Transcript Chapter 2

Chapter 2
Operations on Decimal Numbers
What You Will Learn:
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To add and subtract decimal numbers
To multiply decimal numbers
To divide decimal numbers
To use the order of operations (BEDMAS) to
perform calculations with decimal numbers
To use estimation to check your answers
2.1 – Adding and Subtracting
Decimals
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Before actually performing addition and
subtraction of decimal values, we need to
work on estimating
Estimation provides us with a ‘ballpark’ figure
so we can check our answer
Example:
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Ashley and Marshall live in Winnipeg. They are
traveling to Jasper. The actual distances are given
below:
Ashley estimates that the total trip distance is about
1700 km, while Marshall estimates the distance as
1400 km
Winnipeg to
Minnedosa
Minnedosa
to Yorkton
Yorkton to
Saskatoon
Saskatoon to
Lloydminster
Lloydminster
to Edmonton
Edmonton to
Jasper
209.5
257.9
341.7
274.3
247.8
360.4
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Estimate your own value for the trip distance
Feel free to estimate as closely to the value
as you feel comfortable, but you should be
able to perform the calculation in your head!
My Answer:
Estimation Methods
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There are two main estimation methods
Front-end estimation uses only the first
number in each value and rounds the
remaining values to zero
Relative-size estimation looks at the leading
and second digits to round the values before
estimating
Ex: Estimate 81.95 + 12.50 +
29.30
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Front-End:
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Relative Size:
Ex: Placing Decimals Using
Estimation
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Place the decimals in each of these answers
using estimation (do not calculate them)
423.6 - 107.2 = 3 1 6 4 0
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7.85 + 2.06 + 4.123 = 1 4 0 3 3
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Adding and Subtracting
Decimals
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We use column addition and subtraction to
add and subtract decimals
The reason for this is so that we can align the
decimal places
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a)
b)
c)
Ex: Add the following
3.2 + 6.8
4.51 + 1.76
9.1 + 5.04
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a)
b)
c)
Ex: Subtract the following
8.57 – 3.12
4.07 – 2.64
10.3 – 7.06
Problem Solving
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Leslie has $5.50. She purchases some gum
for $1.29 and an iced tea for $1.79. How
much money does Leslie have left?
2.2 – Multiplying Decimals
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When multiplying decimals, estimation can
again be used to check our answer
Ex: Chris finds 5 books at a cost of $1.65
each. He has $9.00 in change. Can he
afford to buy these books?
Multiplying Decimals
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The process of multiplying decimals is no
different from multiplying any other two
numbers
The number of decimal places in the final
answer depends on the number of decimal
places that you start with
Ex: Multiply the following
a)
b)
c)
1.5 × 3
7.5 × 1.2
3.6 × 4.0
Problem Solving:
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Karl is preparing apple pies for a family
reunion. He will need 4.5 pounds of apples
to make the pies. Apples cost $1.29 / lb.
What will the total cost of the apples be?
2.3 – Dividing Decimals
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Dividing decimal numbers is slightly more
difficult than multiplication
Often it is a good idea to estimate the answer
before working on the question
Ex: Estimate the following to determine
where to place the decimal
a)
15.4 ÷ 3.6 = 4 2 7 7 7 8
b)
4.4 ÷ 0.42 = 1 0 4 7 6 1 9
Division of Decimals
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To divide using decimals, it is easiest to
remove the decimals completely from the
dividend and divisor
We can then use estimation to place the
decimal when we are finished
Ex: Divide the following
a)
1.36 ÷ 0.34
b)
57.9 ÷ 3
Problem Solving
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Juice boxes have a volume of 0.25 L. How
many juice boxes will contain the same
amount of juice as a 1.89 L bottle?
2.4 – Order of Operations
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In mathematics, there are many operations
Rules have been developed to determine the
order in which operations are performed if
there are several different types together
BEDMAS
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BEDMAS is an acronym that is used to help
you to keep in mind what order operations
must be completed in
B:
E:
D:
M:
A:
S:
Examples:
a)
5.3 × 1.2 + 4.5
b)
(3.6 + 4.6) ÷ 2.4 + 5
Problem Solving
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The Edwards family filled up their van with
72.4 L of gas at a cost of 121.9 ¢ / L. They
also bought 4 drinks at a cost of $1.69 each
and 2 ice-cream bars at a cost of $1.39 each.
What is the total cost of their purchase?
Problem Solving
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Murphy walks the same distance on each of
4 days for a total of 5.2 km. Then Murphy
walks 2.1 km on the fifth day. What distance
did Murphy travel on days 4 and 5 together?