Solve Mixed Number Division: 6⅞ ÷ 6½ Step-by-Step

Q: Why can't I just divide the whole numbers and fractions separately?

Mixed numbers represent one value, not separate parts! Dividing 6 by 6 and ⅞ by ½ separately gives wrong results. You must convert to improper fractions first to get the correct answer.

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

Use the formula: improper fraction = (whole × denominator + numerator)/denominator. For $ 6\frac{8}{9} $: (6×9+8)/9 = 62/9.

Q: Why do I flip the second fraction when dividing?

Division by a fraction means multiplying by its reciprocal. So $ \div \frac{13}{2} $ becomes $ \times \frac{2}{13} $. This is a fundamental rule of fraction division!

Q: Should I simplify my answer?

Always check if your answer can be simplified! Look for common factors in the numerator and denominator. In this case, $ \frac{124}{117} $ cannot be simplified further.

Q: What if my answer is greater than 1?

That's normal when dividing similar-sized numbers! $ \frac{124}{117} $ is slightly greater than 1 because 6⅞ is slightly larger than 6½.

Mixed Number Division with Improper Fractions

$(+6\frac{8}{9}):(+6\frac{1}{2})=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solution

00:03 Positive divided by positive is always positive

00:13 Convert mixed numbers to fractions

00:41 Write division as multiplication by reciprocal

00:46 Swap between numerator and denominator

00:54 Make sure to multiply numerator by numerator and denominator by denominator

01:13 Break down the denominator into 2 products to help with calculation

01:21 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

$(+6\frac{8}{9}):(+6\frac{1}{2})=$

Step-by-step solution

Since we are dividing two positive numbers, the result must be a positive number:

$+:+=+$

First, let's convert each mixed number to an improper fraction as follows:

$6\frac{8}{9}=\frac{6\times9+8}{9}=\frac{54+8}{9}=\frac{62}{9}$

$6\frac{1}{2}=\frac{6\times2+1}{2}=\frac{12+1}{2}=\frac{13}{2}$

Now we have the problem:

$\frac{62}{9}:\frac{13}{2}=$

Let's convert the division to multiplication, and don't forget to swap the numerator and denominator:

$\frac{62}{9}\times\frac{2}{13}=$

Let's combine everything into one problem:

$\frac{62\times2}{9\times13}=$

Let's solve the multiplication in the numerator, and factor the denominator into an addition problem as follows:

$\frac{124}{9\times10+9\times3}=$

Let's solve the multiplication problems in the denominator:

$\frac{124}{90+27}=$

Let's combine the denominator and we get:

$\frac{124}{117}$

Final Answer

$\frac{124}{117}$

Key Points to Remember

Essential concepts to master this topic

Rule: Convert mixed numbers to improper fractions before dividing
Technique: Change division to multiplication: $\frac{62}{9} \div \frac{13}{2} = \frac{62}{9} \times \frac{2}{13}$
Check: Multiply answer by divisor: $\frac{124}{117} \times \frac{13}{2} = \frac{62}{9}$ ✓

Common Mistakes

Avoid these frequent errors

Dividing mixed numbers without converting to improper fractions
Don't divide 6⅞ by 6½ directly = wrong process and answer! Mixed numbers must be converted first because division requires single fractions. Always convert to improper fractions: 6⅞ = 62/9 and 6½ = 13/2, then divide.

Practice Quiz

Test your knowledge with interactive questions

Convert $\frac{7}{2}$ into its reciprocal form:

FAQ

Everything you need to know about this question

Why can't I just divide the whole numbers and fractions separately?

Mixed numbers represent one value, not separate parts! Dividing 6 by 6 and ⅞ by ½ separately gives wrong results. You must convert to improper fractions first to get the correct answer.

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

Use the formula: improper fraction = (whole × denominator + numerator)/denominator. For $6\frac{8}{9}$ : (6×9+8)/9 = 62/9.

Why do I flip the second fraction when dividing?

Division by a fraction means multiplying by its reciprocal. So $\div \frac{13}{2}$ becomes $\times \frac{2}{13}$ . This is a fundamental rule of fraction division!

Should I simplify my answer?

Always check if your answer can be simplified! Look for common factors in the numerator and denominator. In this case, $\frac{124}{117}$ cannot be simplified further.

How can I check if my division is correct?

Multiply your answer by the divisor - you should get the dividend! $\frac{124}{117} \times \frac{13}{2} = \frac{62}{9}$ ✓

What if my answer is greater than 1?

That's normal when dividing similar-sized numbers! $\frac{124}{117}$ is slightly greater than 1 because 6⅞ is slightly larger than 6½.

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