Solve Mixed Number Division: 1⅔ ÷ ¾ Step-by-Step

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

Mixed numbers like $ 1\frac{2}{7} $ represent addition (1 + 2/7), which makes division complicated. Converting to improper fractions like $ \frac{9}{7} $ gives you a single fraction that's easier to work with.

Q: How do I remember to multiply by the reciprocal?

"Division is multiplication in disguise!" When you see $ \div \frac{3}{4} $, flip the fraction to $ \frac{4}{3} $ and change ÷ to ×. Think: "Keep, Change, Flip"

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

Divide the numerator by the denominator: $ \frac{12}{7} = 12 \div 7 = 1 $ remainder $ 5 $. So the answer is $ 1\frac{5}{7} $!

Q: Can I use a calculator for this type of problem?

While calculators help with arithmetic, it's important to understand the steps. Practice the manual method first, then use technology to check your work and save time on tests.

Q: What's the easiest way to check my answer?

Multiply your answer by the original divisor: $ 1\frac{5}{7} \times \frac{3}{4} $. If you get back to $ 1\frac{2}{7} $, you're correct!

Mixed Number Division with Reciprocal Multiplication

$1\frac{2}{7}:\frac{3}{4}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:04 Convert mixed number to fraction

00:09 Calculate the numerator and put it back in the exercise

00:19 Convert division to multiplication by reciprocal

00:31 Make sure to multiply numerator by numerator and denominator by denominator

00:36 Calculate the multiplications

00:41 Now convert to mixed number

00:46 Break down 36 into 21 plus 15

00:57 Break down the fraction into whole number and remainder

01:01 Convert whole fraction to whole number, and combine into mixed number

01:10 Simplify what's possible

01:17 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

$1\frac{2}{7}:\frac{3}{4}=$

Step-by-step solution

To solve the division of the mixed fraction $1\frac{2}{7}$ by the fraction $\frac{3}{4}$ , follow these steps:

Step 1: Convert the mixed fraction to an improper fraction: $1\frac{2}{7} = \frac{9}{7}$ .
Step 2: Determine the reciprocal of the divisor fraction: $\text{Reciprocal of } \frac{3}{4} = \frac{4}{3}$ .
Step 3: Multiply the improper fraction by the reciprocal of the divisor: $\frac{9}{7} \times \frac{4}{3} = \frac{36}{21}$ .
Step 4: Simplify the resulting fraction: The greatest common divisor of 36 and 21 is 3. Thus, $\frac{36}{21} = \frac{12}{7}$ .
Step 5: Convert back to a mixed number: The improper fraction $\frac{12}{7} = 1\frac{5}{7}$ .

Therefore, the solution to the problem is $1\frac{5}{7}$ .

Final Answer

$1\frac{5}{7}$

Key Points to Remember

Essential concepts to master this topic

Rule: Convert mixed numbers to improper fractions before dividing
Technique: Division becomes multiplication by reciprocal: $\frac{9}{7} \times \frac{4}{3} = \frac{36}{21}$
Check: Multiply answer by divisor: $1\frac{5}{7} \times \frac{3}{4} = 1\frac{2}{7}$ ✓

Common Mistakes

Avoid these frequent errors

Dividing denominators and numerators directly
Don't divide $1\frac{2}{7} \div \frac{3}{4}$ by dividing 7÷4 and 2÷3 separately = completely wrong approach! This ignores proper fraction division rules and gives meaningless results. Always convert to improper fractions first, then multiply by 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 first?

Mixed numbers like $1\frac{2}{7}$ represent addition (1 + 2/7), which makes division complicated. Converting to improper fractions like $\frac{9}{7}$ gives you a single fraction that's easier to work with.

How do I remember to multiply by the reciprocal?

"Division is multiplication in disguise!" When you see $\div \frac{3}{4}$ , flip the fraction to $\frac{4}{3}$ and change ÷ to ×. Think: "Keep, Change, Flip"

What if I can't simplify the final fraction?

That's okay! Not all fractions can be simplified. But always check for common factors first. In this problem, 36 and 21 both divide by 3, giving us $\frac{12}{7}$ .

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

Divide the numerator by the denominator: $\frac{12}{7} = 12 \div 7 = 1$ remainder $5$ . So the answer is $1\frac{5}{7}$ !

Can I use a calculator for this type of problem?

While calculators help with arithmetic, it's important to understand the steps. Practice the manual method first, then use technology to check your work and save time on tests.

What's the easiest way to check my answer?

Multiply your answer by the original divisor: $1\frac{5}{7} \times \frac{3}{4}$ . If you get back to $1\frac{2}{7}$ , you're correct!

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Solve Mixed Number Division: 1⅔ ÷ ¾ Step-by-Step

Mixed Number Division with Reciprocal Multiplication

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

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

How do I remember to multiply by the reciprocal?

What if I can't simplify the final fraction?

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

Can I use a calculator for this type of problem?

What's the easiest way to check my answer?

🌟 Unlock Your Math Potential

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