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

Video Solution

Solution Steps

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 Solution

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

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 $23$ .