Calculate Total Boxes: Multiply 6½ Average by 10 Shelves

Q: Should I convert the mixed number to a decimal or improper fraction?

Either method works perfectly! Decimal method: $ 6\frac{1}{2} = 6.5 $, so 6.5 × 10 = 65. Fraction method: $ 6\frac{1}{2} = \frac{13}{2} $, so $ \frac{13}{2} \times 10 = \frac{130}{2} = 65 $.

Q: Why can't I just multiply 6 × 10 and add something later?

Because you'd be ignoring half a box on each shelf! With 10 shelves, that's 5 whole boxes you're missing. You must include the fractional part in your multiplication.

Q: How do I convert a mixed number to a decimal quickly?

Take the fraction part and divide: $ \frac{1}{2} = 1 \div 2 = 0.5 $. Then add to the whole number: 6 + 0.5 = 6.5. Easy!

Q: What does 'average' mean in this problem?

Average means the typical number per shelf. If you added up all boxes and divided by 10 shelves, you'd get $ 6\frac{1}{2} $ boxes per shelf on average.

Q: How can I check if 65 is the right answer?

Divide your answer by the number of shelves: 65 ÷ 10 = 6.5. Since 6.5 = $ 6\frac{1}{2} $, this matches the given average perfectly!

Mixed Number Multiplication with Total Calculation

In the warehouse there are 10 shelves.

If the average number of boxes on each shelf is $6\frac{1}{2}$ , then how many boxes are there in the warehouse in total?

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

In the warehouse there are 10 shelves.

If the average number of boxes on each shelf is $6\frac{1}{2}$ , then how many boxes are there in the warehouse in total?

Step-by-step solution

To solve this problem, we will follow a series of logical steps:

Step 1: Identify the given information
Step 2: Convert the mixed number to a decimal or improper fraction
Step 3: Use the appropriate formula to calculate the total number of boxes

Let's work through these steps:

Step 1: We know there are 10 shelves and the average number of boxes per shelf is $6\frac{1}{2}$ .

Step 2: Convert $6\frac{1}{2}$ to an improper fraction or decimal for calculation. As an improper fraction, it becomes $\frac{13}{2}$ , and as a decimal, it is $6.5$ .

Step 3: Using the formula:

\text{Total number of boxes} = \text{Average} \times \text{Number of shelves}

Substituting the values, we get:

\text{Total number of boxes} = 6.5 \times 10

Perform the multiplication:

6.5 \times 10 = 65

Therefore, the total number of boxes in the warehouse is $65$ .

Final Answer

$65$

Key Points to Remember

Essential concepts to master this topic

Rule: Convert mixed numbers to decimals or improper fractions first
Technique: $6\frac{1}{2}$ becomes 6.5, then multiply: 6.5 × 10 = 65
Check: Verify by division: 65 ÷ 10 = 6.5 = $6\frac{1}{2}$ ✓

Common Mistakes

Avoid these frequent errors

Multiplying only the whole number part
Don't multiply just 6 × 10 = 60 and ignore the fraction! This misses half a box per shelf, giving you 5 fewer boxes total. Always convert the entire mixed number to decimal (6.5) or improper fraction first.

Practice Quiz

Test your knowledge with interactive questions

Calculate the average of $$ 10 $$ and $$ 12 $$ .

FAQ

Everything you need to know about this question

Should I convert the mixed number to a decimal or improper fraction?

Either method works perfectly! Decimal method: $6\frac{1}{2} = 6.5$ , so 6.5 × 10 = 65. Fraction method: $6\frac{1}{2} = \frac{13}{2}$ , so $\frac{13}{2} \times 10 = \frac{130}{2} = 65$ .

Why can't I just multiply 6 × 10 and add something later?

Because you'd be ignoring half a box on each shelf! With 10 shelves, that's 5 whole boxes you're missing. You must include the fractional part in your multiplication.

How do I convert a mixed number to a decimal quickly?

Take the fraction part and divide: $\frac{1}{2} = 1 \div 2 = 0.5$ . Then add to the whole number: 6 + 0.5 = 6.5. Easy!

What does 'average' mean in this problem?

Average means the typical number per shelf. If you added up all boxes and divided by 10 shelves, you'd get $6\frac{1}{2}$ boxes per shelf on average.

How can I check if 65 is the right answer?

Divide your answer by the number of shelves: 65 ÷ 10 = 6.5. Since 6.5 = $6\frac{1}{2}$ , this matches the given average perfectly!

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