Solve: Division of Mixed Numbers 5 4/5 ÷ 2 1/10

Q: Why do I need to convert mixed numbers to improper fractions first?

Mixed numbers like $ 5\frac{4}{5} $ can't be divided directly! Converting to improper fractions like $ \frac{29}{5} $ gives you single fractions that follow division rules.

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

Think "dividing by a fraction means multiplying by its flip!" So $ ÷ \frac{21}{10} $ becomes $ \times \frac{10}{21} $. The reciprocal flips numerator and denominator.

Q: Do I always need to simplify the final answer?

Yes! Always check if your fraction can be simplified. Find the GCD of numerator and denominator. Here, $ \frac{290}{105} $ simplifies to $ \frac{58}{21} $ by dividing both by 5.

Q: How do I convert improper fractions back to mixed numbers?

Divide the numerator by denominator: $ 58 ÷ 21 = 2 $ remainder $ 16 $. So $ \frac{58}{21} = 2\frac{16}{21} $. The quotient becomes the whole number, remainder becomes new numerator.

Q: Can I check my answer?

Absolutely! Multiply your answer by the original divisor: $ 2\frac{16}{21} \times 2\frac{1}{10} $. If you get $ 5\frac{4}{5} $, your division is correct!

Mixed Number Division with Reciprocal Method

$5\frac{4}{5}:2\frac{1}{10}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's start by solving the problem.

00:07 First, we need to convert any mixed fractions into improper fractions.

00:31 Next, express the division as a fraction, like a numerator over a denominator.

00:42 Now, multiply by the reciprocal of the divisor. Just flip it upside down.

00:50 Great! Let's calculate the numerator by multiplying the top numbers.

00:57 Now, let's convert the result back to a mixed fraction.

01:01 Break down 290 into 210 plus 80, just to make it simpler.

01:08 Separate the fraction into a whole number part and a remainder.

01:14 Finally, reduce or simplify any parts that can be simplified.

01:23 Convert everything into a whole number, and combine it with the mixed number.

01:28 And there we have it, that's the solution to our question!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$5\frac{4}{5}:2\frac{1}{10}=$

Step-by-step solution

To solve the problem $5\frac{4}{5} \div 2\frac{1}{10}$ , we follow these steps:

Step 1: Convert mixed numbers to improper fractions.
$5\frac{4}{5} = \frac{5 \times 5 + 4}{5} = \frac{25 + 4}{5} = \frac{29}{5}$
$2\frac{1}{10} = \frac{2 \times 10 + 1}{10} = \frac{20 + 1}{10} = \frac{21}{10}$
Step 2: Divide $\frac{29}{5}$ by $\frac{21}{10}$ by multiplying by the reciprocal.
$\frac{29}{5} \div \frac{21}{10} = \frac{29}{5} \times \frac{10}{21}$
Step 3: Multiply the fractions and simplify.
$\frac{29}{5} \times \frac{10}{21} = \frac{29 \times 10}{5 \times 21} = \frac{290}{105}$
Step 4: Simplify $\frac{290}{105}$ .
Find the greatest common divisor (GCD) of 290 and 105. The GCD is 5.
$\frac{290 \div 5}{105 \div 5} = \frac{58}{21}$
Step 5: Convert the improper fraction $\frac{58}{21}$ into a mixed number.
$58 \div 21 = 2$ remainder $16$ , so $\frac{58}{21} = 2\frac{16}{21}$

Therefore, the solution is $2\frac{16}{21}$ .

Final Answer

$2\frac{16}{21}$

Key Points to Remember

Essential concepts to master this topic

Conversion: Change mixed numbers to improper fractions first
Technique: Multiply by reciprocal: $\frac{29}{5} \times \frac{10}{21} = \frac{290}{105}$
Check: Verify by multiplying answer by divisor: $2\frac{16}{21} \times 2\frac{1}{10} = 5\frac{4}{5}$ ✓

Common Mistakes

Avoid these frequent errors

Dividing mixed numbers without converting first
Don't try to divide $5\frac{4}{5} ÷ 2\frac{1}{10}$ directly = messy calculations and wrong answers! This makes the problem much harder and leads to errors. Always convert mixed numbers to improper fractions before dividing.

Practice Quiz

Test your knowledge with interactive questions

$2\frac{5}{6}\times1\frac{1}{4}=$

FAQ

Everything you need to know about this question

Why do I need to convert mixed numbers to improper fractions first?

Mixed numbers like $5\frac{4}{5}$ can't be divided directly! Converting to improper fractions like $\frac{29}{5}$ gives you single fractions that follow division rules.

How do I remember to flip the second fraction?

Think "dividing by a fraction means multiplying by its flip!" So $÷ \frac{21}{10}$ becomes $\times \frac{10}{21}$ . The reciprocal flips numerator and denominator.

Do I always need to simplify the final answer?

Yes! Always check if your fraction can be simplified. Find the GCD of numerator and denominator. Here, $\frac{290}{105}$ simplifies to $\frac{58}{21}$ by dividing both by 5.

How do I convert improper fractions back to mixed numbers?

Divide the numerator by denominator: $58 ÷ 21 = 2$ remainder $16$ . So $\frac{58}{21} = 2\frac{16}{21}$ . The quotient becomes the whole number, remainder becomes new numerator.

Can I check my answer?

Absolutely! Multiply your answer by the original divisor: $2\frac{16}{21} \times 2\frac{1}{10}$ . If you get $5\frac{4}{5}$ , your division is correct!

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