Visual Division Problem: Calculate Equal Column Distribution of Balls

Q: How do I count the balls when they're scattered around?

Look at the entire diagram carefully and count each red ball one by one. Don't worry about where they are now - just focus on getting the total count correct first.

Q: Do I need to actually move the balls to solve this?

No! This is a calculation problem. You just need to figure out mathematically how many balls each column should have for equal distribution.

Q: How can I be sure I counted the columns correctly?

Look for the vertical lines that separate the grid into sections. Count the spaces between these lines - those are your columns. The grid should show 5 columns total.

Q: What does 'equal distribution' actually mean?

Equal distribution means every column gets exactly the same number of balls. So if one column has 2 balls, all columns must have 2 balls.

Equal Distribution with Visual Division

If the balls below are divided so that each column in the table contains an equal number, then how many balls will each column contain?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:07 Let's divide the balls so each column has the same number.

00:11 We'll move each ball, one by one following the diagram. Ready?

00:23 Next, let's solve this using math and averages. Sounds good?

00:29 We'll add up all the balls, then divide by the number of columns. Easy peasy!

00:45 And that's how we find the solution. Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

If the balls below are divided so that each column in the table contains an equal number, then how many balls will each column contain?

Step-by-step solution

To solve this problem, we'll proceed through these steps:

Step 1: Count the total number of balls.
Step 2: Count the number of columns in the table.
Step 3: Divide the total number of balls by the number of columns.

Let's solve the problem:

Step 1: Count the total number of balls.
Upon examining the diagram, we see there are 10 balls represented.

Step 2: Count the number of columns.
From the diagram, there are 5 columns.

Step 3: Divide the total number of balls by the number of columns to find the exact number per column:
$\text{Number of balls per column} = \frac{10}{5} = 2$

Thus, the solution to the problem is that each column will contain 2 balls.

This solution matches the correct answer provided in the question's answer choices.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Division Rule: Total items divided by number of groups equals items per group
Technique: Count all balls (10) ÷ count all columns (5) = 2 balls per column
Check: Multiply back: 2 balls × 5 columns = 10 total balls ✓

Common Mistakes

Avoid these frequent errors

Counting only visible balls in current arrangement
Don't count just the balls already placed in columns = incomplete total! This ignores balls that need to be redistributed and gives wrong results. Always count all balls shown in the entire diagram first.

Practice Quiz

Test your knowledge with interactive questions

If the balls below are divided so that each column in the table contains an equal number, then how many balls will there be in each column?

FAQ

Everything you need to know about this question

How do I count the balls when they're scattered around?

Look at the entire diagram carefully and count each red ball one by one. Don't worry about where they are now - just focus on getting the total count correct first.

What if the balls don't divide evenly into the columns?

In this problem, 10 ÷ 5 = 2 exactly! But if you get a remainder in other problems, that means equal distribution isn't possible with whole balls.

Do I need to actually move the balls to solve this?

No! This is a calculation problem. You just need to figure out mathematically how many balls each column should have for equal distribution.

How can I be sure I counted the columns correctly?

Look for the vertical lines that separate the grid into sections. Count the spaces between these lines - those are your columns. The grid should show 5 columns total.

What does 'equal distribution' actually mean?

Equal distribution means every column gets exactly the same number of balls. So if one column has 2 balls, all columns must have 2 balls.

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