Simplify.

Question

3.4 × 42 + 6 ÷ 3 – (5.7 + 2.1)
A.
48.6
B.
58.6
C.
60.2
D.
53.4

Answer 1

To simplify the given expression \(3.4 \times 42 + 6 \div 3 - (5.7 + 2.1)\), we need to follow the order of operations, often remembered by the acronym PEMDAS:

1. **P**arentheses
2. **E**xponents (not applicable here)
3. **M**ultiplication and **D**ivision (left to right)
4. **ddition and **S**ubtraction (left to right)

Let's break it down step by step:

1. **Parentheses:**
\[
5.7 + 2.1 = 7.8
\]

Now, the expression is:
\[
3.4 \times 42 + 6 \div 3 - 7.8
\]

2. **Multiplication and Division (left to right):**
First, we perform multiplication:
\[
3.4 \times 42 = 142.8
\]

Now the expression is:
\[
142.8 + 6 \div 3 - 7.8
\]

Next, we perform division:
\[
6 \div 3 = 2
\]

Now the expression is:
\[
142.8 + 2 - 7.8
\]

3. **Addition and Subtraction (left to right):**
First, we perform the addition:
\[
142.8 + 2 = 144.8
\]

Now the expression is:
\[
144.8 - 7.8
\]

Finally, we perform the subtraction:
\[
144.8 - 7.8 = 137
\]

So, the simplified result of the expression is \(137\). However, since this result doesn't match any of the options \(A. 48.6\), \(B. 58.6\), \(C. 60.2\), \(D. 53.4\), there may have been a mistake in the provided options.

Rechecking the initial calculations:

\[
3.4 \times 42 = 142.8
\]
\[
6 \div 3 = 2
\]
Adding both:
\[
142.8 + 2 = 144.8
\]
Subtracting \(7.8\):
\[
144.8 - 7.8 = 137
\]

*Indeed the simplified expression gives us the answer 137, none of the provided answer choices (A through D) match this correct calculation.