Solve Mixed Number Division: 2⅐ ÷ ⅝ Step-by-Step

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

Mixed numbers like $ 2\frac{1}{7} $ are harder to divide directly. Converting to $ \frac{15}{7} $ gives you one single fraction that's much easier to work with using the flip-and-multiply rule.

Q: How do I remember to flip the second fraction?

Think "Keep, Change, Flip": Keep the first fraction the same, change division to multiplication, flip the second fraction. So $ \frac{15}{7} \div \frac{5}{7} $ becomes $ \frac{15}{7} \times \frac{7}{5} $.

Q: What if both fractions have the same denominator like here?

Even when denominators are the same, you still must flip the second fraction! The denominators being equal makes the final simplification easier, but doesn't change the division process.

Q: How do I know when to simplify my answer?

Always check if your final fraction can be simplified. Here, $ \frac{105}{35} $ simplifies to 3 because both numbers divide by 35. If you get a whole number, you're done!

Q: Can I check my answer somehow?

Yes! Multiply your answer by the original divisor: $ 3 \times \frac{5}{7} = \frac{15}{7} = 2\frac{1}{7} $. This should equal your original dividend, confirming your answer is correct.

Mixed Number Division with Common Denominators

$2\frac{1}{7}:\frac{5}{7}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Convert a number and fraction to a fraction

00:19 Division equals multiplication by the reciprocal

00:29 Make sure to multiply numerator by numerator and denominator by denominator

00:35 Reduce what we can

00:41 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$2\frac{1}{7}:\frac{5}{7}=$

Step-by-step solution

To solve the problem $2\frac{1}{7} : \frac{5}{7}$ , we proceed as follows:

Step 1: Convert the mixed number $2\frac{1}{7}$ to an improper fraction.

To do this, multiply the whole number part by the denominator and add the numerator: $(2 \times 7) + 1 = 14 + 1 = 15$ . Therefore, $2\frac{1}{7} = \frac{15}{7}$ .

Step 2: Find the reciprocal of the fraction $\frac{5}{7}$ .

The reciprocal of $\frac{5}{7}$ is $\frac{7}{5}$ .

Step 3: Multiply $\frac{15}{7}$ by $\frac{7}{5}$ .

The multiplication is: $\frac{15}{7} \times \frac{7}{5} = \frac{15 \times 7}{7 \times 5} = \frac{105}{35}$ .

Step 4: Simplify $\frac{105}{35}$ .

To simplify, divide both the numerator and the denominator by their greatest common factor, which is 35: $\frac{105 \div 35}{35 \div 35} = \frac{3}{1} = 3$ .

Thus, the solution to the problem $2\frac{1}{7} : \frac{5}{7}$ is $3$ .

Final Answer

$3$

Key Points to Remember

Essential concepts to master this topic

Rule: Convert mixed numbers to improper fractions before dividing
Technique: Division becomes multiplication: $\frac{15}{7} \div \frac{5}{7} = \frac{15}{7} \times \frac{7}{5}$
Check: Multiply answer by divisor: $3 \times \frac{5}{7} = \frac{15}{7} = 2\frac{1}{7}$ ✓

Common Mistakes

Avoid these frequent errors

Dividing numerators and denominators separately
Don't divide $\frac{15}{7} \div \frac{5}{7}$ by doing 15÷5 and 7÷7 = $\frac{3}{1}$ directly! This skips the reciprocal step and only works by accident here. Always flip the second fraction and multiply: $\frac{15}{7} \times \frac{7}{5}$ .

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?

Mixed numbers like $2\frac{1}{7}$ are harder to divide directly. Converting to $\frac{15}{7}$ gives you one single fraction that's much easier to work with using the flip-and-multiply rule.

How do I remember to flip the second fraction?

Think "Keep, Change, Flip": Keep the first fraction the same, change division to multiplication, flip the second fraction. So $\frac{15}{7} \div \frac{5}{7}$ becomes $\frac{15}{7} \times \frac{7}{5}$ .

What if both fractions have the same denominator like here?

Even when denominators are the same, you still must flip the second fraction! The denominators being equal makes the final simplification easier, but doesn't change the division process.

How do I know when to simplify my answer?

Always check if your final fraction can be simplified. Here, $\frac{105}{35}$ simplifies to 3 because both numbers divide by 35. If you get a whole number, you're done!

Can I check my answer somehow?

Yes! Multiply your answer by the original divisor: $3 \times \frac{5}{7} = \frac{15}{7} = 2\frac{1}{7}$ . This should equal your original dividend, confirming your answer is correct.

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Solve Mixed Number Division: 2⅐ ÷ ⅝ Step-by-Step

Mixed Number Division with Common Denominators

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

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

How do I remember to flip the second fraction?

What if both fractions have the same denominator like here?

How do I know when to simplify my answer?

Can I check my answer somehow?

🌟 Unlock Your Math Potential

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