Arithmetic Expressions | A

Question 5

What happens to the value of an expression if we increase or decrease the value of one of its terms?

Some expressions are given in following three columns. In each column, one or more terms are changed from the first expression. Go through the example (in the first column) and fill the blanks, doing as little computation as possible.

Solution

Understand the Question

When we increase or decrease the value of a term in an addition expression, the total sum changes by the exact same amount.
If a term is increased by $n$ , the value of the expression increases by $n$ .
If a term is decreased by $n$ , the value of the expression decreases by $n$ .
When multiple terms are altered, the overall value changes by the net sum of the individual changes, allowing us to find new values with minimal computation.

Step 1 · Column 1 Calculations

Diagram 1

Base expression: $53 + (-16) = 37$

Second expression ( $54$ is $1$ more than $53$ ): $54 + (-16) = 37 + 1 = 38$

Third expression ( $-15$ is $1$ more than $-16$ ): $53 + (-15) = 37 + 1 = 38$

Step 2 · Column 2 Calculations

Diagram 2

Base expression: $53 + (-16) = 37$

Second expression ( $52$ is $1$ less than $53$ ): $52 + (-16) = 37 - 1 = 36$

Third expression ( $-17$ is $1$ less than $-16$ ): $53 + (-17) = 37 - 1 = 36$

Step 3 · Column 3 Calculations

Diagram 3

First expression:

\begin{aligned} (-87) + (-16) &= -(87 + 16) \\ &= -103 \end{aligned}

Second expression ( $-88$ is $1$ less than $-87$ , and $-15$ is $1$ more than $-16$ , net change $= -1 + 1 = 0$ ): $(-88) + (-15) = -103$

Third expression ( $-86$ is $1$ more than $-87$ , and $-18$ is $2$ less than $-16$ , net change $= 1 - 2 = -1$ ): $(-86) + (-18) = -103 - 1 = -104$

Fourth expression ( $-97$ is $10$ less than $-87$ , and $-26$ is $10$ less than $-16$ , net change $= -10 - 10 = -20$ ): $(-97) + (-26) = -103 - 20 = -123$

Answer

Column 1:

Second expression: $38$
Third expression: $38$

Column 2:

Second expression: $36$
Third expression: $36$

Column 3:

First expression: $-103$
Second expression: $-103$
Third expression: $-104$
Fourth expression: $-123$

Common Mistakes

Negative Number Direction: Incorrectly assuming that $-15$ is smaller than $-16$ . In reality, $-15 > -16$ (an increase of $+1$ ), while $-17 < -16$ (a decrease of $-1$ ).
Recalculating from Scratch: Computing the entire arithmetic sum directly instead of tracking the relative change ( $+1$ , $-1$ , $-20$ , etc.) from the reference expression.

Question 5

More questions in A

Expression Engineer!