Question

Debbie tried to evaluate an expression. Here is her work:
23+57–32–16÷2
=
(8+57–9)–16÷2 Step 1
=
(8+35–9)–16÷2 Step 2
=
(43–9)–16÷2 Step 3
=
34–16÷2 Step 4
=
18÷2 Step 5
=
9 Step 6
Is Debbie's work correct?




Questions

Answer 1

Let’s evaluate the expression \(23 + 57 - 32 - 16 \div 2\) step by step to see if Debbie's work is correct.

The order of operations (PEMDAS/BODMAS) dictates that we handle division and multiplication before addition and subtraction.

1. **Evaluate the division first:**
\[
16 \div 2 = 8
\]
Now substitute this back into the expression:
\[
23 + 57 - 32 - 8
\]

2. **Now simplify the expression from left to right:**
- First, calculate \(23 + 57\):
\[
23 + 57 = 80
\]
- Then, subtract \(32\):
\[
80 - 32 = 48
\]
- Finally, subtract \(8\):
\[
48 - 8 = 40
\]

So, the correct value of the expression \(23 + 57 - 32 - 16 \div 2\) is **40**.

Now let’s examine Debbie's work:

- **Step 1:** She rewrote it as \((8 + 57 – 9) – 16 ÷ 2\). This seems incorrect as she did not maintain the original numbers.
- **Step 2:** She simplified to \((8 + 35 – 9) – 16 ÷ 2\), which is also not correct.
- Steps 3 to 6 follow in a way that continues to deviate from the original expression, leading her to an incorrect result of 9.

In conclusion, **Debbie's work is not correct**. The proper result of the expression is **40**, not 9.