Calculate Unit Price: Finding Cost per Pencil in $2.5 ÷ 5 Problem

Division Word Problems with Decimal Fractions

Robert bought 5 pencils, paying $2.5 at the checkout.

How much did each pencil cost?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the price of each pencil
00:03 Number of pencils according to the data
00:06 The total price paid
00:09 Let's mark the price of one pencil with unknown X
00:12 Multiply the number of pencils by their price and equate to total price
00:15 Isolate the unknown X
00:19 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Robert bought 5 pencils, paying $2.5 at the checkout.

How much did each pencil cost?

2

Step-by-step solution

To solve this problem, we'll calculate the cost per pencil as follows:

Robert bought 5 pencils for a total of $2.5 \$2.5 . We need to find the cost of each pencil by dividing the total cost by the number of pencils:

  • Total cost = $2.5 \$2.5
  • Number of pencils = 5
  • Cost per pencil = Total cost / Number of pencils

Perform the calculation:

Cost per pencil=2.55 \text{Cost per pencil} = \frac{2.5}{5}

Calculating 2.55\frac{2.5}{5}, we convert 2.5 to a fraction: 52\frac{5}{2}. So, the division becomes:

52÷5=52×15=510=12 \frac{5}{2} \div 5 = \frac{5}{2} \times \frac{1}{5} = \frac{5}{10} = \frac{1}{2}

Therefore, each pencil cost $0.5\$0.5 or 12 \frac{1}{2} dollar.

The correct choice reflecting this calculation is: 12 \frac{1}{2} .

This confirms with the provided correct answer.

The solution to the problem is that each pencil cost 12\frac{1}{2} dollar.

3

Final Answer

12 \frac{1}{2}

Key Points to Remember

Essential concepts to master this topic
  • Division Rule: Total cost ÷ number of items = unit price
  • Technique: Convert 2.5÷5=52÷5=12 2.5 ÷ 5 = \frac{5}{2} ÷ 5 = \frac{1}{2}
  • Check: Multiply back: 5×12=2.5 5 × \frac{1}{2} = 2.5

Common Mistakes

Avoid these frequent errors
  • Adding instead of dividing total cost and quantity
    Don't add $2.5 + 5 = $7.5! This gives the wrong operation and makes no sense for finding unit price. Always divide total cost by number of items to find cost per item.

Practice Quiz

Test your knowledge with interactive questions

Robert bought 5 pencils, paying $2.5 at the checkout.

How much did each pencil cost?

FAQ

Everything you need to know about this question

Why do I divide instead of multiply?

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Think about it logically: if 5 pencils cost $2.50 total, each pencil must cost less than the total. Division splits the total cost equally among all items.

Should my answer be in decimal or fraction form?

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Both 12 \frac{1}{2} and $0.50 are correct! The question asks for fractions, so fraction form is preferred. Always match the format requested.

How do I convert 2.5 to a fraction?

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Remember: 2.5 = 2 and 5 tenths = 212=52 2\frac{1}{2} = \frac{5}{2} . This makes the division easier: 52÷5 \frac{5}{2} ÷ 5

What does 'unit price' actually mean?

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Unit price means the cost of one single item. It helps you compare prices and understand how much you pay for each individual thing you buy.

How can I check if my answer makes sense?

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  • Multiply your answer by 5: 5×12=2.5 5 × \frac{1}{2} = 2.5
  • Ask yourself: Is $0.50 per pencil reasonable? Yes!

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