Solve 3/4 ÷ 1 2/3: Mixed Number Division Step-by-Step

Q: Why can't I just divide by the mixed number as it is?

Mixed numbers like $ 1\frac{2}{3} $ have two parts (whole and fraction), making division confusing. Converting to improper fractions like $ \frac{5}{3} $ gives you one number to work with!

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

Use this formula: Multiply whole number by denominator, add numerator, keep same denominator. For $ 1\frac{2}{3} $: $ \frac{(1 \times 3) + 2}{3} = \frac{5}{3} $

Q: Why do I multiply by the reciprocal instead of dividing?

Dividing by a fraction is the same as multiplying by its flip! So $ ÷\frac{5}{3} $ becomes $ \times\frac{3}{5} $, which is much easier to calculate.

Q: Do I need to simplify my final answer?

Always check if you can simplify! In this case, $ \frac{9}{20} $ is already in lowest terms since 9 and 20 share no common factors besides 1.

Fraction Division with Mixed Number Conversion

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

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Convert mixed number to fraction

00:08 Calculate the numerator and substitute back into the exercise

00:19 Convert division to multiplication by reciprocal

00:32 Make sure to multiply numerator by numerator and denominator by denominator

00:39 Calculate the products

00:44 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

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

Step-by-step solution

To solve the problem $\frac{3}{4}:1\frac{2}{3}$ , follow these steps:

Step 1: Convert the mixed number $1\frac{2}{3}$ to an improper fraction.
Step 2: Rewrite the division problem using the reciprocal of the divisor.
Step 3: Multiply the fractions.

Let’s proceed through each step:

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

$1\frac{2}{3} = \frac{1 \times 3 + 2}{3} = \frac{3 + 2}{3} = \frac{5}{3}$

Step 2: The division $\frac{3}{4} : \frac{5}{3}$ becomes $\frac{3}{4} \times \frac{3}{5}$ (multiply by the reciprocal).

Step 3: Multiply the two fractions:

$\frac{3}{4} \times \frac{3}{5} = \frac{3 \times 3}{4 \times 5} = \frac{9}{20}$

Thus, the answer is $\frac{9}{20}$ .

The correct answer is choice 3: $\frac{9}{20}$ .

Final Answer

$\frac{9}{20}$

Key Points to Remember

Essential concepts to master this topic

Conversion: Change mixed numbers to improper fractions first
Technique: Multiply by reciprocal: $\frac{3}{4} \times \frac{3}{5} = \frac{9}{20}$
Check: $\frac{9}{20} \times \frac{5}{3} = \frac{45}{60} = \frac{3}{4}$ ✓

Common Mistakes

Avoid these frequent errors

Dividing directly by mixed numbers without conversion
Don't try to divide $\frac{3}{4} ÷ 1\frac{2}{3}$ directly = confusing and wrong answers! Mixed numbers must be converted to improper fractions first. Always convert $1\frac{2}{3}$ to $\frac{5}{3}$ before dividing.

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 by the mixed number as it is?

Mixed numbers like $1\frac{2}{3}$ have two parts (whole and fraction), making division confusing. Converting to improper fractions like $\frac{5}{3}$ gives you one number to work with!

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

Use this formula: Multiply whole number by denominator, add numerator, keep same denominator. For $1\frac{2}{3}$ : $\frac{(1 \times 3) + 2}{3} = \frac{5}{3}$

Why do I multiply by the reciprocal instead of dividing?

Dividing by a fraction is the same as multiplying by its flip! So $÷\frac{5}{3}$ becomes $\times\frac{3}{5}$ , which is much easier to calculate.

Do I need to simplify my final answer?

Always check if you can simplify! In this case, $\frac{9}{20}$ is already in lowest terms since 9 and 20 share no common factors besides 1.

What if I get a different denominator in my answer choices?

Double-check your conversion and multiplication! Common errors include wrong improper fraction conversion or forgetting to multiply numerators together and denominators together separately.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Mixed Fractions questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime