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

 a) b) c) Ex: Add the following 3.2 + 6.8

4.51 + 1.76

9.1 + 5.04

 a) b) c) Ex: Subtract the following 8.57 – 3.12

4.07 – 2.64

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) b) c) 1.5 × 3 7.5 × 1.2

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?