Solve Fraction Division: 2/3 ÷ 3/8 Step-by-Step

Fraction Division with Reciprocal Method

Complete the following exercise:

23:38=? \frac{2}{3}:\frac{3}{8}=\text{?}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 Instead of division, we'll use multiplication by the reciprocal
00:09 We'll switch between the numerator and denominator of the fraction
00:15 Make sure to multiply numerator by numerator and denominator by denominator
00:22 Let's calculate the products
00:28 Break down 16 into 9 plus 7
00:35 Break down the fraction into a whole number and remainder
00:41 Any number divided by itself always equals 1
00:47 Convert to a mixed fraction
00:50 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Complete the following exercise:

23:38=? \frac{2}{3}:\frac{3}{8}=\text{?}

2

Step-by-step solution

To solve the division of fractions 23\frac{2}{3} by 38\frac{3}{8}, we follow these steps:

  • Step 1: Identify the reciprocal of the second fraction 38\frac{3}{8}. The reciprocal is 83\frac{8}{3}.

  • Step 2: Multiply the first fraction 23\frac{2}{3} by the reciprocal 83\frac{8}{3}:

23×83\frac{2}{3} \times \frac{8}{3}

  • Step 3: Multiply the numerators together and the denominators together:

2×83×3=169\frac{2 \times 8}{3 \times 3} = \frac{16}{9}

  • Step 4: Simplify the resulting fraction, if possible. In this case, 169\frac{16}{9} is already in its simplest form.

  • Step 5: Convert the improper fraction 169\frac{16}{9} to a mixed number:

16÷9=116 \div 9 = 1 remainder 77, so the mixed number is 1791\frac{7}{9}.

Therefore, the solution to the problem is 179 {1\frac{7}{9}} .

3

Final Answer

179 1\frac{7}{9}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Division by a fraction equals multiplication by its reciprocal
  • Technique: Flip 38 \frac{3}{8} to 83 \frac{8}{3} , then multiply: 23×83=169 \frac{2}{3} \times \frac{8}{3} = \frac{16}{9}
  • Check: Convert 179 1\frac{7}{9} back to improper: 169 \frac{16}{9}

Common Mistakes

Avoid these frequent errors
  • Multiplying the fractions directly without finding reciprocal
    Don't multiply 23×38=624 \frac{2}{3} \times \frac{3}{8} = \frac{6}{24} = 14 \frac{1}{4} ! This treats division like multiplication and gives the wrong answer. Always flip the second fraction first, then multiply.

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?

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Dividing by a fraction is the same as multiplying by its reciprocal. Think of it as: "How many 38 \frac{3}{8} 's fit into 23 \frac{2}{3} ?" Flipping makes this calculation possible!

What's a reciprocal exactly?

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A reciprocal is when you flip the numerator and denominator. For 38 \frac{3}{8} , the reciprocal is 83 \frac{8}{3} . When you multiply a fraction by its reciprocal, you always get 1!

Do I always get a mixed number as the answer?

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Not always! If your improper fraction's numerator is smaller than the denominator, it's already a proper fraction. Only convert to mixed numbers when the numerator is larger than the denominator.

How do I convert 169 \frac{16}{9} to a mixed number?

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Divide the numerator by the denominator: 16 ÷ 9 = 1 remainder 7. The quotient (1) becomes the whole number, the remainder (7) stays as the numerator, and 9 stays as the denominator: 179 1\frac{7}{9} .

Can I simplify before multiplying?

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Absolutely! Look for common factors you can cancel. In this problem, you could cancel the 3's: 23×83 \frac{2}{3} \times \frac{8}{3} , but since there are no matching factors between numerator and denominator, we multiply straight across.

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