In the other exercises that you did above, did you notice that subtracting a negative number was the same as adding the corresponding positive number?

Question

Homi · Accepted Answer

Understand the Question

Subtracting a positive number from a value means moving in the negative direction (to the left on a horizontal number line or downwards in a lift).
Subtracting a negative number reverses this direction, resulting in movement in the positive direction (to the right or upwards).
In general, for any integer $a$ and positive integer $b$ : $a - (-b) = a + b$

Step 1 · Subtracting a Negative Number on the Number Line

On a number line, subtracting a positive number corresponds to moving to the left: $5 - 3 = 2$

Subtracting a negative number reverses the direction of movement from left to right, which is equivalent to adding a positive number. Diagram 1

\begin{aligned} 5 - (-3) &= 5 + 3 \\ &= 8 \end{aligned}

Step 2 · Verification Using the Lift Analogy

Consider a vertical lift where the ground floor is $0$ , floors above are positive, and floors below are negative:

Moving down $3$ floors from floor $5$ : $5 - 3 = 2$
Moving up $3$ floors from floor $5$ : $5 + 3 = 8$
Undoing the action of going down $3$ floors (subtracting $-3$ ) means moving up $3$ floors:

\begin{aligned} 5 - (-3) &= 5 + 3 \\ &= 8 \end{aligned}

Thus, subtracting a negative number is always equivalent to adding its positive counterpart.

Answer

Yes, subtracting a negative number is the same as adding the corresponding positive number ( $a - (-b) = a + b$ ).

Common Mistakes

Double Negative Confusion: Incorrectly concluding that two negative signs next to each other in $a - (-b)$ remain negative instead of turning into an addition operation ( $a + b$ ).
Number Line Direction Error: Moving to the left instead of right when subtracting a negative value.

Question 12

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