Solve Fraction Division: 2/4 ÷ 1/3 Step-by-Step

Fraction Division with Reciprocal Method

Complete the following exercise:

24:13=? \frac{2}{4}:\frac{1}{3}=\text{?}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:07 Let's solve this step by step.
00:10 Instead of dividing, we'll multiply by the reciprocal. That means flipping the fraction.
00:16 We switch the numerator and the denominator.
00:23 Now, multiply the numerators together, and then the denominators.
00:29 Next, calculate those multiplications.
00:36 Let's break down six into four plus two.
00:40 Now, simplify the fraction into a whole number and remainder.
00:45 Remember, any number divided by itself equals one.
00:50 Try to reduce the fraction as much as you can.
00:53 Be sure to divide both numbers, the top and bottom.
00:59 Then, calculate each portion carefully.
01:02 Convert your result to a mixed fraction if needed.
01:07 And that's our final solution. Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Complete the following exercise:

24:13=? \frac{2}{4}:\frac{1}{3}=\text{?}

2

Step-by-step solution

To solve this problem, let's follow these steps:

  • Step 1: Simplify the fraction 24 \frac{2}{4} .
  • Step 2: Find the reciprocal of 13 \frac{1}{3} .
  • Step 3: Multiply the simplified fraction by the reciprocal.
  • Step 4: Simplify the resulting fraction if needed.

Now, let's work through each step:
Step 1: Simplify 24 \frac{2}{4} to 12 \frac{1}{2} by dividing both the numerator and the denominator by 2.
Step 2: The reciprocal of 13 \frac{1}{3} is 31 \frac{3}{1} .
Step 3: Multiply 12×31 \frac{1}{2} \times \frac{3}{1} . This gives us 1×32×1=32 \frac{1 \times 3}{2 \times 1} = \frac{3}{2} .
Step 4: 32 \frac{3}{2} is an improper fraction. Convert it to a mixed number, 112 1\frac{1}{2} .

Therefore, the solution to the division 24:13 \frac{2}{4}:\frac{1}{3} is 112 1\frac{1}{2} .

3

Final Answer

112 1\frac{1}{2}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Division by a fraction equals multiplication by its reciprocal
  • Technique: 24÷13=12×31=32 \frac{2}{4} ÷ \frac{1}{3} = \frac{1}{2} × \frac{3}{1} = \frac{3}{2}
  • Check: Convert improper fraction to mixed number: 32=112 \frac{3}{2} = 1\frac{1}{2}

Common Mistakes

Avoid these frequent errors
  • Dividing numerators and denominators directly
    Don't divide 24÷13 \frac{2}{4} ÷ \frac{1}{3} as 2÷14÷3=2113 \frac{2÷1}{4÷3} = \frac{2}{1\frac{1}{3}} = messy decimal! This creates complex fractions and wrong answers. Always flip the second fraction and multiply instead.

Practice Quiz

Test your knowledge with interactive questions

\( \frac{1}{3}+\frac{1}{4}= \)

FAQ

Everything you need to know about this question

Why do I flip the second fraction and multiply?

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Division by a fraction is the same as multiplying by its reciprocal. Think of it this way: "How many 13 \frac{1}{3} 's fit into 12 \frac{1}{2} ?" means 12×3 \frac{1}{2} × 3 !

What's a reciprocal and how do I find it?

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A reciprocal is a fraction flipped upside down. For 13 \frac{1}{3} , the reciprocal is 31 \frac{3}{1} . For whole numbers like 5, write it as 51 \frac{5}{1} first, then flip to get 15 \frac{1}{5} .

Should I simplify fractions before or after dividing?

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It's usually easier to simplify first! In this problem, 24 \frac{2}{4} simplifies to 12 \frac{1}{2} , making the multiplication simpler: 12×31 \frac{1}{2} × \frac{3}{1} .

How do I convert an improper fraction to a mixed number?

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Divide the numerator by the denominator. For 32 \frac{3}{2} : 3 ÷ 2 = 1 remainder 1, so the answer is 112 1\frac{1}{2} .

Can I leave my answer as an improper fraction?

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Both forms are correct! 32 \frac{3}{2} and 112 1\frac{1}{2} represent the same value. Check what format your teacher prefers - many prefer mixed numbers for final answers.

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