Question

Tisha tried to evaluate an expression. Here is her work:
490÷729–23
=
490÷499–23 Step 1
=
109–23 Step 2
=
90–23 Step 3
=
883 Step 4
=
264 Step 5
Is Tisha's work correct?

Answer 1

Let's go through Tisha's steps to see if her calculations are correct.

1. **Starting expression:**
\[
490 \div 729 - 23
\]

2. **Step 1:**
Tisha wrote:
\[
490 \div 499 - 23
\]
This is incorrect. The division should be \(490 \div 729\), not \(490 \div 499\).

3. **Step 2:**
Tisha wrote:
\[
109 - 23
\]
This is based on her incorrect previous step and cannot be evaluated as accurate since she didn't calculate \(490 \div 729\).

4. **Step 3:**
Tisha wrote:
\[
90 - 23
\]
Again, this is based on incorrect prior calculations.

5. **Step 4:**
Tisha concludes:
\[
= 883
\]
This is also not based on valid calculations.

6. **Step 5:**
Tisha wrote:
\[
= 264
\]
This too is incorrect.

Since Tisha made an error in Step 1, all subsequent steps are based on that error.

Let's compute the expression correctly:
1. Calculate \(490 \div 729\):
\[
490 \div 729 \approx 0.6717
\]

2. Then subtract \(23\) from that result:
\[
0.6717 - 23 \approx -22.3283
\]

Tisha's work is incorrect, and the correct value of the expression \(490 \div 729 - 23\) is approximately \(-22.3283\).