Unit 4: Adding & Subtracting Common Fractions
Topic C: Problems Using Common Fractions
Review again the five steps for problem solving.
Step 1: Read, find the question.
Step 2: Get the necessary information from the problem.
Step 3: Decide on the arithmetic operation.
Step 4: Estimate the answer, using rounded numbers. Does the answer to the problem seem sensible?
Step 5: Solve the problem using the actual numbers. Check. Is the answer close to the estimate?
Fraction problems with mixed numbers are easily estimated by rounding the fraction to the nearest whole number.
If the problem uses proper fractions it is harder to estimate the answer using a rounded number because proper fractions will round off to either 0 or 1, which isn’t too useful. However, to figure out the operation to use (Step 3), it sometimes helps to substitute whole numbers for the proper fraction; this may help you to make sense of the problem. Drawing a sketch might also be helpful.
Exercise 1
Decide on the arithmetic operation ( + , −, × , ÷ ) and then solve
- The following recipe for Macaroni and Cheese is very tasty. It feeds six people. Look at the recipe and then complete the chart according to these questions.
- You want to make enough macaroni and cheese for 9 people. That is [latex]\tfrac{9}{6}[/latex] ([latex]1\tfrac{1}{2}[/latex]) of the recipe.
- Figure out all the quantities. Figure out the quantities for 3/4 the recipe, so it is the right amount for 3 people.Tasty Macaroni and Cheese
Ingredients for 6 people Quantities for 9
people ([latex]1\tfrac{1}{2}[/latex] x )Quantities for 3 people ( [latex]\tfrac{1}{2}[/latex] x ) [latex]1\dfrac{3}{4}[/latex] cup elbow macaroni [latex]\dfrac{3}{4}[/latex] cup chopped onion [latex]\dfrac{1}{2}[/latex] cup chopped green pepper 10 sliced mushrooms 3 tbsp. butter or margarine [latex]1\dfrac{1}{2}[/latex] tbsp. flour 1 tsp. dry mustard [latex]\dfrac{3}{4}[/latex] tsp. salt [latex]\dfrac{1}{4}[/latex] tsp. oregano [latex]2\dfrac{1}{2}[/latex] cups milk [latex]2\dfrac{1}{2}[/latex] cups shredded cheddar cheese [latex]\dfrac{1}{2}[/latex] cup fine dry breadcrumbs
- Jack spent his school day this way: [latex]1\tfrac{1}{4}[/latex] hours on English, [latex]1\tfrac{3}{4}[/latex] hours on math, [latex]\tfrac{1}{2}[/latex] hour on science and 2 hours on lunch and coffee breaks. How long was his school day?
- The canoe trip usually takes [latex]4\tfrac{1}{4}[/latex] hours for the 34 kilometre trip. What is the average time per kilometre?
- The “Walkyerbunsoff” Club members walk [latex]4\tfrac{3}{4}[/latex] kilometres around the shopping mall six mornings a week.
- How far do they walk each week?
- How far do they walk in one year if they keep the same schedule? (52 weeks = 1 year)
- The test has 30 multiple choice questions to be completed in [latex]\tfrac{3}{4}[/latex] of an hour. How much time can be spent on each question? (It might be easier to work with minutes. 1 hour = 60 minutes, so [latex]\tfrac{3}{4}[/latex] of an hour =? minutes.)
- The gas tank was filled before the family left Hazelton. When they pulled into Prince Rupert that afternoon, the gas gauge showed they had used [latex]\tfrac{5}{8}[/latex]of the gas.
- What fraction of the gas was left?
- The full gas tank holds 54 litres. How many litres of gas did they use in the trip from Hazelton to Prince Rupert?
- About [latex]\tfrac{2}{5}[/latex] of the population of our city has an Italian background. The population is 6500. How many people in our city have an Italian background?
- The four children carefully planted 3 rows of corn together and promised to share the work and the corn. Only [latex]2\tfrac{1}{4}[/latex] rows of corn came up. How much of a row does each child need to look after?
- Gail was supposed to babysit for [latex]2\tfrac{3}{4}[/latex] hours, but she didn’t feel well so her sister Debbie said she would come for [latex]\tfrac{1}{2}[/latex] of the time. How long did each sister babysit?
- The stocks closed at [latex]6\tfrac{1}{8}[/latex] on Monday. On Tuesday they fell [latex]\tfrac{1}{4}[/latex] . What was the value of the stocks at closing on Tuesday?
- The same stocks had a good day on Wednesday. They rose [latex]\tfrac{3}{4}[/latex] from the Tuesday closing price (see question j). What was the value of the stocks at closing on Wednesday?
- Victor and his family heat their house with wood. Last year, they cut and
hauled [latex]12\tfrac{1}{2}[/latex] cords of wood from the bush. At [latex]\tfrac{1}{2}[/latex] cord per pick-up truck load, how many trips did they have to make with their one truck? - Canadian Mortgage Housing Corporation (CMHC) suggests that when you buy a home, the cost of the house should be no more than 2 1/2 times your annual income. Between them, John and Pam Miller have a gross annual income of $68 000. About how much would CMHC say they should spend on a house?
- The loaded logging trucks cover 38 1/2 km from the logging site down the steep logging roads to the highway in 1 1/4 hours. What is their average speed in kilometres per hour?
Answers to Exercise 1
-
- Tasty Macaroni and Cheese
Ingredients for 6 people Quantities for 9
people ([latex]1\tfrac{1}{2}[/latex] x )Quantities for 3 people ( [latex]\tfrac{1}{2}[/latex] x ) [latex]1\dfrac{3}{4}[/latex] cup elbow macaroni [latex]2\dfrac{5}{8}[/latex] cups [latex]\dfrac{7}{8}[/latex] cup [latex]\dfrac{3}{4}[/latex] cup chopped onion [latex]1\dfrac{1}{8}[/latex]cup [latex]\dfrac{3}{8}[/latex] cup [latex]\dfrac{1}{2}[/latex] cup chopped green pepper [latex]\dfrac{3}{4}[/latex] cup [latex]\dfrac{1}{4}[/latex] cup 10 sliced mushrooms 15 5 3 tbsp. butter or margarine [latex]4\dfrac{1}{2}[/latex] tbsp. [latex]1\dfrac{1}{2}[/latex] tbsp. [latex]1\dfrac{1}{2}[/latex] tbsp. flour [latex]2\dfrac{1}{4}[/latex] tbsp. [latex]\dfrac{3}{4}[/latex] tbsp. 1 tsp. dry mustard [latex]1\dfrac{1}{2}[/latex] tsp. [latex]\dfrac{1}{2}[/latex] tsp. [latex]\dfrac{3}{4}[/latex] tsp. salt [latex]1\dfrac{1}{8}[/latex] tsp. [latex]\dfrac{3}{8}[/latex] tsp. [latex]\dfrac{1}{4}[/latex] tsp. oregano [latex]\dfrac{3}{8}[/latex] tsp. [latex]\dfrac{1}{8}[/latex] tsp. [latex]2\dfrac{1}{2}[/latex] cups milk [latex]3\dfrac{3}{4}[/latex] cups [latex]1\dfrac{1}{4}[/latex] cups [latex]2\dfrac{1}{2}[/latex] cups shredded cheddar cheese [latex]3 \dfrac{3}{4}[/latex] cups [latex]1\dfrac{1}{4}[/latex] cups [latex]\dfrac{1}{2}[/latex] cup fine dry breadcrumbs [latex]\dfrac{3}{4}[/latex] cup [latex]\dfrac{1}{4}[/latex] cup
- Tasty Macaroni and Cheese
- [latex]5\dfrac{1}{2}[/latex] hours
- [latex]\dfrac{1}{8}[/latex] hours/km or [latex]7\dfrac{1}{2}[/latex] min/km
- answers
- [latex]28\dfrac{1}{2}[/latex] km
- 1482 km
- [latex]1\dfrac{1}{2}[/latex] minutes/question
- answers
- [latex]\dfrac{3}{8}[/latex] tank
- [latex]33\dfrac{3}{4}[/latex]
- 2600 people
- [latex]\dfrac{3}{4}[/latex] of a row
- [latex]1\dfrac{3}{8}[/latex] hours
- [latex]5\dfrac{7}{8}[/latex]
- [latex]6\dfrac{5}{8}[/latex]
- 25 trips
- $170 000
- 31 km/h