Let's look at each of the given addition problems to check if there is an error of addition by one. An error of addition by one means the sum given differs by exactly one from the actual sum.
### Option A: [tex]\( 6453 + 2345 = 8698 \)[/tex]
First, let's calculate the sum of [tex]\( 6453 \)[/tex] and [tex]\( 2345 \)[/tex]:
[tex]\[ 6453 + 2345 = 8798 \][/tex]
The given result is [tex]\( 8698 \)[/tex]. The difference between [tex]\( 8698 \)[/tex] and [tex]\( 8798 \)[/tex] is:
[tex]\[ 8798 - 8698 = 100 \][/tex]
This is not an error of addition by one.
### Option B: [tex]\( 2876 + 4123 = 6999 \)[/tex]
Next, let's calculate the sum of [tex]\( 2876 \)[/tex] and [tex]\( 4123 \)[/tex]:
[tex]\[ 2876 + 4123 = 6999 \][/tex]
The given result is also [tex]\( 6999 \)[/tex]. The actual sum matches the given result exactly. Therefore, this is not an error of addition by one.
### Option C: [tex]\( 4572 + 5324 = 9896 \)[/tex]
Now, calculate the sum of [tex]\( 4572 \)[/tex] and [tex]\( 5324 \)[/tex]:
[tex]\[ 4572 + 5324 = 9896 \][/tex]
The given result is also [tex]\( 9896 \)[/tex]. The actual sum matches the given result exactly. Hence, this is not an error of addition by one.
### Option D: [tex]\( 5621 + 2356 = 7977 \)[/tex]
Finally, calculate the sum of [tex]\( 5621 \)[/tex] and [tex]\( 2356 \)[/tex]:
[tex]\[ 5621 + 2356 = 7977 \][/tex]
The given result is also [tex]\( 7977 \)[/tex]. The actual sum matches the given result exactly. Therefore, this is not an error of addition by one.
Since none of the provided options show an error of addition by one, it appears that none of the given examples (A, B, C, or D) are errors of addition by one.
