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Ratios and Rates Notes 1 Ratios and Rates Essential Vocabulary Ratio: A ratio is a comparison of two numbers using division. A ratio that compares a to b can be written in three different ways. a. Words a to b b. Fraction c. Colon a:b ? a b

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  • Ratios and Rates Notes

    1

    Ratios and Rates

    Essential Vocabulary

    Ratio:  A ratio is a comparison of two numbers usingdivision.  A ratio that compares a to b can be written in three different ways.

    a.  Words a to b

    b.  Fraction

    c.  Colon a : b

    ?

    ab

  • Ratios and Rates Notes

    2

    Examples: Write each examples as a ratio in three different ways.  Write the ratio in both nonsimplified form and in simplest form.

    a.  There are 14 boys and 10 girls in class. Compare the number of boys in class to the number of girls in class.

    Examples: Write each examples as a ratio in three different ways.  Write the ratio in both nonsimplified form and in simplest form.

    b.  Three out of five dentists prefer Brand X toothpaste.  Compare the dentists who prefer Brand X to the number of dentists who do not.

  • Ratios and Rates Notes

    3

    Examples: Write each examples as a ratio in three different ways.  Write the ratio in both nonsimplified form and in simplest form.

    c.  85 people surveyed preferred Jiff peanut butter and 15 people preferred Skippy peanut butter.  Compare the number of people who preferred Jiff to the total number surveyed.

    Equivalent Ratios

    Equivalent ratios are ratios that have the same value.

    For example and are equivalent because

            =  1.25 and           = 1.25

    1512

    2520

    1512

    2520

    ?

  • Ratios and Rates Notes

    4

    Examples:  Determine if the following ratios are equivalent

    a. and

    b.      25 to 2.5   and 

    c.              and

    1810

    3 : 1 23

    20 2

    15 3 11    :  2

    26

    56

    Rate:  A rate is a ratio of two quantities that have 

    different units.

    Equivalent rates:  Equivalent rates are two rates 

    that have the same values.

    More Essential Vocabulary

    ?

    ?

  • Ratios and Rates Notes

    5

    Examples: Write a rate for each situation, and create an equivalent rate with the given conditions.

    A.  Sue types 75 words per minute.

         a.  Write and properly label a rate.

         b.   How many words can Sue type per hour?

    Examples: Write a rate for each situation, and create an equivalent rate with the given conditions.

    B.  Lightning strikes about 100 times per second      around the world.

         a.  Write and properly label a rate.

         b.   About how many times does lightning strike             per minute around the world.

  • Ratios and Rates Notes

    6

    Examples: Write a rate for each situation, and create an equivalent rate with the given conditions.

    C.  Materials cost $0.87 for 30 inches.

         a.  Write and properly label a rate.

         b.   How much money could that be per foot?

    Examples: Write a rate for each situation, and create an equivalent rate with the given conditions.

    D.  The object moved 15 meters in 5 minutes.

         a.  Write and properly label a rate.

         b.   How many centimeters would that be per            hour?

  • Ratios and Rates Notes

    7

    Unit Rate

    A unit rate is a rate that has a denominator of 1 unit.

    To write an equivalent rate, find an equivalent rate with a denominator of 1 unit.  To find a unit rate, divide the distance (or frequency) by the amount of time (or number of units).?

    ?

    ?

    Examples:  Write each situation as a unit rate.

    a.   24 pages in 15 minutes

    b.   18 degrees in 6 minutes

    c.   3 lbs. for $2

  • Attachments

    Rates and Proportions Vocabulary.doc

    Rates, Ratios, and ProportionsVOCABULARY

    Word

    Definition

    Example

    1

    Congruent

    Same size and shape; corresponding sides and angles are equal

    (Symbol:

    )

    @

    4

    1

    1

    4

    1

    5

    1

    5

    =

    ·

    =

    ·

    EMBED Equation.3

    DEF

    ABC

    D

    @

    D

    2

    Convert (conversion)

    To change from one form to another

    Time conversion: 1 minute = 60 seconds

    Length conversion: 12 inches = 1 foot

    3

    Corresponding

    In similar figures, parts that in the same location and are in proportion

    SA corresponds to MO

    OR corresponds to AL

    4

    Cross multiplying

    One method to prove proportions are equal

    15

    10

    9

    6

    =

    90

    90

    10

    9

    15

    6

    =

    ·

    =

    ·

    5

    Customary system

    A system of measurement in the U.S.

    Length: inch, foot, yard mile

    Capacity: ounce, cup, pint, quart, gallon

    Weight: ounce, pound, ton

    6

    Equivalent rates

    Rates that have the same value (are equal)

    min

    1

    5720

    1

    65

    feet

    hour

    miles

    =

    4

    1

    1

    4

    1

    5

    1

    5

    =

    ·

    =

    ·

    Because

    mile

    feet

    hour

    hour

    miles

    1

    5280

    min

    60

    1

    1

    65

    ·

    ·

    7

    Equivalent ratios

    Ratios that have the same value (are equal)

    24

    15

    8

    5

    and

    are equivalent ratios because both ratios equal 0.625

    8

    Formula

    A mathematical statement or rule

    Convert 40 degrees Celsius to degrees Fahrenheit using the formula

    32

    5

    9

    +

    =

    C

    F

    :

    F

    F

    0

    104

    32

    )

    40

    (

    5

    9

    =

    +

    =

    9

    Indirect measurement

    A technique that uses proportions to find a measurement when direct measurement is not possible

    On a map, 1 inch = 25 miles. If a distance between two cities is 8 inches, how many miles is it?

    miles

    inches

    miles

    inch

    ?

    8

    25

    1

    =

    miles

    x

    miles

    x

    200

    8

    25

    =

    ·

    =

    10

    Metric

    A system of measurement based on tens

    Kilo- Hecto- Deka- (base) Deci- Centi- Milli-

    Base units

    Capacity: liter

    Length: meter

    Mass: gram

    11

    Multiplicative Identity Property

    Any number multiplied by one will always give a product of the original number (the number keeps its identity)

    12

    Percent

    A ratio meaning “out of 100” (Symbol: %)

    %

    40

    100

    40

    =

    %

    75

    100

    75

    20

    15

    =

    =

    13

    Polygon

    A closed figure formed from line segments that meet only at their endpoints

    Examples Non-Examples

    14

    Proportion

    An equation that states that two terms are equal

    18

    15

    6

    5

    =

    a

    a

    b

    a

    13

    5

    52

    20

    =

    15

    Rate

    A fixed ratio between two things

    Cell phone plan: 8 cents/minute

    Bag of candy: $1.49/lb

    16

    Ratio

    A comparison of two numbers; can be written in words, as a fraction, or with a colon

    There are 3 boys and 4 girls in the class. What is the ratio of boys to girls?

    Words 3 to 4

    Fraction

    4

    3

    Colon 3:4

    17

    Similar

    Figures that are the same shape but not necessarily the same size

    (Symbol: ~)

    18

    Standard system

    Another name for the customary system

    Length: inch, foot, yard mile

    Capacity: ounce, cup, pint, quart, gallon

    Weight: ounce, pound, ton

    19

    Unit Analysis

    The mathematical process used to convert from one measurement to another

    Convert 25 miles per hour to feet per second

    sec

    1

    3

    2

    36

    sec

    3600

    1

    1

    5280

    1

    25

    feet

    hour

    mile

    feet

    hour

    miles

    =

    ·

    ·

    20

    Unit Rate

    A rate that has a denominator of one unit

    Apples cost

    lbs

    1

    79

    .

    0

    $

    Speed limit is

    hour

    miles

    1

    65

    � EMBED Equation.3 ���

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    SMART Notebook

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