Which answer choice shows the correct way to use compensation to find the difference:
1
,
518
−
1
,
294
?
A.
subtract 1,300, add 6
B.
subtract 1,300, subtract 6
C.
subtract 1,200, add 6
D.
subtract 1,200, subtract 6
Add or subtract.
(m2 – m – 3) + (m – 4)
A. m2 + m – 1
B. m2 + 2m – 7
C. m2 – 7
D. m2 – 1
Simplify the expression by combining like terms:
(m2 – m – 3) + (m – 4) = m2 – m – 3 + m – 4
= m2 + (-m + m) + (-3 – 4)
= m2 – 7
Answer: C. m2 – 7
The correct way to use compensation to find the difference between 1,518 and 1,294 is:
C. subtract 1,200, add 6
To use compensation to find the difference between 1,518 and 1,294, you would first round each number to a more convenient value, then subtract or add the difference. Here's how you can do it:
1. Round 1,518 to the nearest hundred: 1,500
2. Round 1,294 to the nearest hundred: 1,300
Now, you have two rounded numbers: 1,500 and 1,300. The difference between these rounded numbers is 200 (1,500 - 1,300).
Finally, you need to adjust the difference to get the actual difference between the original numbers:
- Original difference: 1,518 - 1,294 = 224
- Rounded difference: 200
To find the actual difference, you need to compensate for the rounding. Since the rounded difference is 200, and the actual difference is 224, you need to "add back" the difference.
So, the correct answer choice that shows how to use compensation is:
A. subtract 1,300, add 6
By subtracting 1,300, you represent the rounded value of 1,518 (1,500), and by adding 6, you compensate for the difference between the rounded and actual values.