Solve Mixed Number Division: 1½ ÷ 6 Step-by-Step

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

Mixed numbers like $ 1\frac{1}{2} $ are harder to work with directly. Converting to improper fractions like $ \frac{3}{2} $ makes the division much easier to handle!

Q: How do I remember to flip and multiply for division?

Think: "Dividing by a number is the same as multiplying by its reciprocal." So $ \div 6 $ becomes $ \times \frac{1}{6} $. The second fraction always flips!

Q: Should I leave my answer as a fraction or decimal?

Both $ \frac{1}{4} $ and 0.25 are correct! Choose based on what the problem asks for. Fractions show exact values, while decimals are easier to compare.

Q: What if I get confused with the steps?

Follow this order: 1) Convert mixed number, 2) Change division to multiplication, 3) Multiply across, 4) Simplify. Take it one step at a time!

Q: How can I check if my answer makes sense?

Ask yourself: "Is my answer smaller than the original number?" When dividing by numbers greater than 1, your result should be smaller than what you started with.

Mixed Number Division with Improper Fractions

Solve the following problem:

$\frac{1\frac{1}{2}}{6}=\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's break down the fraction. We'll use the factorization law. Ready?

00:19 First, express the number one as a fraction. Just write it as one over one.

00:26 Now, let's rewrite the exercise step by step.

00:31 Find a common denominator. Then, combine the fractions on top.

00:38 You will notice, we have a fraction over another fraction.

00:47 Here's a trick. When dividing fractions, multiply by the reciprocal.

01:06 Now, we'll apply the factorization law to break down twelve into factors.

01:13 This helps us reduce the fraction easily. Almost there!

01:19 We'll find the solution in fraction form first.

01:22 Finally, let's convert it to a decimal fraction. Good job!

01:27 And there you have it! That's the solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following problem:

$\frac{1\frac{1}{2}}{6}=\text{?}$

Step-by-step solution

Let's first look at the numerator of the fraction. We will convert it to an addition exercise containing two fractions:

$1+\frac{1}{2}$

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

This leaves us with:

$\frac{\frac{2}{2}+\frac{1}{2}}{6}=$

$\frac{\frac{2+1}{2}}{6}=$

$\frac{\frac{3}{2}}{\frac{6}{1}}=$

Let's now multiply the two fractions together—numerator by numerator and denominator by denominator:

$\frac{1\times3}{2\times6}=$

$\frac{3}{12}=\frac{3}{3\times4}$

Finally, simplify:

$\frac{3}{3\times4}=\frac{1}{4}$

$\frac{1}{4}=0.25$

Final Answer

$0.25$

Key Points to Remember

Essential concepts to master this topic

Convert: Change mixed numbers to improper fractions before dividing
Technique: Division becomes multiplication: $\frac{3}{2} \div 6 = \frac{3}{2} \times \frac{1}{6}$
Check: Multiply answer by divisor: $0.25 \times 6 = 1.5 = 1\frac{1}{2}$ ✓

Common Mistakes

Avoid these frequent errors

Dividing whole number by fraction incorrectly
Don't divide 6 by 1½ instead of 1½ by 6 = gives 4 instead of 0.25! This reverses the division operation completely. Always check which number is being divided by which, and convert mixed numbers first.

Practice Quiz

Test your knowledge with interactive questions

$$ 100+5-100+5 $$

FAQ

Everything you need to know about this question

Why do I need to convert the mixed number first?

Mixed numbers like $1\frac{1}{2}$ are harder to work with directly. Converting to improper fractions like $\frac{3}{2}$ makes the division much easier to handle!

How do I remember to flip and multiply for division?

Think: "Dividing by a number is the same as multiplying by its reciprocal." So $\div 6$ becomes $\times \frac{1}{6}$ . The second fraction always flips!

Should I leave my answer as a fraction or decimal?

Both $\frac{1}{4}$ and 0.25 are correct! Choose based on what the problem asks for. Fractions show exact values, while decimals are easier to compare.

What if I get confused with the steps?

Follow this order: 1) Convert mixed number, 2) Change division to multiplication, 3) Multiply across, 4) Simplify. Take it one step at a time!

How can I check if my answer makes sense?

Ask yourself: "Is my answer smaller than the original number?" When dividing by numbers greater than 1, your result should be smaller than what you started with.

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Solve Mixed Number Division: 1½ ÷ 6 Step-by-Step

Mixed Number Division with Improper Fractions

❤️ 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 first?

How do I remember to flip and multiply for division?

Should I leave my answer as a fraction or decimal?

What if I get confused with the steps?

How can I check if my answer makes sense?

🌟 Unlock Your Math Potential

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