Question 5

Changing a term in an addition changes the sum by the same amount.

Step 1 — Column 1 Calculations

We start with the first expression. The sum of 53 and -16 is 37.

$53 + (-16) = 37$

Next, we look at the second expression. The first number, 54, is one more than 53. The second number, -16, stays the same. So, the sum will be one more than 37.

$54 + (-16) = 37 + 1$

$\boxed{38}$

Now, we consider the third expression. The first number, 53, stays the same. The second number is -15. We compare -15 with -16. -15 is one more than -16. So, the sum will be one more than 37.

$53 + (-15) = 37 + 1$

$\boxed{38}$

Step 2 — Column 2 Calculations

We use the first expression again. The sum of 53 and -16 is 37.

$53 + (-16) = 37$

Next, we look at the second expression. The first number, 52, is one less than 53. The second number, -16, stays the same. So, the sum will be one less than 37.

$52 + (-16) = 37 - 1$

$\boxed{36}$

Now, we consider the third expression. The first number, 53, stays the same. The second number is -17. We compare -17 with -16. -17 is one less than -16. So, the sum will be one less than 37.

$53 + (-17) = 37 - 1$

$\boxed{36}$

Step 3 — Column 3 Calculations

Let us find the sum for the first expression. We add -87 and -16.

$(-87) + (-16) = -(87 + 16)$

$= -103$

$\boxed{-103}$

Next, we look at the second expression. The first number, -88, is one less than -87. The second number, -15, is one more than -16. One term decreased by 1. The other term increased by 1. The total change to the sum is zero. So, the sum remains the same.

$(-88) + (-15) = -103$

$\boxed{-103}$

Now, we consider the third expression. The first number, -86, is one more than -87. The second number, -18, is two less than -16. One term increased by 1. The other term decreased by 2. The total change to the sum is $1 + (-2) = -1$. So, the sum will be one less than -103.

$(-86) + (-18) = -103 - 1$

$\boxed{-104}$

Finally, we look at the fourth expression. The first number, -97, is ten less than -87. The second number, -26, is ten less than -16. One term decreased by 10. The other term decreased by 10. The total change to the sum is $(-10) + (-10) = -20$. So, the sum will be twenty less than -103.

$(-97) + (-26) = -103 - 20$

$\boxed{-123}$

Answer

(i) Column 1, second expression: 38 (ii) Column 1, third expression: 38 (iii) Column 2, second expression: 36 (iv) Column 2, third expression: 36 (v) Column 3, first expression: -103 (vi) Column 3, second expression: -103 (vii) Column 3, third expression: -104 (viii) Column 3, fourth expression: -123