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A3.8 · Compare unit prices to determine the best buy

Learn to compare unit prices to determine the best buy through clear examples and targeted practice.

Ontario Grade 11 Mathematics

Earning and Purchasing

A practical way to compare packages of different sizes

At a grocery store or workplace, two packages can have different sizes and different prices. Looking only at the shelf price can make one option seem better than it is. A unit price tells you the cost for one common unit, such as one kilogram or one cup. In this lesson, you will calculate unit prices and use them to decide which option costs less for the amount you receive.

What you will learn

1. What a unit price means

A unit is one chosen measure of something. For groceries, the unit might be one kilogram, one litre, or one item. A unit price is the cost for one of those units. For example, a price per kilogram lets you compare packages that contain different amounts of the same product.
First check that the products are the same kind and that their amounts can be compared. Two bags of the same type of rice can be compared by price per kilogram. A bag of rice and a bottle of juice cannot be ranked as a best buy by comparing unit prices, because they are different products and use different measures.
To find a unit price, divide the package price by the amount in the package. The result is the price for one unit of that amount. For example, if a package costs CAD 6 for 3 kilograms, divide 6 by 3 to get CAD 2 per kilogram.
A lower unit price means you pay less for the same amount of the same product. It usually identifies the best buy when your goal is to spend less per unit. It does not mean you must buy the larger package. For this comparison, focus on the unit price.
unit price=package pricepackage amount\text{unit price} = \frac{\text{package price}}{\text{package amount}}

2. Make a fair comparison

Shelf labels may already show a unit price. Check the label carefully: it might give a price per 100 grams, per kilogram, per litre, or per item. The units must match before you compare the numbers. A price per 100 grams cannot be compared directly with a price per kilogram until both prices are expressed using the same unit.
If no unit price is shown, calculate it with a calculator. Enter the package price divided by the amount. Keep the unit with your answer, such as CAD per kilogram. The unit is important because it tells you what the number means.
You can also use a spreadsheet. Put each package price in one column and its amount in another. In a third column, divide the price by the amount. For example, if the price is in cell B2 and the amount is in C2, enter `=B2/C2`. Copy the calculation for the other packages. Then compare the results, making sure each result uses the same unit.
Round money sensibly. If a calculator displays many decimal places, two decimal places is usually clear for a price in dollars. If two results are very close, keep more digits until you can tell which is lower. Do not round early, because early rounding can hide a small difference.

3. Read the result and decide

After calculating, compare the unit prices, not just the package prices. A larger package may cost more at the checkout but less for each kilogram or item. A smaller package may have a lower total price but a higher cost per unit.
The calculation is useful only when the amounts are expressed in comparable units. If one package is listed in grams and another in kilograms, convert one amount so both use grams or both use kilograms before comparing. For example, 1 kilogram is 1,000 grams. This measurement fact lets you put the amounts on the same basis.
Keep enough digits during the calculation to make a fair choice. If one option works out to CAD 1.48 per kilogram and another to CAD 1.52 per kilogram, the first has the lower unit price. State the result clearly: name the option and its unit price, and say why it is the better buy per unit.
The best buy in this lesson means the option with the lowest unit price among the comparable choices. The total amount you pay is different from the unit price. Keep those ideas separate when you explain your decision.

4. A simple decision routine

Use the same routine each time you compare prices. First, confirm that you are comparing the same product. Next, check the package amounts and choose one common unit. Then calculate each unit price, keeping the unit beside each answer. Finally, choose the lowest result and explain the comparison.
A quick estimate can help you notice a calculator-entry mistake. If a package costs about CAD 10 and contains about 5 kilograms, a result near CAD 2 per kilogram makes sense. A result near CAD 20 per kilogram would suggest that you may have divided in the wrong order or entered the amount incorrectly.
Do not choose based only on package size or on which package has the lowest total price. The question is which option costs less for one comparable unit. Careful labels, matching units, and a correct division make the answer clear.

Unit-price comparison for the oats

PackageAmountPackage pricePrice per kilogram
Small bag0.75 kgCAD 3.30CAD 4.40/kg
Large bag1.2 kgCAD 4.92CAD 4.10/kg

Worked example

Compare two bags of oats

A 750-gram bag of oats costs CAD 3.30. A 1.2-kilogram bag of the same oats costs CAD 4.92. Which bag has the lower price per kilogram?
  1. Match the amounts
    The first amount is in grams and the second is in kilograms. Convert 750 grams to kilograms so both amounts can be compared using the same unit.
    750 g=0.75 kg750\text{ g} = 0.75\text{ kg}
  2. Find the first unit price
    Divide the first package price by its amount in kilograms. This gives the cost for one kilogram of oats.
    CAD 3.30÷0.75=CAD 4.40/kg\text{CAD }3.30 \div 0.75 = \text{CAD }4.40/\text{kg}
  3. Find the second unit price
    Use the same calculation for the larger bag. Keeping the unit as kilograms makes the two results a fair comparison.
    CAD 4.92÷1.2=CAD 4.10/kg\text{CAD }4.92 \div 1.2 = \text{CAD }4.10/\text{kg}
  4. Compare and decide
    The larger bag has the lower price per kilogram. Its shelf price is higher, but each kilogram costs less.
    4.10<4.404.10 < 4.40
Answer: The 1.2-kilogram bag is the better buy per kilogram at CAD 4.10 per kilogram.
Check: A quick estimate supports the result: CAD 4.92 for a little more than 1 kilogram should be a little less than CAD 4.92 per kilogram.

Worked example

Compare packs of disposable cups

A workplace needs disposable cups. One box has 80 cups and costs CAD 6.40. Another box has 120 cups and costs CAD 9.00. Which box has the lower price per cup?
  1. Use the same unit
    Both packages contain the same kind of item, and both amounts are already counted in cups. No conversion is needed.
    1 cup1\text{ cup}
  2. Calculate the first price per cup
    Divide the first box price by its number of cups to find the cost of one cup.
    CAD 6.40÷80=CAD 0.08/cup\text{CAD }6.40 \div 80 = \text{CAD }0.08/\text{cup}
  3. Calculate the second price per cup
    Divide the second box price by its number of cups. Now both answers are in CAD per cup.
    CAD 9.00÷120=CAD 0.075/cup\text{CAD }9.00 \div 120 = \text{CAD }0.075/\text{cup}
  4. Compare without rounding too soon
    The second answer is less than eight cents per cup. Keeping the extra decimal places shows that it is cheaper per cup, even though its total price is higher.
    0.075<0.080.075 < 0.08
Answer: The 120-cup box is the better buy per cup at CAD 0.075 per cup.
Check: At eight cents per cup, 120 cups would cost CAD 9.60. The box costs CAD 9.00, so its actual price per cup is lower than eight cents.

Common mistakes and how to avoid them

Choosing the package with the lowest total price.
Correction: Calculate price per unit for each package. The lowest total price does not always mean the lowest unit price.
Comparing a price per 100 grams with a price per kilogram as if the units match.
Correction: Convert or recalculate so both unit prices use the same unit before deciding.
Dividing the package amount by the price.
Correction: Divide the price by the amount. This gives the cost for one unit.
Rounding a close result too early.
Correction: Keep extra digits while comparing, then round the final answer clearly.

Lesson summary

Check your understanding

Question 1

Two identical brands of juice are compared. A 2-litre carton costs CAD 5.20, and a 3-litre carton costs CAD 7.20. Which is the better buy per litre?
  1. The 2-litre carton, at CAD 2.60 per litre
  2. The 3-litre carton, at CAD 2.40 per litre
  3. The 2-litre carton, because its package price is lower
  4. They cost the same per litre
Show answer and explanation
The 3-litre carton, at CAD 2.40 per litre
The unit prices are CAD 5.20 divided by 2, or CAD 2.60 per litre, and CAD 7.20 divided by 3, or CAD 2.40 per litre. The lower unit price is the 3-litre carton.

Question 2

A 500-gram bag of the same coffee costs CAD 8.50. What is its price per kilogram?
  1. CAD 4.25 per kilogram
  2. CAD 8.50 per kilogram
  3. CAD 17.00 per kilogram
  4. CAD 0.017 per kilogram
Show answer and explanation
CAD 17.00 per kilogram
Five hundred grams is 0.5 kilogram. Divide CAD 8.50 by 0.5 to get CAD 17.00 per kilogram.

Question 3

Why should two unit prices use the same unit before you compare them?
  1. So each price describes the cost for the same amount
  2. So the package prices become equal
  3. So the larger package always wins
  4. So you do not need to divide
Show answer and explanation
So each price describes the cost for the same amount
Matching units makes the costs comparable. A price per kilogram and a price per 100 grams describe different amounts until one is converted or recalculated.

Key terms

Unit
One chosen measure or item, such as one kilogram or one cup.
Unit price
The cost for one chosen unit of a product.
Convert
Change a measurement to an equal amount written in a different unit.
Best buy
For this lesson, the comparable option with the lowest unit price.

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About this lesson

Published by DoAssignment. This AI-assisted lesson follows Ontario Grade 11 Mathematics (MEL3E), expectation A3.8. It is a study resource, not an official curriculum publication.

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