Solve: 200 ÷ (-200×200) - Complete Order of Operations

Q: Why don't I just work left to right like in reading?

Math has special rules called order of operations! When division and multiplication appear together, you work left to right, but you must first identify what you're dividing BY. Here, you're dividing by the entire expression $ (-200\times200) $.

Q: Why is the answer negative?

When you divide a positive number (200) by a negative number (-40000), the result is always negative. Think: $ \frac{200}{-40000} = -\frac{1}{200} $, which is negative!

Q: Can I rewrite this as a fraction to make it clearer?

Absolutely! Writing $ \frac{200}{-200\times200} $ makes it much clearer what you're dividing by. Then simplify: $ \frac{200}{-40000} = -\frac{1}{200} $.

Q: Wait, shouldn't the answer be -1/200, not -200?

Great catch! Let's check: $ \frac{200}{-200\times200} = \frac{200}{-40000} = -\frac{1}{200} $. You're absolutely right - the answer should be $ -\frac{1}{200} $, not -200!

Order of Operations with Mixed Division

$200:-200\cdot200=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Let's write division as a fraction

00:11 Positive divided by negative always equals negative

00:24 Let's reduce what we can

00:29 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

$200:-200\cdot200=$

Step-by-step solution

Let's solve the exercise from left to right.

First, we'll write the division problem in the form of a fraction:

$\frac{200}{-200}\times200=$

We should note that we are dividing a positive number by a negative number, so the result will necessarily be a negative number:

$-\frac{200}{200}\times200=$

Let's simplify the 200 and we get:

$-200$

Final Answer

$-200$

Key Points to Remember

Essential concepts to master this topic

Rule: Division and multiplication have equal priority, work left to right
Technique: Rewrite $200:(-200\times200)$ as $\frac{200}{-200}\times200$
Check: $\frac{200}{-200} = -1$ , then $-1 \times 200 = -200$ ✓

Common Mistakes

Avoid these frequent errors

Working left to right instead of following order of operations
Don't solve 200÷(-200) first = -1, then multiply by 200! This ignores order of operations where multiplication and division are equal priority. Always identify what's in the divisor: here it's (-200×200), so calculate that first.

Practice Quiz

Test your knowledge with interactive questions

What will be the sign of the result of the next exercise?

$(-2)\cdot(-4)=$

FAQ

Everything you need to know about this question

Why don't I just work left to right like in reading?

Math has special rules called order of operations! When division and multiplication appear together, you work left to right, but you must first identify what you're dividing BY. Here, you're dividing by the entire expression $(-200\times200)$ .

How do I know what the divisor is in this problem?

Look for the division symbol (:). Everything after it until the next operation of equal or lower priority becomes your divisor. Here it's $(-200\times200)$ , which equals $-40000$ .

Why is the answer negative?

When you divide a positive number (200) by a negative number (-40000), the result is always negative. Think: $\frac{200}{-40000} = -\frac{1}{200}$ , which is negative!

Can I rewrite this as a fraction to make it clearer?

Absolutely! Writing $\frac{200}{-200\times200}$ makes it much clearer what you're dividing by. Then simplify: $\frac{200}{-40000} = -\frac{1}{200}$ .

Wait, shouldn't the answer be -1/200, not -200?

Great catch! Let's check: $\frac{200}{-200\times200} = \frac{200}{-40000} = -\frac{1}{200}$ . You're absolutely right - the answer should be $-\frac{1}{200}$ , not -200!

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