Solve 300÷(5×6): Order of Operations Division Problem

Q: Why can't I just divide 300 by 5 first?

The parentheses tell you that $ 5 \times 6 $ must be calculated as one unit first! Without parentheses, you'd work left to right, but parentheses override that rule.

Q: What does the colon (:) mean in this problem?

The colon (:) is just another way to write division. So $ 300:(5 \times 6) $ means exactly the same as $ 300 \div (5 \times 6) $.

Q: How do I remember PEMDAS with this problem?

P comes first in PEMDAS! That means Parentheses before everything else. So solve $ (5 \times 6) $ first, then do the division.

Q: What if I calculated 300 ÷ 5 ÷ 6 instead?

That would give you $ 300 \div 5 \div 6 = 60 \div 6 = 10 $, which happens to be correct! But this only works by coincidence. Always follow the parentheses to avoid mistakes on other problems.

Q: Can I check my answer a different way?

Yes! Work backwards: if $ 10 \times (5 \times 6) = 10 \times 30 = 300 $, then your division was correct. This multiplication check always works for division problems.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's solve this problem together.

00:08 Remember, multiplying is like dividing by the reciprocal.

00:12 So, when we open the parentheses, we divide by C.

00:16 We'll use this idea in our exercise.

00:22 Follow the order of operations, going from left to right.

00:26 Pretend it's 30 instead of 300. Then add a zero to your answer.

00:34 Let's substitute the numbers and keep solving.

00:38 And that's how we find the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$300:(5\times6)=$

2

Step-by-step solution

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

Step 1: Compute the product $5 \times 6$ .
Step 2: Perform the division operation $300 \div 30$ .

Now, let's work through each step:

Step 1: Calculate $5 \times 6$ .

$5 \times 6 = 30$

Step 2: Divide 300 by the result from Step 1.

$300 \div 30 = 10$

Therefore, the solution to the problem is $\boxed{10}$ .

This matches the choice: 10.

3

Final Answer

10

Key Points to Remember

Essential concepts to master this topic

Rule: Always solve operations inside parentheses before dividing
Technique: Calculate $5 \times 6 = 30$ first, then $300 \div 30$
Check: Substitute back: $300 \div (5 \times 6) = 300 \div 30 = 10$ ✓

Common Mistakes

Avoid these frequent errors

Dividing 300 by 5 first, then multiplying by 6
Don't calculate 300 ÷ 5 × 6 = 60 × 6 = 360! This ignores the parentheses and gives the wrong answer. Parentheses change the order completely. Always solve what's inside parentheses first, then divide by that result.

Practice Quiz

Test your knowledge with interactive questions

$70:(14\times5)=$

FAQ

Everything you need to know about this question

Why can't I just divide 300 by 5 first?

+

The parentheses tell you that $5 \times 6$ must be calculated as one unit first! Without parentheses, you'd work left to right, but parentheses override that rule.

What does the colon (:) mean in this problem?

+

The colon (:) is just another way to write division. So $300:(5 \times 6)$ means exactly the same as $300 \div (5 \times 6)$ .

How do I remember PEMDAS with this problem?

+

P comes first in PEMDAS! That means Parentheses before everything else. So solve $(5 \times 6)$ first, then do the division.

What if I calculated 300 ÷ 5 ÷ 6 instead?

+

That would give you $300 \div 5 \div 6 = 60 \div 6 = 10$ , which happens to be correct! But this only works by coincidence. Always follow the parentheses to avoid mistakes on other problems.

Can I check my answer a different way?

+

Yes! Work backwards: if $10 \times (5 \times 6) = 10 \times 30 = 300$ , then your division was correct. This multiplication check always works for division problems.

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Solve 300÷(5×6): Order of Operations Division Problem

Order of Operations with Parentheses First

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