Solve Mixed Number Division: 6½ ÷ 1¼ Step-by-Step

Q: Why do I multiply by the reciprocal when dividing fractions?

Division by a fraction means "how many groups of that size fit?" Multiplying by the reciprocal gives the same result but is much easier to calculate!

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

Divide the numerator by the denominator! For $ \frac{26}{5} $: 26 ÷ 5 = 5 remainder 1, so the answer is $ 5\frac{1}{5} $.

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

Yes! Always check if your fraction can be reduced. Look for common factors in the numerator and denominator, then divide both by the greatest common factor.

Mixed Number Division with Improper Fractions

$6\frac{1}{2}:1\frac{1}{4}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Convert mixed numbers to fractions

00:21 Write division as a fraction

00:26 Multiply by the reciprocal

00:40 Calculate the multiplications

00:47 Now convert to a mixed number

00:50 Break down 52 into 50 plus 2

00:54 Break down the fraction into whole number and remainder

00:59 Reduce what's possible

01:04 Convert proper fraction to whole number and add to mixed number

01:09 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$6\frac{1}{2}:1\frac{1}{4}=$

Step-by-step solution

To solve this problem, we'll convert the mixed numbers to improper fractions and then perform the division.

Step 1: Convert $6\frac{1}{2}$ to an improper fraction:

$6\frac{1}{2} = \frac{13}{2}$ .

Step 2: Convert $1\frac{1}{4}$ to an improper fraction:

$1\frac{1}{4} = \frac{5}{4}$ .

Step 3: Divide the two improper fractions:

$\frac{13}{2} \div \frac{5}{4} = \frac{13}{2} \times \frac{4}{5}$ .

Step 4: Multiply the fractions:

$\frac{13}{2} \times \frac{4}{5} = \frac{13 \times 4}{2 \times 5} = \frac{52}{10}$ .

Step 5: Simplify $\frac{52}{10}$ :

$\frac{52}{10} = \frac{26}{5} = 5\frac{1}{5}$ .

Therefore, the solution to the problem is $5\frac{1}{5}$ .

Final Answer

$5\frac{1}{5}$

Key Points to Remember

Essential concepts to master this topic

Conversion: Transform mixed numbers into improper fractions before dividing
Division Rule: Multiply by reciprocal: $\frac{13}{2} \div \frac{5}{4} = \frac{13}{2} \times \frac{4}{5}$
Verification: Check by multiplying answer by divisor: $5\frac{1}{5} \times 1\frac{1}{4} = 6\frac{1}{2}$ ✓

Common Mistakes

Avoid these frequent errors

Dividing mixed numbers without converting to improper fractions first
Don't try to divide $6\frac{1}{2} \div 1\frac{1}{4}$ directly = confusion and wrong answers! Mixed numbers can't be divided using standard fraction rules. Always convert to improper fractions first: $\frac{13}{2} \div \frac{5}{4}$ .

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

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

Multiply the whole number by the denominator, then add the numerator! For $6\frac{1}{2}$ : (6 × 2) + 1 = 13, so it becomes $\frac{13}{2}$ .

Why do I multiply by the reciprocal when dividing fractions?

Division by a fraction means "how many groups of that size fit?" Multiplying by the reciprocal gives the same result but is much easier to calculate!

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

Divide the numerator by the denominator! For $\frac{26}{5}$ : 26 ÷ 5 = 5 remainder 1, so the answer is $5\frac{1}{5}$ .

Do I always need to simplify my final answer?

Yes! Always check if your fraction can be reduced. Look for common factors in the numerator and denominator, then divide both by the greatest common factor.

What if I get a whole number as my answer?

That's perfectly normal! If your improper fraction divides evenly (like $\frac{20}{4} = 5$ ), then your final answer is just that whole number.

How can I check if my division is correct?

Multiply your answer by the original divisor - you should get the dividend! If $5\frac{1}{5} \times 1\frac{1}{4} = 6\frac{1}{2}$ , then your division is correct.

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