Calculate 2/3 of 18: Finding White Balls in a Box

Fraction Multiplication with Whole Numbers

If there are 18 balls in a box of which 23 \frac{2}{3} are white:

How many white balls are there in the box in total?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Determine the number of white balls
00:04 In order to calculate the number of balls, multiply by the total amount
00:21 Break down into factors and reduce wherever possible
00:31 Here is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

If there are 18 balls in a box of which 23 \frac{2}{3} are white:

How many white balls are there in the box in total?

2

Step-by-step solution

To solve this problem, we will determine the number of white balls in the box using a fraction of the total number of balls.

We are given the total number of balls in the box as 18, and we know that 23 \frac{2}{3} of these balls are white. To find the number of white balls, we follow these steps:

  • Step 1: Identify the total quantity, which is 18 balls.
  • Step 2: Use the given fraction 23 \frac{2}{3} to find the number of white balls.
  • Step 3: Multiply the total number of balls by the fraction of white balls: 18×23 18 \times \frac{2}{3} .

Perform the calculation:

18×23=18×0.6667=12 18 \times \frac{2}{3} = 18 \times 0.6667 = 12

Alternatively, calculate directly using fractions:

18×23=18×23=363=12 18 \times \frac{2}{3} = \frac{18 \times 2}{3} = \frac{36}{3} = 12

Thus, the total number of white balls in the box is 12.

Therefore, the correct answer is choice 12.

3

Final Answer

12

Key Points to Remember

Essential concepts to master this topic
  • Rule: To find fraction of a number, multiply the number by the fraction
  • Technique: Calculate 18×23=18×23=363=12 18 \times \frac{2}{3} = \frac{18 \times 2}{3} = \frac{36}{3} = 12
  • Check: White balls (12) plus other balls should equal total balls (18) ✓

Common Mistakes

Avoid these frequent errors
  • Adding the fraction to the whole number instead of multiplying
    Don't add 18 + 2/3 = 18.67! This gives you more balls than the total, which is impossible. Always multiply the whole number by the fraction to find 'part of' a quantity.

Practice Quiz

Test your knowledge with interactive questions

Convert the fraction into a percentage:

\( \frac{2}{100}=\text{?} \)

FAQ

Everything you need to know about this question

Why do I multiply instead of divide when finding a fraction of something?

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When you see 'fraction of' something, it means multiply! Think of it as taking that portion. For example, 23 \frac{2}{3} of 18 means you take 2 parts out of every 3 parts.

How do I multiply a whole number by a fraction?

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Two ways: Method 1: Convert to decimal: 18×0.667=12 18 \times 0.667 = 12 . Method 2: Multiply numerator first: 18×23=18×23=363=12 18 \times \frac{2}{3} = \frac{18 \times 2}{3} = \frac{36}{3} = 12

What if my answer doesn't come out to a whole number?

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That's okay! Sometimes you get fractions or decimals as answers. In this problem, we got exactly 12 because 18 divides evenly by 3, but mixed numbers are valid answers too.

How can I check if 12 white balls makes sense?

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Use logic! If 23 \frac{2}{3} are white, then 13 \frac{1}{3} are other colors. Check: 13 \frac{1}{3} of 18 = 6 other balls. Total: 12 + 6 = 18 ✓

Why is 2/3 of 18 the same as 18 × 2/3?

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The word 'of' in math means multiply! It's like saying '2 parts out of every 3 parts of 18'. Both expressions give you the same calculation and the same answer.

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