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

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A recipe calls for 400g of flour and 200g of sugar. What is the ratio of flour to sugar in the recipe?

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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