Solve: Dividing 2⅝ by ⅘ - Mixed Number and Fraction Division

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

Converting makes division much easier! Working with improper fractions like $ \frac{19}{7} $ lets you use the simple rule: multiply by the reciprocal. Mixed numbers make this rule harder to apply.

Q: How do I find the reciprocal of a fraction?

Just flip the fraction! The reciprocal of $ \frac{4}{5} $ is $ \frac{5}{4} $. The numerator becomes the denominator and vice versa.

Q: Do I always need to convert my final answer to a mixed number?

Not always, but it's often preferred for answers greater than 1. Mixed numbers like $ 3\frac{11}{28} $ are easier to understand than improper fractions like $ \frac{95}{28} $.

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

Divide the numerator by the denominator: For $ \frac{95}{28} $, divide 95 ÷ 28 = 3 remainder 11, so the answer is $ 3\frac{11}{28} $.

Q: Can I simplify the fraction before converting to mixed number?

Yes, always check! But $ \frac{95}{28} $ is already in lowest terms since 95 and 28 share no common factors other than 1.

Mixed Number Division with Fraction Reciprocals

$2\frac{5}{7}:\frac{4}{5}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:06 Convert from number and fraction to fraction

00:18 Division equals multiplication by reciprocal

00:30 Make sure to multiply numerator by numerator and denominator by denominator

00:41 Break down 95 into 84 and 11

00:49 Break down the fraction into whole number and remainder

00:54 Convert from whole fraction to whole number

01:00 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

$2\frac{5}{7}:\frac{4}{5}=$

Step-by-step solution

To solve the problem of dividing the mixed number $2\frac{5}{7}$ by the fraction $\frac{4}{5}$ , we will follow the outlined steps:

Step 1: Convert the mixed number to an improper fraction.

For $2\frac{5}{7}$ : Multiply the whole number $2$ by the denominator $7$ , giving $2 \times 7 = 14$ .
Add the numerator $5$ to this result, giving $14 + 5 = 19$ . Thus, $2\frac{5}{7} = \frac{19}{7}$ .

Step 2: Divide the improper fraction by $\frac{4}{5}$ by multiplying by the reciprocal of $\frac{4}{5}$ , which is $\frac{5}{4}$ .

Perform the multiplication: $\frac{19}{7} \times \frac{5}{4} = \frac{19 \times 5}{7 \times 4} = \frac{95}{28}$ .

Step 3: Convert the result back to a mixed number if needed.

Divide $95$ by $28$ to find the whole part; $28$ goes into $95$ three times, with a remainder.
The remainder is $95 - (28 \times 3) = 95 - 84 = 11$ .
Therefore, $\frac{95}{28}$ is written as the mixed number $3\frac{11}{28}$ .

Therefore, the solution is $3\frac{11}{28}$ .

Final Answer

$3\frac{11}{28}$

Key Points to Remember

Essential concepts to master this topic

Conversion: Change mixed numbers to improper fractions first
Division Rule: Multiply by reciprocal: $\frac{19}{7} \times \frac{5}{4} = \frac{95}{28}$
Check: Convert back to mixed number and verify calculation ✓

Common Mistakes

Avoid these frequent errors

Trying to divide mixed numbers directly without conversion
Don't divide $2\frac{5}{7} \div \frac{4}{5}$ directly = confusing mess! This makes the problem unnecessarily complicated and leads to errors. Always convert mixed numbers to improper fractions first, then divide by multiplying with the reciprocal.

Practice Quiz

Test your knowledge with interactive questions

$\frac{1}{2}:3=$ $$ $$ $$

FAQ

Everything you need to know about this question

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

Converting makes division much easier! Working with improper fractions like $\frac{19}{7}$ lets you use the simple rule: multiply by the reciprocal. Mixed numbers make this rule harder to apply.

How do I find the reciprocal of a fraction?

Just flip the fraction! The reciprocal of $\frac{4}{5}$ is $\frac{5}{4}$ . The numerator becomes the denominator and vice versa.

Do I always need to convert my final answer to a mixed number?

Not always, but it's often preferred for answers greater than 1. Mixed numbers like $3\frac{11}{28}$ are easier to understand than improper fractions like $\frac{95}{28}$ .

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

Divide the numerator by the denominator: For $\frac{95}{28}$ , divide 95 ÷ 28 = 3 remainder 11, so the answer is $3\frac{11}{28}$ .

Can I simplify the fraction before converting to mixed number?

Yes, always check! But $\frac{95}{28}$ is already in lowest terms since 95 and 28 share no common factors other than 1.

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