Let's analyze the mistake Kay made when she added 253 and 14 and came up with a sum of 393.
1. Correct Sum Calculation:
First, let's find the correct sum of 253 and 14:
[tex]\[
253 + 14 = 267
\][/tex]
2. Difference Between Kay's Sum and the Correct Sum:
Kay's incorrect sum is 393. To find the error, we calculate:
[tex]\[
393 - 267 = 126
\][/tex]
3. Identifying Possible Mistakes:
- Lining Up Digits: Kay's mistake does not indicate a problem with lining up digits correctly. The error is a specific numerical miscalculation, not a place value misalignment.
- Addition of Ones Place:
Kay correctly added the ones place. The addition of 3 ones (from 253) and 4 ones (from 14) should yield 7 ones:
[tex]\[
3 + 4 = 7
\][/tex]
This matches the correct calculation.
- Addition of Tens Place:
Kay correctly added the tens place. The addition of 5 tens (from 253) and 1 ten (from 14) should yield 6 tens:
[tex]\[
5 + 1 = 6
\][/tex]
This matches the correct calculation.
- Mistake 1: Adding 1 Hundred Instead of 1 Ten:
It seems Kay added 1 hundred instead of 1 ten:
[tex]\[
253 + 100 = 353
\][/tex]
Adding an extra hundred contributed significantly to the error.
- Mistake 2: Adding 4 Tens Instead of 4 Ones:
It also seems Kay added 4 tens instead of 4 ones:
[tex]\[
353 + 40 = 393
\][/tex]
By adding 40 (4 tens) instead of 4 (4 ones), she further increased the error to reach her incorrect sum.
4. Summarizing the Mistakes:
Based on the analysis, the errors include:
- Kay added 1 hundred to 253 instead of 1 ten.
- Kay added 4 tens to 253 instead of 4 ones.
Therefore, the final result of Kay's errors includes the two specific additions:
- Kay added 1 hundred to 253 instead of 1 ten.
- Kay added 4 tens to 253 instead of 4 ones.
