Solve the Expression: 9/9 ÷ 3 Step-by-Step Solution

Q: Why does 9/9 equal 1?

When the numerator and denominator are the same, you're dividing a number by itself, which always equals 1. Think of it as: "I have 9 items, and I'm dividing them into 9 equal groups - each group has 1 item!"

Q: What's the difference between ÷ and : symbols?

Both symbols mean division - they're just different ways to write it! $ a \div b $ and $ a : b $ both mean "a divided by b".

Q: Can I just write the answer as a decimal instead?

Yes! $ \frac{1}{3} $ equals approximately 0.333... But since the answer choices are fractions, it's better to keep your answer as an exact fraction rather than a rounded decimal.

Q: How do I remember the division rule for fractions?

Remember: "Dividing by a number is the same as multiplying by its flip!" So dividing by 3 becomes multiplying by $ \frac{1}{3} $.

Q: What if I got 1/9 as my answer?

Check your work! If you got $ \frac{1}{9} $, you might have skipped simplifying $ \frac{9}{9} = 1 $ first, or mixed up the order of operations. Always simplify fractions before doing other operations.

Fraction Division with Simplification Steps

Complete the following exercise:

$\frac{9}{9}:3=\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:05 Let's write the number as a fraction

00:09 Any number divided by 1 is always equal to itself

00:13 Make sure to divide numerator by numerator and denominator by denominator

00:20 Let's calculate the quotients

00:25 We want to reduce the fraction as much as possible

00:28 Make sure to divide both numerator and denominator

00:33 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

Complete the following exercise:

$\frac{9}{9}:3=\text{?}$

Step-by-step solution

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

Step 1: Simplify the given fraction.
Step 2: Convert the division by a whole number into multiplication by its reciprocal.
Step 3: Perform the multiplication and simplify if needed.

Now, let's work through each step:
Step 1: Simplify the fraction $\frac{9}{9}$ . Since the numerator and denominator are the same, it simplifies to $1$ .
Step 2: Convert the division $1 \div 3$ into multiplication by using the reciprocal: $\frac{1}{3}$ . Therefore, $1 \div 3$ becomes $1 \times \frac{1}{3}$ .
Step 3: Perform the multiplication: $1 \times \frac{1}{3} = \frac{1}{3}$ .

Therefore, the solution to the problem is $\frac{1}{3}$ , which corresponds to the answer choice $\frac{1}{3}$ .

Final Answer

$\frac{1}{3}$

Key Points to Remember

Essential concepts to master this topic

Simplification: Any fraction with equal numerator and denominator equals 1
Division Rule: $a \div b = a \times \frac{1}{b}$ for any division
Check: Verify $\frac{1}{3} \times 3 = 1$ matches original $\frac{9}{9}$ ✓

Common Mistakes

Avoid these frequent errors

Trying to divide fractions directly without simplifying first
Don't compute $\frac{9}{9} \div 3$ as $\frac{9}{9 \times 3} = \frac{9}{27} = \frac{1}{3}$ ! While this gives the right answer by luck, it's unnecessarily complicated and error-prone. Always simplify $\frac{9}{9} = 1$ first, then divide: $1 \div 3 = \frac{1}{3}$ .

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 does 9/9 equal 1?

When the numerator and denominator are the same, you're dividing a number by itself, which always equals 1. Think of it as: "I have 9 items, and I'm dividing them into 9 equal groups - each group has 1 item!"

What's the difference between ÷ and : symbols?

Both symbols mean division - they're just different ways to write it! $a \div b$ and $a : b$ both mean "a divided by b".

Can I just write the answer as a decimal instead?

Yes! $\frac{1}{3}$ equals approximately 0.333... But since the answer choices are fractions, it's better to keep your answer as an exact fraction rather than a rounded decimal.

How do I remember the division rule for fractions?

Remember: "Dividing by a number is the same as multiplying by its flip!" So dividing by 3 becomes multiplying by $\frac{1}{3}$ .

What if I got 1/9 as my answer?

Check your work! If you got $\frac{1}{9}$ , you might have skipped simplifying $\frac{9}{9} = 1$ first, or mixed up the order of operations. Always simplify fractions before doing other operations.

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