Carry The Two

Natural Number - positive integers (whole numbers) 1, 2, 3... 'Counting numbers' used when you are counting one to one objects Whole Number - not fractions nor decimals.  Unlike natural numbers, we include 0 when referring to whole numbers Integers - a number that is not a fraction whole numbers; integers can also be negative whole numbers: ...-2, -1, 0, 1, 2... Rational Number  - a number that can be written as a ratio; a number that can be written as a fraction with the numerator and denominator expressed as whole numbers: 7/1, 9/2 Irrational Number  - Real numbers that cannot be expressed as simple fractions;  π is irrational because it cannot be written as a simple fraction Real Number  - rational and irrational numbers; any number that can be found on a number line. Infinity is not a real number.  Imaginary numbers are also not considered real numbers Imaginary Number  - A number that, when squared, gives a negative result; imaginary numbers are represented by the

Equivalent Ratios Two ratios are equivalent if their cross products are equal.  Compare the cross products by cross multiplying: Multiply the denominator of one fraction by the numerator of the other fraction.  If the cross products are equal then the ratios are equivalent. Another Method Ratios are used in order to find how two or more quantities are related.  In order determine whether you have equivalent ratios, you must multiply or divide both sides by the same number. The first two problems use the first method above whereas the last two problems use the second method above. Problems #1 Are the following ratios equivalent? 2:3 and 10:12 Step 1 Determine the cross products by multiplying the numerator of the first fraction by the denominator of the second: 2 x 12 = 24 Step 2 Determine the second cross product by multiplying the denominator of the first fraction by the numerator of the second: 3 x 30 = 90 Step 3 Compare the cross products to determine if th

Slope The slope of a line tells you how steep the line is. Formula To find the slope of a line, we take the change in y divided by the change in x: Some call this equation "rise over run": Therefore, in order to find the slope, you divide the difference of the y-coordinates of a point or a line by the difference of the x-coordinates. Problem #1 What is the slope? Step 1 Select any 2 points on the line Point 1: (-1, -2) Point 2: (2, 2) Step 2 Put those point into the slope formula Therefore: = 4/3 Answer: The slope of the line is 4/3 Problem #2 What is the slope? Step 1 Select any 2 points on the line Point 1: (-2, 5) Point 2: (-4, 4) Step 2 Put those point into the slope formula Therefore: = -1/-2 which equals: 1/2 Answer: The slope of the line is 1/2

Monomial A monomial is a polynomial with only one term. Greatest Common Factor of Monomials In order to find the Greatest Common Factor of a monomial, (1) first you must take each monomial and write it's prime factorization, (2) next, identify the common factors, (3) finally, multiply the common factors together. Problem #1 Find the greatest common factor: 9 x 2 , 6x 3 Step 1 Find the prime factorization of each monomial 9 x 2 = 3  ·  3  ·  x   ·  x 6x 3 = 2  ·  3  ·  x   ·  x  ·  x Step 2 Identify the common factors: 3, x and x Step 3 Multiply the common factors together 3  ·  x  ·  x = 3 x 2 Answer: The Greatest Common Factor is 3 x 2 Problem #2 Find the greatest common factor: 4 , 6x 2 Step 1 Find the prime factorization of each monomial 4 = 2  ·  2  6x 2 = 2  ·  3  ·  x   ·  x  Step 2 Identify the common factors: 2 Step 3 Multiply the common factors together 2

Slope-Intercept Form Slope-intercept form is written as follows: y = mx + b 'm' is the slope 'b' is the y-intercept Problem #1 Write an equation in slope-intercept form for a line whose slope is 5 and whose y-intercept is 7. Step 1 Remember that slope-intercept form is written: y = mx + b Step 2 Plug-in the given slope (5) and y-intercept (7): Answer:  y = 5x + 7 Problem #2 Identify the slope and y-intercept of the following equation: y = -x + 3 Step 1 Determine the slope: Although there is no number in the 'm' portion of the equation, since it is '-x' the slope is -1 Step 2 Determine the y-intercept: In this equation the y-intercept is 3 Answer:  Slope = -1; y-intercept = 3 You may find the following video helpful: https://www.youtube.com/watch?v=u3spOO-m_Gg