Unit Prices with Decimals and Fractions

Whether you are comparing grocery prices or calculating a fair wage, unit prices are a practical everyday skill — and they appear regularly on the GED Math test. A unit price tells you the cost of exactly one unit of something, making it easy to compare two different package sizes or two different deals. This lesson covers unit prices with both decimals and fractions.

What Is a Unit Price?

A unit price (or unit rate) is the price for a single unit of a product. You find it by dividing the total price by the number of units:

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Unit \(\color{blue}{\text{ Price } = \text{ Total }}\) \(\color{blue}{\text{ Price } \div \text{ Number }}\) of Units

Once you know the unit price, you can compare products of different sizes by looking at which one costs less per unit.

How to Calculate Unit Prices

1. Unit price with a whole number or decimal quantity

Divide the price (as a decimal) by the number of units.

• 3 lb of apples for \(4.50: Unit price = \)\(\color{blue}{4.50 \div 3}\) = $1.50 per lb
• 2.5 gallons of juice for \(7.75: Unit price = \)\(\color{blue}{7.75 \div 2.5}\) = $3.10 per gallon
• 4 notebooks for \(6.20: Unit price = \)\(\color{blue}{6.20 \div 4}\) = $1.55 each

2. Unit price with a fractional quantity

Dividing by a fraction is the same as multiplying by its reciprocal.

• ¾ lb of cheese for $3.00: Unit price = $3.00 ÷ ¾ = $\(\color{blue}{3.00 \times \frac{4}{3}}\) = $4.00 per lb

3. Compare two products (best-buy problem)

Calculate the unit price of each option, then choose the lower unit price.

• 12 oz for \(2.40: Unit price = \)\(\color{blue}{2.40 \div 12}\) = $0.20 per oz
• 16 oz for \(3.04: Unit price = \)\(\color{blue}{3.04 \div 16}\) = $0.19 per oz
• The 16 oz package is the better deal ($0.19 < $0.20 per oz).

Step-by-Step Summary

1. Identify the total price and the quantity.
2. Write the unit price formula: Unit \(\color{blue}{\text{ Price } = \text{ Total }}\) \(\color{blue}{\text{ Price } \div \text{ Quantity }}\).
3. If the quantity is a fraction, multiply the price by the reciprocal of the fraction.
4. Round to the nearest cent if necessary.
5. For best-buy comparisons, compare unit prices and choose the lower one.

Watch: Unit Rates with Decimals (Math with Mr. J)

Math with Mr. J walks through step-by-step examples of calculating unit rates when quantities involve decimals:

Worked Examples

Example 1: A 3 lb bag of oranges costs $4.50. A 5 lb bag costs $7.00. Which is the better deal?

3 lb bag: $\(\color{blue}{4.50 \div 3}\) = $\(\color{blue}{\frac{1.50}{\text{ lb }}}\). 5 lb bag: $\(\color{blue}{7.00 \div 5}\) = $\(\color{blue}{\frac{1.40}{\text{ lb }}}\).
The 5 lb bag is the better deal at $1.40 per pound.

Example 2: A recipe uses ½ lb of butter costing $2.40. What is the price per pound?

Unit price = \(2.40 ÷ ½ = \)\(\color{blue}{2.40 \times 2}\) = $4.80 per lb.

Example 3: A store sells 1.5 liters of soda for $2.25 and 2.5 liters for $3.50. Which has the lower unit price?

1.5 L: $\(\color{blue}{2.25 \div 1.5}\) = $\(\color{blue}{\frac{1.50}{L}}\). 2.5 L: $\(\color{blue}{3.50 \div 2.5}\) = $\(\color{blue}{\frac{1.40}{L}}\).
The 2.5-liter bottle costs less per liter.

Example 4: A worker earns $93.50 for 8.5 hours. What is the hourly rate?

Unit rate = $\(\color{blue}{93.50 \div 8.5}\) = $11.00 per hour.

More Practice: Rates with Fractions (Khan Academy)

Khan Academy demonstrates how to calculate rates when the quantities are given as fractions — an important skill for GED fraction word problems:

Exercises

1. A 6-pack of water costs $3.54. What is the cost per bottle?
2. A ¾-lb block of cheddar costs $4.50. What is the price per pound?
3. Brand A: 24 oz for $3.84. Brand B: 32 oz for $4.96. Which brand costs less per ounce?
4. A car travels 187.5 miles on 7.5 gallons of gas. What is the fuel efficiency in miles per gallon?
5. A seamstress earns $45 for sewing &frac52; yards of fabric. What is the rate per yard?
6. Two sizes of granola: 1.5 lb for $5.40 and 2.5 lb for $8.50. Which is the better value?

Answers

1. $\(\color{blue}{3.54 \div 6}\) = $0.59 per bottle
2. \(4.50 ÷ ¾ = \)\(\color{blue}{4.50 \times \frac{4}{3}}\) = $6.00 per lb
3. Brand A: $\(\color{blue}{3.84 \div 24}\) = $\(\color{blue}{\frac{0.16}{\text{ oz }}}\); Brand B: $\(\color{blue}{4.96 \div 32}\) = $\(\color{blue}{\frac{0.155}{\text{ oz }}}\). Brand B costs less per oz.
4. \(\color{blue}{187.5 \div 7.5}\) = 25 mpg
5. $\(\color{blue}{45 \div (\frac{5}{2})}\) = $\(\color{blue}{45 \times \frac{2}{5}}\) = $18 per yard
6. 1.5 lb: $\(\color{blue}{5.40 \div 1.5}\) = $\(\color{blue}{\frac{3.60}{\text{ lb }}}\); 2.5 lb: $\(\color{blue}{8.50 \div 2.5}\) = $\(\color{blue}{\frac{3.40}{\text{ lb }}}\). 2.5 lb is the better value.

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Frequently Asked Questions

What is the difference between unit price and unit rate?

A unit price specifically refers to cost per one unit of a product (e.g., dollars per ounce). A unit rate is a broader term for any ratio where the denominator is 1 (e.g., miles per hour, words per minute). Unit price is a type of unit rate focused on money.

How do I divide by a fraction to find a unit price?

Dividing by a fraction is the same as multiplying by its reciprocal. If you paid $3.00 for ¾ lb, then price per lb = $3.00 ÷ ¾ = $\(\color{blue}{3.00 \times \frac{4}{3}}\) = $4.00 per lb. Flip the fraction and multiply.

Is a lower unit price always the better deal?

In terms of cost alone, yes — the lower unit price means you pay less for each unit. However, always consider whether you can actually use the larger quantity before it expires or goes to waste. On the GED, you will typically just compare unit prices mathematically.

Related Topics

• Word Problems: Finding Two-Variable Equations
• Word Problems Involving Rates and Ratios
• Equivalent Rates
• Multiplying and Dividing Decimals
• Dividing Mixed Numbers