Solve the Fraction Division: 8/9 ÷ 4 Step-by-Step

Q: Why do I flip the number when dividing fractions?

Division means "how many times does this number fit into that number?" When you divide by 4, you're asking how many 4s fit into $ \frac{8}{9} $. Flipping 4 to $ \frac{1}{4} $ and multiplying gives you that answer!

Q: How do I know when to simplify my answer?

Always check if the numerator and denominator share common factors. In $ \frac{8}{36} $, both 8 and 36 are divisible by 4, so you get $ \frac{2}{9} $.

Q: Can I just divide the numerator by the whole number?

Sometimes, but be careful! This only works when the numerator is evenly divisible. For $ \frac{8}{9} ÷ 4 $, you could do $ \frac{8÷4}{9} = \frac{2}{9} $, but the reciprocal method always works.

Q: Why is the GCD important when simplifying?

The GCD (Greatest Common Divisor) helps you simplify in one step instead of multiple steps. For $ \frac{8}{36} $, the GCD is 4, so divide both parts by 4 to get $ \frac{2}{9} $ immediately!

Fraction Division with Whole Numbers

Solve the following exercise:

$\frac{8}{9}:4=\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's solve this problem step by step.

00:10 First, we'll write the number as a fraction by putting it over 1.

00:15 Remember, when we divide a number by 1, the value stays the same.

00:20 Now, here's an important rule: we divide the top number by the top number, and the bottom number by the bottom number.

00:27 Let's work out these divisions carefully.

00:30 And there we have it! That's our final answer.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following exercise:

$\frac{8}{9}:4=\text{?}$

Step-by-step solution

To solve the problem of dividing the fraction $\frac{8}{9}$ by the whole number 4, we will follow the reciprocal method.

Step 1: Express the whole number 4 as a fraction: $4 = \frac{4}{1}$ .
Step 2: Find the reciprocal of $\frac{4}{1}$ , which is $\frac{1}{4}$ .
Step 3: Multiply the original fraction $\frac{8}{9}$ by $\frac{1}{4}$ :
$\frac{8}{9} \times \frac{1}{4} = \frac{8 \times 1}{9 \times 4} = \frac{8}{36}.$
Step 4: Simplify the fraction $\frac{8}{36}$ . The greatest common divisor (GCD) of 8 and 36 is 4:
$\frac{8 \div 4}{36 \div 4} = \frac{2}{9}.$

Thus, the result of dividing $\frac{8}{9}$ by 4 is $\frac{2}{9}$ .

Final Answer

$\frac{2}{9}$

Key Points to Remember

Essential concepts to master this topic

Rule: Dividing by a number equals multiplying by its reciprocal
Technique: Convert $4$ to $\frac{4}{1}$ , then flip to get $\frac{1}{4}$
Check: Multiply your answer by 4 to get back to original fraction ✓

Common Mistakes

Avoid these frequent errors

Multiplying the fraction by the whole number instead of dividing
Don't multiply $\frac{8}{9} \times 4 = \frac{32}{9}$ ! This makes the fraction bigger, not smaller. Always remember that division by 4 means multiply by $\frac{1}{4}$ to make the result smaller.

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 number when dividing fractions?

Division means "how many times does this number fit into that number?" When you divide by 4, you're asking how many 4s fit into $\frac{8}{9}$ . Flipping 4 to $\frac{1}{4}$ and multiplying gives you that answer!

How do I know when to simplify my answer?

Always check if the numerator and denominator share common factors. In $\frac{8}{36}$ , both 8 and 36 are divisible by 4, so you get $\frac{2}{9}$ .

Can I just divide the numerator by the whole number?

Sometimes, but be careful! This only works when the numerator is evenly divisible. For $\frac{8}{9} ÷ 4$ , you could do $\frac{8÷4}{9} = \frac{2}{9}$ , but the reciprocal method always works.

What if I get a bigger fraction after dividing?

That's impossible! When you divide a positive fraction by a number greater than 1, the result must be smaller than the original fraction. If you got bigger, check your work - you probably multiplied instead of dividing.

Why is the GCD important when simplifying?

The GCD (Greatest Common Divisor) helps you simplify in one step instead of multiple steps. For $\frac{8}{36}$ , the GCD is 4, so divide both parts by 4 to get $\frac{2}{9}$ immediately!

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