Solve Mixed Number Division: 2 2/7 ÷ 3/4 Step by Step

Mixed Number Division with Reciprocal Method

227:34= 2\frac{2}{7}:\frac{3}{4}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:05 Let's solve this problem step by step.
00:09 First, let's change the mixed number to a fraction.
00:14 Calculate the new numerator. Then, put it back into the equation.
00:27 Now, change division to multiplication by flipping the second fraction.
00:37 Multiply the numerators together, and then multiply the denominators.
00:42 Great! Let's calculate these products.
00:46 Next, convert the fraction back to a mixed number.
00:50 Break 64 into 63 plus 1 for easier conversion.
00:58 Separate the fraction into a whole number and remainder.
01:04 Combine everything into a single mixed number.
01:10 And there you have it! That's the solution to our problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

227:34= 2\frac{2}{7}:\frac{3}{4}=

2

Step-by-step solution

To solve the division problem 227:342\frac{2}{7}:\frac{3}{4}, follow these steps:

  • Convert the mixed number to an improper fraction:

2272\frac{2}{7} can be rewritten as 2×7+27=14+27=167\frac{2 \times 7 + 2}{7} = \frac{14 + 2}{7} = \frac{16}{7}.

  • Rewrite the division as multiplication by the reciprocal:

Instead of dividing by 34\frac{3}{4}, multiply by its reciprocal: 167×43\frac{16}{7} \times \frac{4}{3}.

  • Perform the multiplication:

Calculate: 16×47×3=6421\frac{16 \times 4}{7 \times 3} = \frac{64}{21}.

  • Convert the improper fraction to a mixed number.

Divide 64 by 21: the quotient is 3 and the remainder is 1, giving us the mixed number:

  • 64÷21=364 \div 21 = 3 remainder 11.
  • The mixed number is 31213\frac{1}{21}.

Therefore, the result of 227÷342\frac{2}{7} \div \frac{3}{4} is 3121\boxed{3\frac{1}{21}}.

3

Final Answer

3121 3\frac{1}{21}

Key Points to Remember

Essential concepts to master this topic
  • Conversion: Change mixed number to improper fraction first
  • Technique: Multiply by reciprocal: 167×43=6421 \frac{16}{7} \times \frac{4}{3} = \frac{64}{21}
  • Check: Convert back to mixed: 64 ÷ 21 = 3 remainder 1 = 3121 3\frac{1}{21} ✓

Common Mistakes

Avoid these frequent errors
  • Dividing the fractions directly without using reciprocal
    Don't try to divide 167÷34 \frac{16}{7} \div \frac{3}{4} by dividing numerators and denominators separately = completely wrong method! Division of fractions requires multiplication by the reciprocal. Always flip the second fraction and multiply: 167×43 \frac{16}{7} \times \frac{4}{3} .

Practice Quiz

Test your knowledge with interactive questions

\( \frac{1}{2}:4= \)

FAQ

Everything you need to know about this question

Why do I need to convert the mixed number to an improper fraction first?

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Mixed numbers like 227 2\frac{2}{7} can't be divided directly. Converting to improper fraction 167 \frac{16}{7} gives you one fraction that's easier to work with in division problems.

How do I remember to flip the second fraction?

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Think "Keep, Change, Flip"! Keep the first fraction the same, change division to multiplication, and flip (find reciprocal of) the second fraction.

What if I get a really big improper fraction like 64/21?

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No problem! Just divide the numerator by denominator: 64 ÷ 21 = 3 with remainder 1. So 6421=3121 \frac{64}{21} = 3\frac{1}{21} .

Can I simplify before multiplying?

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Yes, absolutely! Look for common factors you can cancel first. For example, 16 and 4 have a common factor of 4, which makes the multiplication easier.

How do I check if my final mixed number is correct?

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Convert your answer back to improper fraction and multiply by the divisor. You should get the original dividend: 3121×34=6421×34=167=227 3\frac{1}{21} \times \frac{3}{4} = \frac{64}{21} \times \frac{3}{4} = \frac{16}{7} = 2\frac{2}{7} ✓

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