Mathematics
Grade 9
15 min
Unit prices with unit conversions
Unit prices with unit conversions
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1
Introduction & Learning Objectives
Learning Objectives
Calculate the unit price of an item given its total price and quantity.
Convert measurements within the metric system (e.g., grams to kilograms, milliliters to liters).
Use conversion factors to convert between metric and imperial systems (e.g., pounds to kilograms, gallons to liters).
Calculate and compare unit prices for items sold in different units of measurement.
Solve multi-step word problems to determine the most economical choice among several options.
Apply the concept of unit pricing with conversions to make informed consumer decisions.
You see a 2-liter bottle of soda for $2.50 and a 12-pack of 355 mL cans for $6.99. Which one is the better deal? 🥤 Let's do the math!
This tutorial will teach you how to become a savvy shopper by combining...
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Key Concepts & Vocabulary
TermDefinitionExample
Unit PriceThe cost for one single unit of an item. It is used to compare the prices of the same product sold in different quantities.If a 5 kg bag of potatoes costs $10, the unit price is $2 per kilogram ($10 / 5 kg).
Unit ConversionThe process of changing a measurement from one unit to another without changing its value.Converting a length of 2.5 kilometers into 2500 meters.
Conversion FactorA ratio or fraction which represents the relationship between two different units and is equal to one. Multiplying a quantity by a conversion factor changes the units but not the value.The conversion factor to change kilograms to grams is (1000 g / 1 kg).
RateA ratio that compares two quantities measured in different units.A price of $12 for 3 pounds of apples is a rate. The uni...
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Core Formulas
Unit Price Formula
\text{Unit Price} = \frac{\text{Total Price}}{\text{Total Quantity}}
Use this formula to find the cost per single unit of measure (e.g., per gram, per liter, per item). This is the first step in comparing products.
Unit Conversion with a Factor
\text{New Quantity} = \text{Original Quantity} \times \frac{\text{Desired Unit}}{\text{Original Unit}}
Use this method to convert a measurement. The fraction is the 'conversion factor'. Arrange it so the 'Original Unit' cancels out, leaving you with the 'Desired Unit'.
4 more steps in this tutorial
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Challenging
You need to buy at least 3 kg of potatoes. Store A sells 2.5 kg bags for $4.00. Store B sells 5 lb bags for $3.50. What is the minimum amount you must spend? (1 kg ≈ 2.20 lbs)
A.$7.00 by buying two bags from Store B.
B.$8.00 by buying two bags from Store A.
C.$4.80 by buying one bag from Store A.
D.$7.50 by buying one bag from each store.
Challenging
Store A sells a 750 g box of cereal for $5.00. Store B sells a 1.2 kg box of the same cereal for $8.50, but today it is on sale for 20% off. Which store offers the better deal today?
A.Store A is the better deal.
B.Store B is the better deal.
C.Both stores offer the same unit price.
D.The better deal cannot be determined.
Challenging
A store has a 'buy one, get one 50% off' deal on 1.5 L bottles of iced tea that normally cost $3.00 each. A different store sells 2 L bottles for $3.80 each. If you buy two bottles from the first store to use the deal, what is the effective unit price per liter, and how does it compare to the second store?
A.$1.50/L, which is cheaper than the second store.
B.$1.50/L, which is more expensive than the second store.
C.$2.00/L, which is more expensive than the second store.
D.$1.80/L, which is cheaper than the second store.
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