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

Subtracting a negative number is like adding a positive number.

Step 1 — Subtracting a Negative Number

Let us think about numbers. We know that $5 - 3 = 2$ . This means starting at 5. Move 3 steps left.

Now, let us try $5 - (-3)$ . Subtracting means moving left. But we take away a negative number. This means we take away a 'go left' action. Taking away 'go left' is like 'go right'. So, $5 - (-3)$ means start at 5. Move 3 steps right.

$5 - (-3)$ $= 5 + 3$

$\boxed{8}$

We see $5 - (-3)$ is same as $5 + 3$ . So, subtracting a negative is like adding its positive.

Diagram 1

Step 2 — The Infinite Lift and Number Line

Imagine an infinite lift. It goes up forever. It goes down forever. The ground floor is 0. Floors above 0 are positive numbers. Floors below 0 are negative numbers. This lift is like a number line. Moving up is like adding positive numbers. Moving down is like adding negative numbers. Or, moving down is like subtracting positive numbers. Moving up is like subtracting negative numbers. For example, going down 3 floors is $-3$ . If you are at floor 5. Go down 3 floors.

$5 - 3$ $= 2$

If you are at floor 5. You want to go to floor 8. You need to go up 3 floors.

$5 + 3$ $= 8$

If you were at floor 5. Someone said 'undo going down 3 floors'. This is like $5 - (-3)$ . 'Undo going down 3 floors' means 'go up 3'.

$5 - (-3)$ $= 5 + 3$ $= 8$

The lift helps us see this clearly.

Answer

(i) Yes, subtracting a negative number is like adding a positive number. (ii) The "infinite lift" is like a number line. Both extend forever from zero. Moving up or right means adding positive numbers. Moving down or left means adding negative numbers. This shows how addition and subtraction change positions.

Question 12

Answer

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