Solve Division Expression: 99÷(33÷10) Step-by-Step Solution

Q: Why can't I just divide from left to right like 99÷33÷10?

The parentheses change everything! $ 99:(33:10) $ means you must do 33÷10 first, then divide 99 by that result. Without parentheses, you'd get a completely different answer.

Q: How do I divide 99 by 3.3 without a calculator?

Think of it as $ \frac{99}{3.3} = \frac{99}{33/10} = 99 \times \frac{10}{33} $. Since 99 = 3 × 33, you get $ 3 \times 33 \times \frac{10}{33} = 3 \times 10 = 30 $!

Q: What does the colon symbol (:) mean in math?

The colon (:) is just another way to write division, like the ÷ symbol. So $ 33:10 $ means exactly the same thing as $ 33÷10 $ or $ \frac{33}{10} $.

Q: How can I check if 30 is really the right answer?

Work backwards! If 30 is correct, then 30 × 3.3 should equal 99. Let's check: $ 30 \times 3.3 = 99 $ ✓. And $ 3.3 \times 10 = 33 $ ✓. Both check out!

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Division is also multiplication by the reciprocal

00:07 Therefore when opening the parentheses, it will end up multiplied by C

00:11 We will use this formula in our exercise

00:16 Let's solve one operation at a time

00:22 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$99:(33:10)=$

2

Step-by-step solution

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

Step 1: Perform the inner division operation.
Step 2: Use the result of Step 1 in the outer division operation.

Now, let's work through each step:

Step 1: Calculate $33:10$ .
This operation is equivalent to dividing 33 by 10, which gives us:
$\frac{33}{10} = 3.3$ .

Step 2: Use the result from Step 1 to perform the division $99:3.3$ .
This operation now becomes:
$\frac{99}{3.3} = 30$ .

Therefore, the solution to the problem is $30$ .

3

Final Answer

30

Key Points to Remember

Essential concepts to master this topic

Rule: Always solve operations inside parentheses first before outer operations
Technique: Calculate 33÷10 = 3.3, then 99÷3.3 = 30
Check: Work backwards: 30 × 3.3 = 99, and 3.3 × 10 = 33 ✓

Common Mistakes

Avoid these frequent errors

Solving division operations from left to right without parentheses
Don't solve 99÷33÷10 = 3÷10 = 0.3! This ignores the parentheses which change the order completely. The parentheses mean 33÷10 happens first, giving 3.3, then 99÷3.3 = 30. Always follow parentheses before other operations.

Practice Quiz

Test your knowledge with interactive questions

$$ 100-(5+55)= $$

FAQ

Everything you need to know about this question

Why can't I just divide from left to right like 99÷33÷10?

+

The parentheses change everything! $99:(33:10)$ means you must do 33÷10 first, then divide 99 by that result. Without parentheses, you'd get a completely different answer.

How do I divide 99 by 3.3 without a calculator?

+

Think of it as $\frac{99}{3.3} = \frac{99}{33/10} = 99 \times \frac{10}{33}$ . Since 99 = 3 × 33, you get $3 \times 33 \times \frac{10}{33} = 3 \times 10 = 30$ !

What does the colon symbol (:) mean in math?

+

The colon (:) is just another way to write division, like the ÷ symbol. So $33:10$ means exactly the same thing as $33÷10$ or $\frac{33}{10}$ .

Why is my answer 30 and not 2970?

+

If you got 2970, you probably multiplied instead of dividing! Remember that $99÷3.3$ asks "how many times does 3.3 go into 99?" The answer is 30 times, not 99 × 3.3.

How can I check if 30 is really the right answer?

+

Work backwards! If 30 is correct, then 30 × 3.3 should equal 99. Let's check: $30 \times 3.3 = 99$ ✓. And $3.3 \times 10 = 33$ ✓. Both check out!

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Solve Division Expression: 99÷(33÷10) Step-by-Step Solution

Order of Operations with Nested Division

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