Simplify This Algebraic Expression: (78 - (39 - 47) - (95 + 3:3/5))?

Question

$78-(39-47)-(95+3:\frac{3}{5})=\text{?}$

00:00 Solve

00:05 Negative times positive is always negative

00:09 Negative times negative is always positive

00:16 Negative times positive is always negative

00:24 Division is also multiplication by the reciprocal

00:35 Let's reduce what we can

00:40 Use the distribution law and split 78 into 70 plus 8

00:44 Use the distribution law and split 39 into 30 and 9

00:48 Use the distribution law and split 47 into 40 plus 7

00:53 Use the distribution law and split 95 into 90 and 5

01:08 Use the substitution law and arrange the exercise to make it easier to solve

01:12 Collect the tens

01:16 Collect the ones

01:31 And this is the solution to the question

To solve the problem $78-(39-47)-(95+3:\frac{3}{5})$ , follow these steps:

Step 1: First, evaluate the expression within the first parentheses: $39-47 = -8$ . Thus, the expression becomes $78 - (-8) - (95 + 3:\frac{3}{5})$ .
Step 2: Simplifying $78 - (-8)$ gives $78 + 8 = 86$ . The expression is now $86 - (95 + 3:\frac{3}{5})$ .
Step 3: Calculate the division within the second parentheses $3:\frac{3}{5}$ by multiplying 3 by the reciprocal of $\frac{3}{5}$ , resulting in $3 \times \frac{5}{3} = 5$ . Thus, $95 + 5 = 100$ .
Step 4: Substitute back into the problem, yielding $86 - 100$ , which equals $-14$ .

Thus, the solution to the problem is $-14$ .

$-14$