fraction, think of a pizza!. Suppose a pizza is cut evenly into 8 pieces. These 8 pieces are the denominator. Now, if you ate 3 of them you ate 3/8 of the pizza. This is not quite half of the pizza. Half of the pizza would be how many pieces? That's right, it would be 4 pieces. This makes the fraction 4/8 which can be reduced to 1/2 or 'half' of the pizza. A fraction can be converted into a decimal or a percent. The following table shows you how to convert between fractions, decimals and percents:

  	... to a fraction	... to a decimal	... to a percent
  From a fraction ...		Divide the numerator of the fraction by the denominator Example 3/4: divide 3 by 4 to get .75	Convert to a decimal, then multiply by 100 Example: 3/4 is the decimal .75 .75 X 100 = 75%
  From a decimal ...	If the decimal has 1 number past the decimal ===> Multiply by 10 to get the numerator and make the denominator 10 Example: .7 X 10 = 7 Fraction is 7/10 If the decimal has 2 numbers past the decimal ===> Multiply by 100 to get the numerator and make the denominator 100 Example: .72 X 100 = 72 Fraction is 72/100 If the decimal has 3 numbers past the decimal ===> Multiply by 1000 to get the numerator and make the denominator 1000 Example: .725 X 1000 = 725 Fraction is 725/1000		Multiply the decimal by 100 Example: .38 X 100 = 38%
  From a percent ...	Make a fraction by making the percent the numerator with a denominator of 100 Example: 38% = 38/100	Divide the percent by 100 Example: 38%: divide 38 by 100 to get .38

  
  
  
• Geometric Sequence
  A geometric sequence is one in which the same number is multiplied or divided by each element to get the next element in the sequence. 2, 4, 8, 16, ... is a geometric sequence.
  
  
• Greatest common factor (GCF)
  The greatest common factor between 2 numbers is the largest factor that they have in common. One good way to find this number is to write down all the factors of both numbers and then find the biggest one that appears in both lists.
  
  For example, find the GCF of 12 and 8:
  
  Factors of 12: 1 , 2 , 3 , 4 , 6 , 12
  Factors of 8 : 1 , 2 , 4 , 8
  
  The largest factor they both have is 4. This is the greatest common factor (GCF).
  Now, can you find the GCF of 22 and 33?
  
  
• Hemisphere
  A hemisphere is half of a sphere (ball). When you cut a grapefruit in half, you have a hemisphere.
  
  
  
• Hexagon
  A hexagon is a 6-sided figure, or polygon.
  A bee's honeycomb is made of little hexagons.
  
  
  
• Horizontal
  Horizontal means lying down or flat, like a floor. This is the opposite of vertical. A horizontal line and a vertical line are perpendicular
  
  
• Hypotenuse
  The hypotenuse of a right triangle is the longest side of the right triangle.
  It is the side opposite the right angle. To learn more about types of triangles see the triangle notes.
  
  
  
• Improper fraction
  An improper fraction is a fraction that has a numerator larger than it's denominator. Here are a few improper fractions:

    3/2         4/3        5/2        12/5         9/5
  

  You can convert an improper fraction to a mixed number by dividing the numerator by the denominator and leaving the remainder over the denominator as a fraction. So the improper fractions above would become the following mixed numbers:

   1 1/2      1 1/3        2 1/2      2  2/5        1 4/5    
  

  For some practice with improper fractions and mixed numbers see the mixed number notes.
  
  
• Inequality
  An inequality is like an equation that uses symbols for "less than"(<) and "greater than"(>) where an equation uses a symbol for "is equal to" (=).
  
  So where the equation:

     X = Y + 5 
  

  says that "X is equal to Y plus 5",

     X < Y + 5
  

  says that "X is less than Y plus 5", and

    X > Y + 5
  

  says that "X is greater than Y plus 5".
  
  Now I have a problem for you:
  
  Substitute the ? in the following expression for the correct inequality symbol:

     5  ?  4
  

  
  
  
• Integer
  An integer is a positive whole number (like 1, 2, 3 .. ),
  a negative whole number (like -1, -2, -3 ... ),
  or zero.
  It is not a decimal number, or a fraction.
  This number line consists of only integers:

   ...---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|...
        -7  -6  -5  -4  -3  -2  -1   0  +1  +2  +3  +4  +5  +6  +7  +8
  

  To learn more about negative integers and the number line, see the negative number notes.
  
  
• Intersection
  When 2 lines cross, they form an intersection:
  
  
  
• Intersection of two sets
  The intersection of two sets are all the elements that appear in both sets. For example, if you have the two sets of numbers: {3,4,5,6,7}, and {5,6,7,8,9,10}, the intersection of these sets is:{5,6,7}. The symbol for intersection is an upside-down capital U, so if we call our first set "A" and our second set "B" then the set {5,6,7} is .
  
  
• Isosceles triangle
  An isosceles triangle is a triangle that has 2 sides and 2 angles the same length. Two of the angles are the same measure also. The triangle to the right is isosceles. For example, if you have a triangle that is isosceles and has one angle that is 100 degrees, what are the other 2 angles?
  Well, the other 2 angles sum to 80 degrees (180 - 100), and both of the other 2 angles are the same, so the sum of the other 2 identical angles is 80 degrees, so each of the other angles must be 40 degrees!
  To learn more about triangles, see the triangle notes.
  
  
  
• Inscribed figure
  An inscribed figure is one that is drawn inside another, usually with the edges touching. For example if you drew a triangle inside a square, the triangle is inscribed in the square.
  
  
• Least common multiple (LCM)
  The least common multiple (LCM) of 2 numbers is the smallest number that they both divide evenly into. One good way to find the least common multiple of 2 numbers is to multiply both numbers by 1,2,3,4,5... and then find the first multiple that appears in both lists.
  For example, find the least common multiple of 6 and 8:
  

  Multiples of 6:   6   12   18   24   30   36   42   48   54   60
  Multiples of 8:   8   16   24   32   40   48   56   64   72   80
  

  The first number that appears in both lists is 24. (48 appears also, but it is not 'least'), so 24 is the LCM of 6 and 8.
  Now, can you find the least common multiple of 10 and 35?
  
  
• Maximum
  The maximum of a set of numbers is the largest one. The maximum of the set {3,2,8,1,9,4,2} is 9.
  
  
• Mean
  The mean of a set of numbers is their average. You find the average of a set of numbers by adding them up and dividing by the number of numbers you have. So, the mean of 3,4,6,9, and 3 is:

              3 + 4 + 6 + 9 + 3      25
              -----------------  =   --  = 5
                     5                5
  

  
  
  
• Median
  The median of a set of numbers is the number in the middle. For example, in the set of numbers {4,6,25}, the median is 6. However the numbers must be in order for the median to be in the middle. If there are an even number of numbers, then the median is the average of the last 2 middle numbers. There are 2 ways to find the median of a set of numbers:
  1. Rewrite the numbers in order, then find the one in the middle
  2. Cross off the highest number, then the lowest, then the highest, lowest, on and on, until only one number is left. That number will be the median.
  This second method works best when you have a large number of numbers.
  So, here is a problem for you:
  What is the median of {9,2,1,6,3}?
  
  
• Minimum
  The minimum of a set of numbers is the smallest one. The minimum of {3,2,8,1,9,2} is 1.
  
  
• Mixed number
  A mixed number is a whole number plus a fraction. Here are a few mixed numbers:

   1 1/2      1 1/3        2 1/2      2  2/5        1 4/5    
  

  You can convert a mixed number to an improper fraction by finding the number of unit fractions in the whole number and then adding the fractional part of the whole number. This sounds hard, but it really isn't. For example, in the first example the 1 changes to 2/2 because there are 2 halves in a whole. In the fourth example, the 2 becomes 10/5 because there are 5 fifths in a whole. Get it? Once you have done this, then you just add the fraction to it. So, each of our examples above becomes:
  

   
    3/2          4/3        5/2        12/5         9/5
  

  
  Now here's a problem for you:
  Convert 3 1/3 to an improper fraction.
  For some practice with improper fractions and mixed numbers see the mixed number notes.
  
  
• Mode
  The mode of a set of numbers is the one that occurs most often. So, in the set {1,5,7,5,9}, the mode is 5 because there are 2 fives and only one of each of the others.
  Now here is a problem for you:
  Find the mode of this set of numbers:
  

     2  6  9  0  5  2  4  1  6  4  5  2
  

  
  
  
• Negative number
  A negative number is a number below zero. It can be an integer or a decimal and is written with a minus sign (-) in front of it, like this: -3
  
  You can get an idea of what a negative number is with a number line, like this one:
  
  

   ---|---|---|---|---|---|---|---|---|---|---|---|---|---|- ...
     -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6
  

  You can see from this number line that you can continue counting down when you get to zero. Negative numbers represent things like very cold temperatures, and overdrawn bank balances!
  
  Here is a problem for you:
  What is the number below - 2?
  
  
• Numerator
  The numerator is the top part of a fraction. For example, in the fraction 3/4, the numerator is 3.
  
  The number on the bottom is called the denominator. This is the number of parts out of the total number of parts that your fraction has. For example, if you cut a pizza into 4 pieces, and you get 3 (the numerator), then you got 3/4 of the pizza.
  Now, here's a question for you:
  In the fraction 5/8, what is the numerator?
  
  
• Obtuse angle
  An obtuse angle is an angle greater than 90 degrees:
  To learn more about angles, see the angle notes.
  
  
• Octagon
  An octagon is an 8-sided figure:
  A stop sign is an octagon:
  
  
  
• Odds
  Odds are a way of expressing a probability as the ratio of the number of things that you are not looking for to the number of things that you are looking for. So the odds against flipping a coin and it coming up heads are 1:1 = 1(even odds), because there are 2 sides of the coin and you are looking for only one of them.
  Now here is a problem for you:
  What are the odds of selecting a club out of a deck of cards?
  
  
• Palindrome
  A palindrome is a number that reads the same from left to right and from right to left. 101 is the smallest 3-digit palindrome. 123454321 is a palindrome.
  
  
• Parallel
  Two lines in a plane are parallel if they never cross:
  The opposite sides of a square are parallel.
  
  
  
• Parallelogram
  A parallelogram is a 4-sided figure in which the opposite sides are parallel. A diamond shape is a parallelogram. Squares and rectangles are special kinds of parallelogram.
  
  
• Parallelepiped
  A parallelepiped is a solid (3-dimensional) figure in which all faces are parallelograms. A special kind of parallelepiped is a rectangular box, like a shoe box.
  It is a solid figure and has a volume.
  
  
• Pentagon
  A pentagon is a 5-sided figure:
  The United States Military Headquarters building (below) is a pentagon.
  
  
  
• Perfect square
  A perfect square is a number that has an whole number square root. For example, 25 is a perfect square, because is 5, a whole number.
  Here's a problem for you:
  Name the next perfect square higher than 25.
  
  
• Perimeter
  The perimeter of a figure is the total distance around the edge of the figure. For example, a square whose sides are 6 inches long has a perimeter of 6 x 4 = 24 inches because it has 4 sides 6 inches long. A rectangle whose length and width are 4 meters and 3 meters has a perimeter of 4 + 4 + 3 + 3 = 14 meters.
  Now, can you tell me what the perimeter of a rectangle whose length is 8 feet and whose width is 3 feet is?
  
  
• Permutation
  A permutation is a way to order a set of things. For example, if your set is the letters in the word WHO, then one other ordering would be WOH. Here are all the possible orderings of the letters in the word WHO:
  

  	WHO  WOH  HWO  HOW  OWH  OHW 
  

  There are 6 different ways to order the letters in the word WHO. To learn more about permutations, see the permutation notes.
  
  
• perpendicular
  Two lines or planes are perpendicular to each other if the angle between them is 90 degrees, or a right angle.
  This means that they meet each other "square".
  
  
  
• 
  (pronounced "pie") is the ratio of a circle's circumference (C) to it's diameter (D), or :
  

       =  C / D
  
  

  Where C is the circumference, and D is the diameter. It is a decimal that goes on forever, and is approximately:
  3.141592653589793..., but we usually just use 3.14
  
  See the circle notes for more on the circle.
  
  
• Plane
  A plane is a flat surface, like a piece of paper or a table top.
  
  
• Polygon
  A polygon is a flat, or plane closed figure made up of at least 3 lines. Triangles, rectangles, octagons, and all other flat figures that have 3 or more sides are polygons. Here is a dodecagon: (a polygon with 12 sides!):
  
  
• Prime number
  A prime number is a number, larger than 1, that can only be divided evenly by itself and 1. The first 4 prime numbers are 2,3,5 and 7. 4 is not a prime because it can be divided by 2. Can you name the next 4 prime numbers?
  
  
• Prime factorization
  Prime factorization is finding the factors of a number that are all prime. Here's how you do it: Find 2 factors of your number. Then look at your 2 factors and determine if one or both of them is not prime. If it is not a prime factor it. Repeat this process until all your factors are prime. Here's an example:
  Find the prime factors of the number 84:

                   84
                  /  \
                42 x  2  (84 is 42 times 2)
               /  \
             21 x  2     (42 is 21 times 2)
            / \
           7 x 3         (21 is 7 times 3)
  
         (7 and 3 are both prime, so we stop!)
  

  So the prime factors of 84 are 7 x 3 x 2 x 2.
  
  Now, here's a problem for you: Find the prime factors of 60.
  
  
• Probability
  Probability is the likelihood of something happening in the future. It is expressed as a number between zero (can never happen) to 1 (will always happen). It can be expressed as a fraction, a decimal, a percent, or as "odds".
  Here is a table of typical probabilities:
  
  

  EVENT	Probability
  	..as a fraction	..as a decimal	..as odds against
  The sun rises in the morning	1	1.	0.
  A flipped coins turns up 'heads'	1/2	.5	1:1
  A card drawn out of a deck is a club	1/4	.25	3:1
  A card drawn out of a deck is a spade,heart, or diamond	3/4	.75	1:3
  A kid flies by flapping her arms	0	0.	infinite

  To learn more about probability, see the probability notes.
  
  
• Pyramid
  A pyramid is a 3-dimensional (solid) figure that has a polygon for a base and has a single vertex that is not in the plane of the polygon base. The Egyptian pyramids have square bases and triangular sides, meeting at the top, the vertex.
  
  
• Pythagorean theorem
  The pythagorean theorem states that, in a right triangle, if you call the hypotenuse c and the other 2 sides a and b, then:
  
  c² = a² + b²
  For example, in a right triangle that has side a = 3 inches and side b = 4 inches, then the hypotenuse (side c) = :
  c² = 3² + 4² =
  c² = 9 + 16 = 25. So c is the , which is 5.
  
  So, now here's a problem for you:
  What is the hypotenuse (side c) of a right triangle whose other sides (sides a and b) are 12 inches and 5 inches?
  If you know the hypotenuse and one of the other two sides of a right triangle, you can use the pythagorean theorem to find the missing side by rearranging the pythagorean theorem. For example, if you call the missing side "b", then:
  
  b² = c² - a²
  Click here to see a proof of why the pythagorean theorem is true.
  
  
• Quadrilateral
  A quadrilateral is a 4-sided figure:
  It can be any shape, as long as it has four sides. A square is a quadrilateral.
  
  Now here is a problem for you:
  Name another quadrilateral figure.
  
  
• Quotient
  A quotient is the result of dividing one number by another. For example, the quotient of 8 and 4 is 8/4 = 2.
  
  
• Radical
  A radical is a square root sign and looks like this: . Most calculators have a on one of the keys.
  
  
• Radius
  The radius of a circle is the distance from it's center to it's edge:
  It is half of the circle's diameter
  
  
  
• Range
  The range of a set of numbers is the highest number minus the lowest number. So, in the set { 2,5,8,2,1,4,3] the highest number is 8 and the lowest number is 1, so the range is
  

      8 - 1 = 7 (range)
  

  If there are any negative numbers in the set, then you have to be really careful, because subtracting a negative number is the same thing as adding the positive number. So, in the set
  

      5  -1  6  -2  0
  

  The highest number is 6 and the lowest number is - 2, so the range is:
  

      6 - (-2) = 6 + 2 = 8
  

  Think of it as the distance between 6 and - 2 on the number line, like this:
  

  ---|---|---|---|---|---|---|---|---|---|---|---|-- ...
    -3  -2  -1   0   1   2   3   4   5   6   7   8   ...
         |<------------ 8 -------------->|
  

  So, here is a problem for you:
  What is the range of this set of numbers?
  

     9   4   8   9   2   -1   3   4
  

  
  
  
• Ratio
  The ratio of 2 numbers is the first number divided by the second number. For example, the ratio of 8 to 4 is 2.
  
  
• Reciprocal
  The reciprocal of a fraction is the fraction turned upside-down. For example the reciprocal of 2/3 is 3/2 , or as a mixed number:

      1  1/2
  

  Now here's a problem for you:
  What is the reciprocal of 3/5? Express your answer as a mixed number.
  
  
• Rectangular prism
  A rectangular prism is a solid figure where all sides are rectangles and all sides meet perpendicular. A brick or a shoebox is a rectangular prism.
  
  
  
• Reducing fractions
  To reduce a fraction means to remove a common factor that the numerator and the denominator both have. This means that you have to factor both the numerator and denominator and then cancel any factors that appear in both the numerator and denominator. Multiply the numbers in the numerator together to get the new numerator. Multiply the numbers in the denominator together to get the new denominator. Here's an example:
  

  	Remove the 3's and you get 2/3
  Here's another example:
  	Remove the 7's and you get 3/4

  
  
  Now here's a problem for you:
  
  For more practice reducing fractions, click here.
  
  
• Right angle
  A right angle is a 90 degree angle. This is the angle 2 things make when they meet 'square', like the floor with the wall, or a table leg with a floor. The symbol for a right angle is a little square like this:
  
  
  
• Right triangle
  A right triangle is a triangle that has one 90 degree angle: A 90 degree angle is called a right angle.
  
  
• Square root
  The square root of a number is a number which multiplied by itself, gives you the original number. Its symbol is called a radical and looks like this: . For example, is 3, because 3 x 3 = 9. Here are a few other square roots:
  

   The  is 4 because 4 x 4 is 16
   The  is 5 because 5 x 5 is 25
  

  
  Now, here's a problem for you:
  What is the square root of 36?
  
  
• Set
  A set is a collection of related things. When a set is listed, it's members are usually listed between curly brackets, like these: { }
  Here are a few sets:
  1. Members of a class whose names start with L: {Lacie,Luke,Lauren}
  2. Days of the week: {Sunday,Monday,Tuesday,Wednesday,Thursday,Friday,Saturday}
  3. Colors of the rainbow: {red,orange,yellow,green,blue,indigo,violet}
  4. Whole numbers between 3 and 10: {4,5,6,7,8,9}
  5. Daily high temperatures in the first week of February: {53,48,49,55,44,51,54}
  
  They can be things or numbers. They can be a collection of almost anything you can think of.
  
  
• Sphere
  A sphere is a round ball, like a basketball or a baseball or a planet: It is a solid figure where all points on it's surface are the same distance from the center of the figure.
  
  
• Square
  A square is a quadrilateral figure that has all sides equal, opposite sides parallel and adjacent sides perpendicular to each other. Here is a square with sides 5 inches long:
  Most floor tiles are squares. Can you find other squares around you?
  
  
• Supplementary angles
  Two angles are said to be supplementary if their sum is 180^o. This makes them add up to make a straight line. If you take a ruler and bring one end down on a table top, the two angles that the table top makes with the ruler (one angle on each side of the ruler) are supplementary angles. See if you can find the missing supplementary angle:
  
  
• Trapezoid
  A trapezoid is a quadrilateral with at least 2 opposite sides parallel:
  If you cut off the top of a triangle parallel with it's base, you will have a trapezoid. A square is a special type of trapezoid.
  
  
  
• Union of two sets
  The union of two sets is everything in both sets. For example if you have the set {3,4,5} and the set {5,6,7}, then the union of these two sets is {3,4,5,6,7}. The symbol for union is a capital U. So mathematically, the above sentence would read:
  
  U {3,4,5} {5,6,7} = {3,4,5,6,7}
  
  
• Vertex
  A vertex of a figure is a corner. The plural of vertex is vertices.
  For example, a triangle has 3 vertices.
  
  Now here's a problem for you:
  How many vertices does a square have?
  
  
• Vertical
  Upright, or standing up, like a telephone pole. This is the opposite of horizontal. A vertical line and a horizontal line are perpendicular
  
  
• Volume
  Volume is the measure of the amount of space inside of a solid figure, like a cube, ball, cylinder or pyramid. It's units are always "cubic", that is, the number of little element cubes that fit inside the figure.
  The formula for the volume of a rectangular prism is:
  
  Area = l x w x h
  where:
  l = length
  w = width
  h = height
  For example, the volume of a shoe box (a parallelepiped that is 4 inches by 6 inches by 12 inches is 4 x 6 x 12 = 288 cubic inches. This means that it would take 288 little 1-inch cubes to fill the shoe box.