Chapter 2 Operations on Decimal Numbers. What You Will Learn: To add and subtract decimal numbers To...
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Transcript of Chapter 2 Operations on Decimal Numbers. What You Will Learn: To add and subtract decimal numbers To...
Chapter 2
Operations on Decimal Numbers
What You Will Learn:
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
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: 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
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
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
Front-End:
Relative Size:
Ex: Placing Decimals Using Estimation
Place the decimals in each of these answers using estimation (do not calculate them)
423.6 - 107.2 = 3 1 6 4 0
7.85 + 2.06 + 4.123 = 1 4 0 3 3
Adding and Subtracting Decimals
We use column addition and subtraction to add and subtract decimals
The reason for this is so that we can align the decimal places
Ex: Add the following
a) 3.2 + 6.8
b) 4.51 + 1.76
c) 9.1 + 5.04
Ex: Subtract the following
a) 8.57 – 3.12
b) 4.07 – 2.64
c) 10.3 – 7.06
Problem Solving
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
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
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) 1.5 × 3
b) 7.5 × 1.2
c) 3.6 × 4.0
Problem Solving:
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
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
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
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
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 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
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
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?