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 =? minute