Ratios and Rates - Vocabulary

Transcription

1 1/19/18 Unit 5 Ratios and Rates - Vocabulary Begin on a new page Write the date and unit in the top corners of the page Write the title across the top line

2 Ratio A comparison of two numbers.

3 Terms of a Ratio The two numbers in a given ratio. ratio: 2 3 terms

4 Equivalent Ratios Two ratios that express the same relationship. 1 2 = 2 4

5 Rate A ratio that compares quantities measured in different units miles 3 hours Ratio Rate

6 Unit Rate A rate in which the denominator is miles 3 hours 20 miles 1 hour Rate Unit Rate

7 Unit Price A unit rate that gives the price for one item. $34 for 4 movie tickets Price $8.50 per ticket Unit Price

8 Be Aware: Sometimes a rate has units that measure the same thing. These units will cancel out. 12 inches 16 inches = inches 3 feet = 9 inches 36 inches = 1 4

9 2/6/18 Unit 5 Unit 5 Graphing Review Begin on a new page Write the date and unit in the top corners of the page Write the title across the top line

10 Cartesian Coordinate System ( 6, 2) Ordered Pair negative Quadrant II (x-coordinate, y-coordinate) Origin (0,0) Quadrant III positive y-axis Quadrant I x-axis positive Quadrant IV negative

11 Rene Descartes ( ) French Philosopher & Mathematician Published Discourse on Method in An appendix to Discourse on Method introduced modern algebraic notation.

12 2/7/18 Unit 5 Unit 5 How to Graph Properly Begin on a new page Write the date and unit in the top corners of the page Write the title across the top line

13 Step 1 - Use the lines

14 Step 2 Draw straight lines

15 Step 3 - Start numbering from the origin. The origin is (0, 0)

16 Step 4 Use a consistent scale

17 Step 5 - Make it big

18 Step 6 Include a title and label the axes when appropriate

19 Your graphs should look like this:

20 How to Graph an Equation: 1. Make a table with three columns. a. Label the first column x. b. Use the equation you are graphing as the label for the middle column. c. Label the third column y. 2. Pick values for x. Make them easy to use. 3. For each value of x, solve for the corresponding value of y. 4. Plot the ordered pairs on a graph. 5. Draw a line through the points.

21 y = 3x + 1 x 3x+1 y

22 y = 3x + 1 x 3x+1 y 0 3(0)

23 y = 3x + 1 x 3x+1 y 0 3(0)

24 y = 3x + 1 x 3x+1 y 0 3(0) (1)+1 2 3

25 y = 3x + 1 x 3x+1 y 0 3(0) (1)

26 y = 3x + 1 x 3x+1 y 0 3(0) (1) (2)+1 3

27 y = 3x + 1 x 3x+1 y 0 3(0) (1) (2)+1 7 3

28 y = 3x + 1 x 3x+1 y 0 3(0) (1) (2) (3)+1

29 y = 3x + 1 x 3x+1 y 0 3(0) (1) (2) (3)+1 10

30 2/13/18 Unit 5 Unit 5 Proportional Relationships and Graphs Begin on a new page Write the date and unit in the top corners of the page Write the title across the top line

31 A graph shows a proportional relationship if: 1. The graph is a straight line AND 2. The line passes through the origin

32 Proportional Relationship?

33 2/14/18 Unit 5 Unit 5 Constant of Proportionality Begin on a new page Write the date and unit in the top corners of the page Write the title across the top line

34 Constant of Proportionality In a proportional relationship y is a constant multiple of x. The constant multiple is called the constant of proportionality. The constant of proportionality is equal to the ratio y x. The constant of proportionality is the same as the unit rate.

35 Constant of Proportionality Example: x y y/x The Constant of = Proportionality is = 4 1 = 4 1

36 2/20/18 Unit 5 Proportions Begin on a new page Write the date and unit in the top corners of the page Write the title across the top line

37 Proportion An equation showing that two ratios are equivalent. Example: 2 = x 3 12 Proportion

38 To Solve a Proportion 1. Multiply both sides of the equation by the denominator under the unknown. 2. IF the unknown is in the denominator, then take the reciprocal of BOTH sides of the proportion first.

39 Example 1: x 3 = x 3 = x = = 7 3

40 Example 2: 12 x = 16 9 x 12 = 9 16 Take the reciprocal of both sides of the proportion 12 x 12 = x = = 27 4

41 2/21/18 Unit 5 Proportional Relationships and Equations Begin on a new page Write the date and unit in the top corners of the page Write the title across the top line

42 Writing an Equation 1. Find the constant of proportionality (m). a. Pick any pair of x, y values. b. Find m = y x 2. The equation is: y = mx

43 Example 1 A vegetable dip has 60 calories per serving. Write an equation that relates the number of calories, y, in x servings of dip. Constant of proportionality (m) = 60 calories 1 serving = 60 calories per serving Equation: y = 60x

44 Example 2 A telemarketer can make 48 calls in 3 hours. Write an equation that relates the number of calls, y, they can make in x hours. Constant of proportionality (m) = 48 calls 3 hours = 16 calls per hour Equation: y = 16x

45 Example 3 Every 4 minutes a copier can make 100 copies. Write an equation that relates the number of copies, y, it can make in x minutes. Constant of proportionality (m) = 100 copies 4 minutes = 25 copies per minute Equation: y = 25x

46 Proportional Relationship TABLE: A relationship is proportional if it can be described by equivalent ratios. GRAPH: The graph is a straight line AND the line passes through the origin EQUATION: Two quantities x and y have a proportional relationship if y is always a constant multiple of x. (y = mx)

47 2/26/18 Unit 5 digits 5.5 Maps and Scale Drawings Begin on a new page Write the date and unit in the top corners of the page Write the title across the top line

48 Scale Drawing An enlarged or reduced drawing of an object that is proportional to the actual object.

49 Scale A ratio that compares a length in a scale drawing to the corresponding length in the actual object.

50 3/05/18 Unit 5c Number Conversion Begin on a new page Write the date and unit in the top corners of the page Write the title across the top line

51 Fraction A number that can be written in the form a, where a and b are b integers. A fraction a is formed by a parts of size 1. b b Example The fraction 2 3 is formed by 2 parts of size 1 3.

52 Decimal Number A number with a decimal point in it. The first digit to the right of the decimal point is the number of tenths, the second digit is the number of one-hundredths, etc. Example 4.56 =

53 Percent A ratio that compares a number to one-hundred. The symbol % means out of one-hundred. Example 1 4 = = 25% = = 88%

54 To Convert a Decimal to a Percent Move the decimal point 2 places to the right. Add a % sign Example: 0.05 = 5%

55 To Convert a Percent to a Decimal Remove the % sign. Move the decimal point 2 places to the left. Example: 25% = 0.25

56 To Convert a Fraction to a Decimal Do the long division problem. Example: 5 8

57 Hundredths Tenths Thousandths To Convert a Decimal to a Fraction Read the place value. Write the digits over the proper denominator (10, 100, 1000.) Example: =

58 To Convert a Fraction to a Percent Method 1 - If possible, convert the fraction to an equivalent fraction with a denominator of 100. The numerator is then the percent. Method 2 Convert to a decimal, and then to a percent. Example: 3 20 = = 15%

59 To Convert a Percent to a Fraction Remove the percent sign Write the number as a fraction over 100. Simplify, if possible. Example: 18% = = 9 50