Solve: (400÷(-5)-[-2(93-61)])÷4 | Order of Operations Challenge

Q: What does the colon symbol mean in 400÷(-5)?

The colon : means division, just like the ÷ symbol. So $ 400:(-5) $ is the same as $ 400÷(-5) = -80 $.

Q: How do I handle the double negative in -(-64)?

A double negative becomes positive! Think of it as: -(-64) = +64. So -80 - (-64) becomes -80 + 64 = -16.

Q: Should I solve the brackets [...] first or the parentheses () first?

Always work from the innermost parentheses outward. So solve (93-61) first, then use that result in the brackets [-2(32)].

Q: Why is my final answer negative?

The final answer is negative because $ \frac{-16}{4} = -4 $. When you divide a negative number by a positive number, the result is always negative!

Order of Operations with Negative Numbers

Solve the following equation:

$\frac{400\colon(-5)-\lbrack-2(93-61)\rbrack}{4}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:13 Let's begin and think about the steps we'll follow.

00:17 Remember, always calculate the parts in parentheses first.

00:53 When you multiply two negative numbers, you get a positive result.

00:59 Multiplication and division come before addition and subtraction.

01:18 And that's how we find the solution. Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following equation:

$\frac{400\colon(-5)-\lbrack-2(93-61)\rbrack}{4}=$

Step-by-step solution

We begin by addressing the numerator of the fraction.

First we solve the division exercise and the exercise within the parentheses:

$400:(-5)=-80$

$(93-61)=32$

We obtain the following:

$\frac{-80-(-2\times32)}{4}=$

We then solve the parentheses in the numerator of the fraction:

$\frac{-80-(-64)}{4}=$

Let's remember that a negative times a negative equals a positive:

$\frac{-80+64}{4}=$

$\frac{-16}{4}=-4$

Final Answer

$-4$

Key Points to Remember

Essential concepts to master this topic

PEMDAS Rule: Parentheses first, then division, then brackets, finally division
Technique: Calculate $400÷(-5) = -80$ and $(93-61) = 32$ separately first
Check: Substitute back: $\frac{-80-(-64)}{4} = \frac{-16}{4} = -4$ ✓

Common Mistakes

Avoid these frequent errors

Ignoring negative signs in multiplication
Don't skip the negative signs when calculating -2(32) = -64! Students often write +64 instead of -64, which gives +16 instead of -4. Always track negative signs carefully through each step of PEMDAS.

Practice Quiz

Test your knowledge with interactive questions

Solve the following exercise:

$12+3\cdot0=$

FAQ

Everything you need to know about this question

Why do I get confused with all the negative signs?

Negative signs can be tricky! Write each step clearly and remember: negative times positive equals negative. So -2 × 32 = -64, not +64.

What does the colon symbol mean in 400÷(-5)?

The colon : means division, just like the ÷ symbol. So $400:(-5)$ is the same as $400÷(-5) = -80$ .

How do I handle the double negative in -(-64)?

A double negative becomes positive! Think of it as: -(-64) = +64. So -80 - (-64) becomes -80 + 64 = -16.

Should I solve the brackets [...] first or the parentheses () first?

Always work from the innermost parentheses outward. So solve (93-61) first, then use that result in the brackets [-2(32)].

Why is my final answer negative?

The final answer is negative because $\frac{-16}{4} = -4$ . When you divide a negative number by a positive number, the result is always negative!

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Solve: (400÷(-5)-[-2(93-61)])÷4 | Order of Operations Challenge

Order of Operations with Negative Numbers

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why do I get confused with all the negative signs?

What does the colon symbol mean in 400÷(-5)?

How do I handle the double negative in -(-64)?

Should I solve the brackets [...] first or the parentheses () first?

Why is my final answer negative?

🌟 Unlock Your Math Potential

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