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Interpret price per item as a rate

Price per item is understood as a unit rate: the ratio of total cost to the number of items, expressed in dollars per item or cents per item. The learner interprets division as finding the rate, uses it to compare equivalent purchases, and multiplies by a quantity to determine total cost while distinguishing unit price from total price; this scope involves whole-item quantities and familiar decimal or fraction values, not compound discounts, taxes, or advanced proportional models.

Detailed Explanation: Interpret price per item as a rate

To find the price per item, divide the total cost by the number of items:

price per item=total costnumber of items\text{price per item}=\frac{\text{total cost}}{\text{number of items}}

The answer is a unit rate, such as dollars per notebook.

Example:
A pack of 4 notebooks costs 6.00.Anotherpackof6notebookscosts. Another pack of 6 notebooks costs $8.40$. Which pack has the lower price per notebook? How much would 10 notebooks cost at the lower rate?

Step 1: Find the price per notebook for each pack.

For the first pack:

$6.00÷4=$1.50\$6.00\div 4=\$1.50

The first pack costs 1.50$ per notebook.

For the second pack:

$8.40÷6=$1.40\$8.40\div 6=\$1.40

The second pack costs 1.40$ per notebook.

Step 2: Compare the unit prices.

Since 1.40islessthanis less than$1.50$, the second pack is the better buy. It has the lower price per notebook.

Step 3: Use the unit price to find the cost of 10 notebooks.

Multiply the price per notebook by the number of notebooks:

$1.40×10=$14.00\$1.40\times 10=\$14.00

So, at the lower rate, 10 notebooks cost 14.00$.

Remember: the total price is the cost of all the items, while the unit price is the cost of one item.

Learn by doing: Interpret price per item as a rate

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Ratios - Unit Rates, Find Best Price - Fractions


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