Solve Fraction Division: 8/9 ÷ 1/9 Step-by-Step

Q: Why do I flip the second fraction when dividing?

Division is the opposite of multiplication. When you divide by $ \frac{1}{9} $, you're asking "how many $ \frac{1}{9} $s fit into $ \frac{8}{9} $?" Flipping gives you $ \frac{9}{1} $, which is the reciprocal.

Q: What does it mean that 8/9 ÷ 1/9 = 8?

It means there are 8 pieces of size $ \frac{1}{9} $ inside $ \frac{8}{9} $. Think of it like: if you have 8 ninth-slices of pizza, how many single ninth-slices is that? Exactly 8!

Q: Can I just cancel the 9s since they're the same?

Be careful! You can only cancel when you're multiplying fractions, not dividing. First change division to multiplication: $ \frac{8}{9} \times \frac{9}{1} $, then you can cancel the 9s.

Q: How do I remember to flip and multiply?

Remember: "Keep, Change, Flip" - Keep the first fraction the same, Change division to multiplication, Flip the second fraction upside down. Then multiply across!

Fraction Division with Same Denominators

Solve the following:

$\frac{8}{9}:\frac{1}{9}=$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following:

$\frac{8}{9}:\frac{1}{9}=$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the given fractions and the operation.
Step 2: Take the reciprocal of the second fraction.
Step 3: Multiply the first fraction by this reciprocal.
Step 4: Simplify the resulting fraction.

Now, let's work through each step:
Step 1: We are given $\frac{8}{9}$ and need to divide it by $\frac{1}{9}$ .
Step 2: Find the reciprocal of $\frac{1}{9}$ , which is $\frac{9}{1}$ .
Step 3: Multiply $\frac{8}{9}$ by $\frac{9}{1}$ :

$\frac{8}{9} \times \frac{9}{1} = \frac{8 \times 9}{9 \times 1} = \frac{72}{9}$

Step 4: Simplify $\frac{72}{9}$ by dividing both the numerator and denominator by 9:

$\frac{72}{9} = 8$

Therefore, the solution to the problem is $8$ .

Final Answer

$8$

Key Points to Remember

Essential concepts to master this topic

Rule: Division of fractions means multiply by the reciprocal
Technique: $\frac{8}{9} \div \frac{1}{9} = \frac{8}{9} \times \frac{9}{1} = 8$
Check: Does $8 \times \frac{1}{9} = \frac{8}{9}$ ? Yes! ✓

Common Mistakes

Avoid these frequent errors

Dividing numerators and denominators separately
Don't solve $\frac{8}{9} \div \frac{1}{9}$ as $\frac{8÷1}{9÷9} = \frac{8}{1} = 8$ by coincidence! This shortcut only works by luck here and fails with different numbers. Always flip the second fraction and multiply: $\frac{8}{9} \times \frac{9}{1}$ .

Practice Quiz

Test your knowledge with interactive questions

Complete the following exercise:

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

FAQ

Everything you need to know about this question

Why do I flip the second fraction when dividing?

Division is the opposite of multiplication. When you divide by $\frac{1}{9}$ , you're asking "how many $\frac{1}{9}$ s fit into $\frac{8}{9}$ ?" Flipping gives you $\frac{9}{1}$ , which is the reciprocal.

What does it mean that 8/9 ÷ 1/9 = 8?

It means there are 8 pieces of size $\frac{1}{9}$ inside $\frac{8}{9}$ . Think of it like: if you have 8 ninth-slices of pizza, how many single ninth-slices is that? Exactly 8!

Can I just cancel the 9s since they're the same?

Be careful! You can only cancel when you're multiplying fractions, not dividing. First change division to multiplication: $\frac{8}{9} \times \frac{9}{1}$ , then you can cancel the 9s.

Why is the answer a whole number instead of a fraction?

When dividing fractions, you often get whole numbers! Here, $\frac{8}{9} \div \frac{1}{9}$ gives us 8 because we're finding how many unit fractions fit into a larger fraction with the same denominator.

How do I remember to flip and multiply?

Remember: "Keep, Change, Flip" - Keep the first fraction the same, Change division to multiplication, Flip the second fraction upside down. Then multiply across!

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