Unit 5: Using Decimals in Real Life
Topic B: Decimal Word Problems
Key Words
Spend a few minutes reviewing the key words that will help you identify addition, subtraction, multiplication and division word problems.
Some key words that point to addition include:
Some key words that point to subtraction include:
- difference
- balance
- minus
- amount left
- subtracted from
- decreased by
- reduced by
- taken away
- less
- compare
Some key words which point to multiplication include:
Some key words which point to division include:
- separated
- split
- cut
- shared
- What is the cost per…?
- unit price
- What is the distance per…?
- average (speed, cost, weight, time)
Read over some of the problems that you have done in each unit to remind yourself of the patterns to expect for different operations.
Steps for Solving Word Problems
Carefully review the five steps to use when solving problems:
Step 1: Question
- Read the problem carefully.
- What is the question being asked?
- Does the problem have two parts?
- Draw a picture to help you see the problem described.
Step 2: Information
- What information is necessary to solve the problem?
- Often you are given extra numbers and information that are not needed.
- Keep the question (destination) in mind.
- Circle the information you need.
- Write that information on the picture you drew.
Step 3: Operation
- Decide what arithmetic operation to use.
- Do you need to add, subtract, multiply, or divide?
- If the problem has two parts, decide what operation you need to do for each part.
- Key words often point to the operation needed.
- Drawing a diagram or sketch is always helpful.
- Write an equation (a number sentence).
Step 4: Estimate
- Estimate the answer to the problem.
- Round the numbers so you can work with them quickly.
- Use the operation you chose in Step 3 and come to a quick answer.
- Does this estimated answer make sense?
- Does it answer the question of the problem?
- Think carefully before you do Step 5.
Step 5: Solve
- Solve the problem using the actual numbers.
- Check your arithmetic.
- Compare your answer in Step 4 to your estimate from Step 3.
- Think again about the question. Does your solution make sense?
- When you write your answer, include the units.
For example: 3 dozen eggs, 7.5 kilometres, 68 people
Exercise 1
- The total weight of an A.T.V. is 293.937 kg. If a hunter who weighs 62.142 kg carried an extra 68.39 kg, how much would her entire A.T.V. weigh when loaded?
- Estimation:
- Actual solution:
- Answer:
- The Head Start shuttle bus drives a route that is 12.73 km long. It drives this route 5 times a day. How many kilometres does the bus drive in one day?
- Estimation:
- Actual solution:
- Answer:
- Mary bought a TV. She made a down payment of $75.00 and then made monthly payments of $56.19 for twelve months. How much did she pay for the TV altogether?
- Estimation:
- Actual solution:
- Answer:
- The total number of employee hours to be paid on the weekly payroll for the Dryer Company was 19 600 hours. The average rate of pay was $9.575 per hour. How much money was paid out in the payroll that week?
- Estimation:
- Actual solution:
- Answer:
- Joe’s truck holds 94.5 L of gasoline. If he can drive from Vancouver to Vanderhoof (896 km) on that much gasoline, calculate the km/L of gasoline for his truck.
Answer to the nearest hundredth of a litre.- Estimation:
- Actual solution:
- Answer:
- Renee’s landlord is going to put new carpet in her living/dining room. The area of the room is 24 square metres. Using the costs below, figure out how much the new carpet will cost Renee’s landlord: (Note that this is a two-step problem.)
carpet $19.95/m²
underlay $4.50/m²
taxes $3.83/m²
labour charges $4.75/m²- Estimation:
- Actual solution:
- Answer:
- Andy went to Mark’s and bought his daughter a pair of jeans for $29.95 and a top for $13.50. The sales tax was $5.21.
- How much did he spend altogether?
- Estimation:
- Actual solution:
- Answer:
- Andy paid for his purchase with a fifty dollar bill. How much change did he get?
- Estimation:
- Actual solution:
- Answer:
- How much did he spend altogether?
- In a recent 48-game season, the Rupert Rampage won 0.625 of their hockey games. How many games did they win? And how many games did they lose? Be sure that your games won and the games lost add up to 48 games when you are finished.
- Estimation:
- Actual solution:
- Answer:
- If Diane takes a job paying $28 606.60 a year, what will her monthly salary be (before deductions)?
- Estimation:
- Actual solution:
- Answer:
- Last year, Treena spent a total of $235.75 on her pay-as-you-go phone plan. What was her average cost per month?
- Estimation:
- Actual solution:
- Answer:
- Samantha’s height and weight have both changed since she was fourteen. Her old height and weight were 160.02 cm and 56.82 kg. Her present height and weight are 165.1 cm and 58.18 kg. Find the increases of both her height and weight.
- Estimation:
- Actual solution:
- Answer:
- A 25-inch flat screen TV can be purchased for $199.99 cash. If you wish to buy it “rent-to-own” you must pay a $50.00 down payment and make monthly payments of $27.50 for six months.
- How much do you pay if you buy “rent-to-own”?
- How much do you save if you pay cash?
Answers to Exercise 1
- Estimation: 300kg + 60 kg + 70 kg ≈ 430 kg
Actual solution: 293.937 kg + 62.142 kg + 68.39 kg = 424.469 kg
Answer: The ATV weighed 424.469 kg when loaded. - Estimation: 13 km × 5 ≈ 65 km per day
Actual solution: 12.73 km × 5 = 63.65 km
Answer: The bus drives 63.65 km a day. - Estimation: $60 × 12 + $75 ≈ $795
Actual solution: $56.19 × 12 + $75.00 = $749.28
Answer: Mary paid $749.28 for the TV set. - Estimation: 20 000 hours × $10.00 ≈ $200 000
Actual solution: 19 600 hours × $9.575 = $187 670
Answer: The Dryer Company paid out $187 670 for the payroll that week. - Estimation: 900 km ÷ 90 L ≈ 10 km/L
Actual solution: 896 km ÷ 94.5 L = 9.48 km/L
Answer: Joe‘s truck uses 9.48 kilometres per litre. - Estimations: $20 + $5 + $4 + $5 ≈ $34, $35 × 25 m2 ≈ $875
Actual solutions: $19.95 + $4.50 + $3.83 + $4.75 = $33.03, $33.03 × 24 m2 = $792.72
Answer: The cost to have the new carpet is $792.72. -
- Estimation: $30 + $14 + $5 ≈ $49
Actual solution: $29.95 + $13.50 + $5.21 = $48.66
Answer: Andy spent $48.66. - Estimation: $50 − $49 ≈ $1
Actual solution: $50 − $48.66 = $1.34
Answer: Andy got $1.34 change from his $50.
- Estimation: $30 + $14 + $5 ≈ $49
- Estimations: 50 × 0.50 ≈ 25 games won, 50 × 0.50 = 25 games lost
Actual solutions: 48×0.625 =30 games won 48 × 0.375 =18 games lost - Estimation: $30000 ÷ 10 ≈ $3000
Actual solution: $28606.60 ÷ 12 = $2383.88
Answer: Diane‘s monthly salary will be $2383.88. - Estimation: $250 ÷ 10 ≈ $25
Actual solution: $235.75 ÷ 12 = $19.65
Answer: Treena paid $19.65 monthly. - Estimation: 165 cm − 160 cm ≈ 5 cm, 58 kg − 57 kg = 1 kg
Actual solution: 165.1 cm − 160.02 cm = 5.08 cm
58.18 kg − 56.82 kg = 1.36 kg
Answer: Samantha’s height has changed by 5.08 cm and her weight has changed by 1.36 kg. -
- $27.50 × 6 = $165
$165 + 50 = $215
Answer: If you pay on time, you will pay $215. - $215 − $199.99 = $15.01
Answer: If you pay cash, you will save $15.01.
- $27.50 × 6 = $165
Topic B: Self-Test
Mark /6 Aim 5 / 6
- A machinist has to bore (drill) a hole through 2.6 cm of steel. He has drilled 1.25 cm. How much farther must he drill?
- Estimation:
- Actual Solution:
- Answer:
- Sebastian picked 6.75 kg of berries and then sold them at a farmer’s market for $2.95 a kg. How much did he make?
- Estimation:
- Actual Solution:
- Answer:
- Karla gets $12.75 per hour at her job. Yesterday she earned $57.38. How many hours did she work?
- Estimation:
- Actual Solution:
- Answer:
Answers to Topic B Self-Test
- Estimation: 3 cm − 1 cm ≈ 2 cm
Actual Solution: 2.6 cm − 1.25 cm = 1.35 cm
He has to drill 1.35 cm farther. - Estimation: 7 kg × $3 ≈ $21
Actual Solution: 6.75 kg × $2.95 = $19.91
Sebastian got $19.91 for his berries. - Estimation: $60 ÷ 12 ≈ 5
Actual Solution: $57.38 ÷ 12.75 = 4.5
Karla worked for 4.5 hours.
Design Your Own House Project Part 4: Fencing and Decorating
Use the graph paper house sketch that you made in Unit 2, Topic B: Subtracting Decimals in the Design Your Own House Project Part 1 do this activity.
Give your house a yard.
- What is the perimeter of the yard?
- Calculate the total area of your yard, not including the area of the house. (area = length × width)
There are two ways to do this. You can calculate the whole area and then subtract the area of the house, or you could calculate the area of each section of the yard (front, back, and two sides) and add them together. - Use a flyer from a hardware store or go online to look at types of fencing (for example, chain-link, cedar, metal, wood panel, picket, etc.). Choose a style of fencing for your yard. Write your choice here.
- Decide what materials you will need to purchase to build your fence. List them here, along with the cost. Some costs will be per unit, and some will be per metre.
Material Quantity Cost (Include units if applicable. e.g. per metre) Total price of material Examples:
Fence posts, cedar, 2m24 $15.26 each $366.24 Fence rails, cedar, 4m, pack of 4 10 $45.36 each $453.60 Total cost of fencing materials: - Calculate the price per metre of your fence.
- When making curtains, it is a good idea to use fabric that is 2.5 times the width of the window. Remember that each of your windows is 1m wide. What length of fabric will you need to buy to make curtains for all four windows?
- Decorate your house with a piece of art that measures 46.5 cm by 83.8 cm. Sketch the art here. Add the dimensions (length and width).
- You will need to build a frame for your artwork. You will need a piece of glass to cover it, and pieces of trim to frame it.
- What size glass should you buy?
- How much trim will you need to buy for your picture frame?
Marking Rubric for House Project Part 4
Sketch:
- The house has a yard and measurements have been clearly marked on the sketch.
Calculations:
- The perimeter of the yard has been calculated correctly.
- The area of the yard has been calculated correctly.
- The total price of each fencing material has been calculated correctly.
- The price per metre of the fence has been calculated correctly.
- The width of fabric necessary to cover all four windows has been calculated correctly.
- The size of glass necessary to cover the artwork has been calculated correctly.
- The amount of trim necessary for the picture frame has been calculated correctly.
The result of an addition question, the answer to an addition question.
The amount altogether.
The result of a subtraction question, the answer. Subtraction gives the difference between two numbers.
Balance has many meanings. In money matters, the balance is the amount left. It might be the amount left in a bank account (bank balance) or it might be the amount you still must pay on a bill (balance owing).
The result of a multiplying question, the answer.
The price for a set amount. E.g., price per litre, price per gram.