Transcript Seminar 3

Seminar 3
Welcome
Agenda
• Decimal/Fraction Notation
• Addition, Subtraction, multiplication/division
with Decimals
42.3245
• 4 tens + 2 ones + 3 tenths + 2 hundredths + 4 thousandths + 5 ten-
thousandths
• We read this number as
• “Forty-two and three thousand two hundred forty-five tenthousandths.”
• The decimal point is read as “and”.
•Write a word name for the number in this
sentence: The top women’s time for the 50 yard
freestyle is 22.62 seconds.
•Write a word name for the number in this
sentence: The top women’s time for the 50 yard
freestyle is 22.62 seconds.
•Twenty-two and sixty-two hundredths
To convert from decimal to fraction notation,
• a) count the number of decimal
places,
4.98
2 places
• b) move the decimal point that
many places to the right, and
4.98
Move
2 places.
498
• c) write the answer over a
denominator with a 1 followed 100
by that number of zeros
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2 zeros
• Write fraction notation for 0.924. Do not
simplify.
• 0.924 =
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• Write fraction notation for 0.924. Do not
simplify.
• Solution
0.924.
3 places
• 0.924
Slide 3- 8
924
0.924 
1000
3 zeros
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Example D
•Write 17.77 as a fraction and as a mixed
numeral.
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Example D
•Write 17.77 as a fraction and as a mixed numeral.
•Solution
•To write as a fraction:
•17.77
17.77
2 places
1777
17.77 
100
2 zeros
To write as a mixed numeral, we rewrite the whole
number part and express the rest in fraction form:
Slide 3- 10
77
17.77  17
100
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To convert from fraction notation to decimal notation
when the denominator is 10, 100, 1000 and so on,
a)
8679
count the number of zeros, and 1000
3 zeros
b) move the decimal point that
8.679. Move
number of places to the left. Leave 3 places.
off the denominator.
8679
 8.679
1000
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Example E
Write decimal notation for
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53
.
10
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Example E
Write decimal notation for
53
.
10
Solution
53
10
5.3.
1 zero
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1 place
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53
 5.3
10
1. In the number 623,841, which digit
tells the number of 10 thousands?
a) 5
b) 8
c) 6
d) 2
Slide 3- 14
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1. In the number 623,841, which digit
tells the number of 10 thousands?
a) 5
b) 8
c) 6
d) 2
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2. Write a word name for 8.032.
a) Eight and thirty-two ten thousandths
b) Eight thousand, thirty-two
c) Eight and thirty-two hundredths
d) Eight and thirty-two thousandths
Slide 3- 16
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2. Write a word name for 8.032.
a) Eight and thirty-two ten thousandths
b) Eight thousand, thirty-two
c) Eight and thirty-two hundredths
d) Eight and thirty-two thousandths
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3. Write decimal notation for
a) 4.3
b) 0.53
c) 0.053
d) 0.0053
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53
.
1000
3. Write decimal notation for
a) 4.3
b) 0.53
c) 0.053
d) 0.0053
Slide 3- 19
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53
.
1000
•Adding with decimal notation is similar to adding
whole numbers.
•First we line up the decimal points so that we can
add corresponding place-value digits.
•Add the digits from the right.
•If necessary, we can write extra zeros to the far
right of the decimal point so that the number of
places is the same.
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Example A
• Add: 4.31 + 0.146 + 14.2
• Solution Line up the decimal points and write
extra zeros.4 . 3 1 0
•
. 1 4 6
•
1 4 . 2 0 0
1 8 . 6 5 6
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Example D
• Subtract 574 – 3.825
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Example D
• Subtract 574 – 3.825
• Solution
3
–
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9
9
10
5 7 4 . 0 0 0
3 . 8 2 5
570
.1 75
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1. Add: 2.15 + 13.07 + 25.
a) 14.47
b) 40.22
c) 59.57
d) 47.81
Slide 3- 24
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1. Add: 2.15 + 13.07 + 25.
a) 14.47
b) 40.22
c) 59.57
d) 47.81
Slide 3- 25
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4. Subtract: 70 – 8.231.
a) 61.231
b) 62.769
c) 62.231
d) 61.769
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4. Subtract: 70 – 8.231.
a) 61.231
b) 62.769
c) 62.231
d) 61.769
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To multiply using decimals:
a) Ignore the decimal points,
and multiply as though both
factors were whole numbers.
b) Then place the decimal point in
the result. The number of decimal
places in the product is the sum of the
number of places in the factors.
(count places from the right).
Slide 3- 28
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0.8  0.43
2
0.43
 0.8
344
0.43
 0.8
0.344
Ignore the
decimal points
for now.
(2 decimal places)
(1 decimal place)
(3 decimal places)
•To divide by a whole number;
•a) place the decimal point
•directly above the decimal
•point in the dividend, and
0.84
7 5.88
560
Divisor
•b) divide as though
•dividing whole numbers.
Slide 3- 29
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Quotient
Dividend
28
28
0
Remainder
Review for Projects
• A recipe for a drink calls for 1/5 quart water
and ¾ quart apple juice.
• How much liquid is needed?
• 2/5 + 1/4 = 8/20 + 5/20 = 13/20
• Now if the recipe is doubled?
13/20
• 13/20 + 13/20 = 26/20 =1 6/20= 1 3/10
• Or
• 13/20 * 2 = 13/20 *2/1 =26/20 = 1 6/20 =
1 3/10
If the recipe is halved?
13/20
• 13/20 / 2 = 13/20 / 2/1 = 13/20 * ½= 13/40
Simplify and convert to decimal
2/5 x 1/6=
Simplify and convert to decimal
• 2/5 x 1/6= 3/30=1/10
• Now change into decimal
1/10
• Simplest way is to use a calculator
• First off, we'll interpret the fraction bar to
mean "divided by." This means that 1/10 is
the same as 1 divided by 10.
• Now, we'll just do what the fraction bar says:
divide 1.0 by 10:
• And that's about it! 1/10 written as a decimal
to 1 decimal places is 0.1.
Mileage
Molly bought gasoline when the odometer read
8,678.9. After the next filling, the odometer
read 8,999.9. It took 9.8 gal to fill the tank.
• a) How many miles did she drive?
• b) How many miles per gallon (mpg) did the
car get?
Molly bought gasoline when the odometer read 8,678.9. After
the next filling, the odometer read 8,999.9. It took 9.8 gal to fill
the tank.
• First Step Subtraction
• 8,999.9
- 8,678.9
321 .0 She drove 321 miles
Next divide 321 by 9.8 = 32.7 miles to the
gallon.
Drew filled his truck’s gas tank and noted that
the odometer read 62,957.1. After the next
filling, the odometer read 63,247.5. It took
17.6 gal to fill the tank. How many miles per
gallon did the truck get?
Drew filled his truck’s gas tank and noted that the odometer read 62,957.1. After the next filling,
the odometer read 63,247.5. It took 17.6 gal to fill the tank. How many miles per gallon did the
truck get?
63247.5
-62957.1
290. 4
290.4 / 17.6 = 16.5