Solve: Multiplying 4 × 2/3 - Step-by-Step Solution

Whole Number and Fraction Multiplication

4×23= 4\times\frac{2}{3}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:04 Let's solve this problem.
00:08 First, move the multiplier to the top, the numerator.
00:12 Alright, let's do the multiplication.
00:15 Now, convert it into a mixed fraction.
00:18 Break down eight into six plus two.
00:23 Then, split the fraction into a whole number and a remainder.
00:30 Convert the improper fraction to a whole number, and mix them together for the mixed fraction.
00:42 And that's how you solve the problem! Well done!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

4×23= 4\times\frac{2}{3}=

2

Step-by-step solution

To solve this problem, we'll multiply the whole number 4 by the fraction 23 \frac{2}{3} as follows:

  • Step 1: Convert the whole number 4 into a fraction. This can be written as 41 \frac{4}{1} .
  • Step 2: Use fraction multiplication rules: multiply the numerators together and the denominators together.
  • Step 3: So, multiply the numerators: 4×2=8 4 \times 2 = 8 .
  • Step 4: Multiply the denominators: 1×3=3 1 \times 3 = 3 .
  • Step 5: The result is 83 \frac{8}{3} .
  • Step 6: Since 83 \frac{8}{3} is an improper fraction, convert it to a mixed number.
    8÷3=2 8 \div 3 = 2 with a remainder of 2.
    Thus, 83=223 \frac{8}{3} = 2\frac{2}{3} .

Therefore, the solution to the problem is 223 2\frac{2}{3} .

3

Final Answer

223 2\frac{2}{3}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Convert whole number to fraction form for easier multiplication
  • Technique: Write 4 as 41 \frac{4}{1} , then multiply: 41×23=83 \frac{4}{1} \times \frac{2}{3} = \frac{8}{3}
  • Check: Convert improper fraction to mixed number: 83=223 \frac{8}{3} = 2\frac{2}{3}

Common Mistakes

Avoid these frequent errors
  • Multiplying whole number by only the numerator
    Don't multiply 4 × 2 = 8 and ignore the denominator! This gives 8 instead of 223 2\frac{2}{3} . Always multiply the whole number by the entire fraction using proper fraction multiplication rules.

Practice Quiz

Test your knowledge with interactive questions

\( 4:\frac{6}{8}= \)

FAQ

Everything you need to know about this question

Why do I need to convert 4 to a fraction?

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Converting 4 to 41 \frac{4}{1} helps you use the standard fraction multiplication rule: multiply numerators together and denominators together. This keeps your work organized and reduces errors.

Can I just multiply 4 × 2 and keep the 3 as denominator?

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Yes, that's a shortcut! Since 4×23=4×23=83 4 \times \frac{2}{3} = \frac{4 \times 2}{3} = \frac{8}{3} . Both methods give the same answer, so use whichever feels more comfortable.

How do I know when to convert to a mixed number?

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Convert to a mixed number when the fraction is improper (numerator larger than denominator). For 83 \frac{8}{3} , since 8 > 3, convert it to 223 2\frac{2}{3} .

What if my answer comes out as a whole number?

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That's great! If there's no remainder when dividing, your answer is just a whole number. For example, 6×13=2 6 \times \frac{1}{3} = 2 with no fractional part.

Is there a faster way to multiply whole numbers and fractions?

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Yes! You can multiply the whole number by the numerator and keep the same denominator: 4×23=4×23=83 4 \times \frac{2}{3} = \frac{4 \times 2}{3} = \frac{8}{3} . This skips the conversion step!

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