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    RECORDED CLASSES

    MATH 202

     

    DECIMALS

     

    Every number has

    a decimal point.

     

    But it is often

    left unwritten.

     

    It goes to the right

    of the ones position.

     

    values between

    two integers

     

    rational numbers

     

    Deci- means 10

    divisions of ten.

     

    Tenths position

    to the decimals right

     

    the numerals value

    divided by ten

     

    0.3

    equals 3/10

     

    Positions follow

    in smaller amounts.

     

    hundredths position

    thousandths position

     

    divide by 100

    divide by 1000

     

    0.34

    equals 34/100

     

    0.347

    equals 347/1000

     

    Each position allows

    smaller values

    INDEX

     

    MATH 202

    1. Decimals 444

    2. Decimal Addition 333

    3. Subtracting Decimals 333

    4. Multiplying Decimals 333

    5. Dividing Decimals 1 333

     

     

     

     

     

     

    Rounding numbers

     

    Round the decimal

    to the hundredths position.

     

    closest numeral

    in that position

     

    0.347

     

    round up

    to 0.35

     

    0.342

     

    round down

    to 0.34

     

    more positions

    more accuracy

     

     

     

     

     

     

    DECIMAL ADDITION

    Meaning Clusters


    You wait

    for the bus

    for 10.5 minutes.

     

    You ride

    on the bus

    for 1.25 minutes.

     

    You want to know

    how much time

    you spent.

     

    Line up the numbers

    by their decimal points

    and work right to left.

     

     10. 5 minutes

    + 1. 25 minutes

     

    5 is the only digit

    in the hundredths position.

     

     10. 5 minutes

    + 1. 25 minutes

         .   5 minutes

     

    Add 2 and 5

    from the tenths position.

     

    2 + 5 = 7

     

     10. 5 minutes

    + 1. 25 minutes

         . 75 minutes

     

    Add 0 + 1

    from the ones position.

     

    0 + 1 = 1

     

     10. 5 minutes

    + 1. 25 minutes

       1. 75 minutes

     

    1 is the only digit

    in the tens position.

     

    10. 5 minutes

    + 1. 25 minutes

      11. 75 minutes

    MEMORY TRIGGERS TESTS

     

     

    ______wait__________________________

     

    ___________________________________

     

     

    ______ride__________________________


    ___________________________________


    _____________________time__________

     

    ___________________________________


    Line up_____________________________

     

    ___________________________________

     

     

    __________________digit_____________

     

    ___________________________________

     

     

    Add________________________________

     

    ___________________________________

     

     

    ______________minutes______________

     

    ___________________________________

    __________________________ones_____

    ___________________________________

     

    10.5________________________________

     

    ___________________________________


    _____________only___________________

    ___________________________________


    Speed Learning format by Carl Peterson ©2005

     

     

    SUBTRACTING DECIMALS

    Meaning Clusters

     

    You want to go

    to an amusement park

    50 kilometers away.

     

    You travel

    34.27 kilometers.

     

    How many kilometers

    remain in the trip?

     

    Subtract the number

    of kilometers traveled

    from the total distance.

     

       50

    – 34.27

     

    Expand the 50

    with a decimal point

    and zeros in the tenths

    and hundredths position.

     

       50.00

    – 34.27

     

    Subtract the digits

    in the hundredths position.

     

    0 – 7 = -7

     

    Borrow a one

    from the 0

    in the tenths position

    turning it into a 9.

     

    -7 + 10 = 3

     

       50.09 0

    – 34.2  7

                3

     

    Subtract the digits

    in the tenths position.

     

    9 – 2 = 7

     

       50.09 0

    – 34.2  7

           .7  3

     

    Subtract the digits

    in the ones position.

     

    0 – 4 = -4

     

    Borrow a one

    from the 5

    in the tens position.

     

    -4 + 10 = 6

    5 – 1 = 4

     

       54 0.09 0

    3  4. 2  7

           6. 7  3

     

    Subtract the digits

    in the tens position.

     

    4 – 3 = 1

     

       54  0.09 0

    – 3   4. 2  7

       1   6. 7  3

     

    The amusement park

    is 16.73 kilometers away.

     

    MEMORY TRIGGERS TESTS

     

    Subtract____________________________

     

    ___________________________________

     

     

    Borrow_____________________________


    ___________________________________


    ___________________digits____________

     

    ___________________________________


    _____________________tenths_________

     

    ___________________________________

     

    Speed Learning format by Carl Peterson ©2005

     

     

    MULTIPLYING DECIMALS

    Meaning Clusters

     

    A worm travels

    1.24 meters per hour.

     

    If the worm crawls

    for .2 hours

    how far will

    it travel?

     

    1.24

    ×  .2

     

    Multiply the digit

    of the bottom factor

    by the digit

    in the hundredths position

    of the top factor.

     

    2 × 4 = 8      1.24

                         ×  .2

                              8

     

    Repeat this process

    with the digits

    in the tenths position

    and ones position

    of the top factor.

     

    2 × 2 = 4      1.24

                         ×  .2_

                           4 8

     

    2 × 1 = 2       1.24

                          ×  .2_

                         2 4 8

     

    Count the number

    of decimal places

    in both factors.

     

    There are two

    decimal places

    in the top factor

    and one more

    in the bottom factor.

     

    2 + 1 = 3

     

    The product will have

    three decimal places.  

     

    Shift the decimal point

    three places

    to the left.

     

     1.24

    ×   .2_

    .2 4 8

     

    The worm crawls

    .248 meters.

     

    MEMORY TRIGGERS TESTS

     

    Multiply____________________________

     

    ___________________________________

     

     

    _____________hundredths____________


    ___________________________________


    Repeat_____________________________

     

    ___________________________________


    ____________________position________

     

    ___________________________________


    Count______________________________

    ___________________________________


    ________________decimal_____________

    ___________________________________



    _____________________factor_________

    ___________________________________


    _____product_______________________


    Speed Learning format by Carl Peterson ©2005

     

     

    DIVIDING DECIMALS 1

    Meaning Clusters


    When dividing two terms

    with decimal places

    move the point

    an equal number

    of spaces

    in both terms.

     

    2.56 ÷ .32 = 256 ÷ 32 = 8

     

    Both point move

    two spaces right.

     

    Think of it

    as multiplying

    the terms by 1.

     

    Remember that

    100/100 = 1.

     

    2.56  x 100

    0.32     100

     

    The multiplicative

    identity property

    says that any value

    multiplied by 1

    remains the same.

     

    Terms with

    many zeros can

    also be simplified.

     

    26,000,000 ÷ 13,000,000

     

    Move the decimal point

    6 places left.

     

    26.000000 ÷ 13.000000

    = 26 ÷ 13 = 2

     

    Always remember

    to move the point

    the same direction

    in both terms.

     

    With decimal points

    or multiple zeros

    find the easiest

    common place

    and divide.

     

    MEMORY TRIGGERS TESTS

     

     

    _____dividing______________________

     

    ___________________________________

     

     

    ______________point_________________


    ___________________________________


    ________________multiplying_________

     

    ___________________________________


    Remember__________________________

     

    ___________________________________

     

     

    _____________identity________________

     

    ___________________________________

     

     

    Terms______________________________

     

    ___________________________________

     

     

    Move______________________________

     

    ___________________________________


    26.000000___________________________

    ___________________________________

    __________________same_____________

     

    ___________________________________

    ____________________zeros___________

    ___________________________________


    Speed Learning format by Carl Peterson ©2005