Solve Mixed Number Division: 3 2/5 ÷ 6 3/7 Step-by-Step

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

Because mixed numbers represent one combined value! Dividing $ 3\frac{2}{5} $ means you're dividing all of it, not just the parts. Converting to improper fractions like $ \frac{17}{5} $ shows the true total value.

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

Formula: Multiply whole number by denominator, then add numerator. For $ 3\frac{2}{5} $: (3 × 5) + 2 = 17, so it becomes $ \frac{17}{5} $.

Q: What's the reciprocal and why do I flip it?

The reciprocal flips the numerator and denominator. For $ \frac{45}{7} $, the reciprocal is $ \frac{7}{45} $. Division by a fraction equals multiplication by its reciprocal - this is a fundamental rule!

Q: How do I know if my final fraction is simplified?

Check if the numerator and denominator share any common factors. For $ \frac{119}{225} $, since 119 and 225 have no common factors besides 1, it's already simplified.

Q: Can I leave my answer as a mixed number instead?

You can convert $ \frac{119}{225} $ back to a mixed number, but since the numerator (119) is smaller than the denominator (225), it would just be $ 0\frac{119}{225} $, so the improper fraction is cleaner!

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

Solve the following:

$3\frac{2}{5}:6\frac{3}{7}=$

2

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Convert the mixed numbers into improper fractions.
Step 2: Multiply by the reciprocal of the second fraction.
Step 3: Simplify the resulting fraction.

Now, let's work through each step:

Step 1: Conversion to improper fractions.
For the mixed number $3\frac{2}{5}$ :

Convert to an improper fraction: $3\frac{2}{5} = \frac{3 \times 5 + 2}{5} = \frac{17}{5}$

For the mixed number $6\frac{3}{7}$ :

Convert to an improper fraction: $6\frac{3}{7} = \frac{6 \times 7 + 3}{7} = \frac{45}{7}$

Step 2: Division using multiplication by the reciprocal.
Instead of dividing $\frac{17}{5}$ by $\frac{45}{7}$ , multiply by the reciprocal of $\frac{45}{7}$ :

\frac{17}{5} \div \frac{45}{7} = \frac{17}{5} \times \frac{7}{45}

Multiply the numerators and denominators:

= \frac{17 \times 7}{5 \times 45} = \frac{119}{225}

Step 3: Simplification of the fraction.
The fraction $\frac{119}{225}$ is already in its simplest form, as $119$ and $225$ have no common factors greater than 1.

Therefore, the solution to the problem is $\frac{119}{225}$ .

3

Final Answer

$\frac{119}{225}$

Key Points to Remember

Essential concepts to master this topic

Conversion: Change mixed numbers to improper fractions first
Division Rule: Multiply by reciprocal: $\frac{17}{5} \times \frac{7}{45} = \frac{119}{225}$
Check: Verify answer is in simplest form by finding GCD ✓

Common Mistakes

Avoid these frequent errors

Trying to divide mixed numbers directly
Don't divide $3\frac{2}{5} \div 6\frac{3}{7}$ without converting first = confusing mess! Mixed numbers can't be divided directly because the whole and fractional parts interfere with each other. Always convert to improper fractions first, then use the reciprocal method.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

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

+

Because mixed numbers represent one combined value! Dividing $3\frac{2}{5}$ means you're dividing all of it, not just the parts. Converting to improper fractions like $\frac{17}{5}$ shows the true total value.

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

+

Formula: Multiply whole number by denominator, then add numerator. For $3\frac{2}{5}$ : (3 × 5) + 2 = 17, so it becomes $\frac{17}{5}$ .

What's the reciprocal and why do I flip it?

+

The reciprocal flips the numerator and denominator. For $\frac{45}{7}$ , the reciprocal is $\frac{7}{45}$ . Division by a fraction equals multiplication by its reciprocal - this is a fundamental rule!

How do I know if my final fraction is simplified?

+

Check if the numerator and denominator share any common factors. For $\frac{119}{225}$ , since 119 and 225 have no common factors besides 1, it's already simplified.

Can I leave my answer as a mixed number instead?

+

You can convert $\frac{119}{225}$ back to a mixed number, but since the numerator (119) is smaller than the denominator (225), it would just be $0\frac{119}{225}$ , so the improper fraction is cleaner!

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