Solve the Complex Negative Number Equation: -55 - (-94 - (-32)) + 12 ÷ 3/4 = ?

Q: Why does subtracting a negative become addition?

Think of it as removing debt! If you subtract a debt of $32 (which is negative), you're actually gaining $32. So $-94 - (-32)$ means "start at -94 and remove a debt of 32," giving you $-94 + 32 = -62$.

Q: How do I handle nested parentheses without getting confused?

Work from inside out! Start with the innermost parentheses first: $(-32)$, then $(-94 - (-32))$, and finally the outer expression. Use different colored pens or highlight each level as you work through it.

Q: What's the difference between 12 ÷ 3/4 and 12 ÷ 3 ÷ 4?

$12 ÷ \frac{3}{4}$ means dividing by the fraction 3/4, so you multiply by its reciprocal: $12 × \frac{4}{3} = 16$. But $12 ÷ 3 ÷ 4 = 4 ÷ 4 = 1$ gives a completely different answer!

Q: How can I check if my order of operations is correct?

Use the PEMDAS acronym: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right). Write each step clearly and double-check that you're following this exact sequence.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:04 Negative times negative is always positive

00:15 Division is also multiplication by the inverse

00:25 Negative times positive is always negative

00:28 Factor 12 into factors 4 and 3

00:31 Reduce what's possible

00:37 Use the distribution law and split 55 into 50 and 5

00:41 Use the distribution law and split 94 into 90 and 4

00:46 Use the distribution law and split 32 into 30 and 2

00:50 Use the distribution law and split 16 into 10 and 6

00:57 Use the substitution law and arrange the exercise to make it easier to solve

01:06 Combine the tens

01:10 Combine the ones

01:13 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

$-55-(-94-(-32))+12:\frac{3}{4}=\text{?}$

2

Step-by-step solution

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

Step 1: Simplify the nested expressions and handle the negative signs.
Step 2: Perform the division operation involving the fraction.
Step 3: Combine the results from the two operations.

Now, let's work through each step:

Step 1: Address the nested subtraction.

First, simplify the innermost expression: $-94 - (-32)$ .

Recall that subtracting a negative is equivalent to addition: $-94 - (-32) = -94 + 32 = -62$ .

Now substitute this result back into the main expression: $-55 - (-62)$ .

Again, subtracting a negative is addition: $-55 - (-62) = -55 + 62 = 7$ .

Step 2: Resolve the division by a fraction.

Calculate $12 \div \frac{3}{4}$ :

Dividing by a fraction is equivalent to multiplying by its reciprocal: $12 \times \frac{4}{3} = \frac{48}{3} = 16$ .

Step 3: Combine results.

Now we add the results from steps 1 and 2: $7 + 16 = 23$ .

Therefore, the solution to the problem is $23$ .

3

Final Answer

$23$

Key Points to Remember

Essential concepts to master this topic

Parentheses First: Resolve innermost expressions before working outward completely
Technique: Subtracting negative becomes addition: $-94 - (-32) = -94 + 32$
Check: Follow PEMDAS strictly and verify final calculation: $7 + 16 = 23$ ✓

Common Mistakes

Avoid these frequent errors

Incorrectly handling double negatives in nested expressions
Don't change $-55 - (-94 - (-32))$ to $-55 - (-94 + (-32))$ = wrong signs throughout! This creates cascading errors in every step. Always work from innermost parentheses outward, carefully applying the rule that subtracting a negative equals adding a positive.

Practice Quiz

Test your knowledge with interactive questions

$70:(14\times5)=$

FAQ

Everything you need to know about this question

Why does subtracting a negative become addition?

+

Think of it as removing debt! If you subtract a debt of $32 (which is negative), you're actually gaining $32. So $-94 - (-32)$ means "start at -94 and remove a debt of 32," giving you $-94 + 32 = -62$ .

How do I handle nested parentheses without getting confused?

+

Work from inside out! Start with the innermost parentheses first: $(-32)$ , then $(-94 - (-32))$ , and finally the outer expression. Use different colored pens or highlight each level as you work through it.

What's the difference between 12 ÷ 3/4 and 12 ÷ 3 ÷ 4?

+

$12 ÷ \frac{3}{4}$ means dividing by the fraction 3/4, so you multiply by its reciprocal: $12 × \frac{4}{3} = 16$ . But $12 ÷ 3 ÷ 4 = 4 ÷ 4 = 1$ gives a completely different answer!

How can I check if my order of operations is correct?

+

Use the PEMDAS acronym: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right). Write each step clearly and double-check that you're following this exact sequence.

What if I get a different answer than the choices given?

+

Go back and check your work step by step! Common errors include: mixing up signs with negatives, forgetting to multiply by the reciprocal when dividing by fractions, or rushing through parentheses. Take your time with each operation.

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Solve the Complex Negative Number Equation: -55 - (-94 - (-32)) + 12 ÷ 3/4 = ?

Order of Operations with Nested Negatives

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