Question

Add:

(a)$-2+\left(-5\right)$

(b)$-2+5$

(c)$2+\left(-5\right)$$2+\left(-5\right)$

Short answer

(a)$-7$

(b) 3

(c)$-3$

Step-by-step solution

Part (a). Step 1. Given Information: 

Consider the given expression $-2+\left(-5\right)$.

Part (a). Step 2. Perform addition using drawings. 

The first number is $-2$and the second number is .

Draw 2 red circles first to represent $-2$and 5 red circles to represent $-5$.

In the above diagram, there are 7 red circles.

Since the red color is used to represent negative numbers, the above diagram implies that the result is $-7$.

So, the value is $-2+\left(-5\right)=-7$.

Part (b). Step 1. Given Information: 

Consider the given expression $-2+5$.

Part (b). Step 2. Perform addition using drawings.

The first number is $-2$and the second number is 5.

Draw 5 blue circles to represent the number 5 and 2 red circles to represent the number $-2$.

Note that each red circles cancels one blue circle so the value of the pair having one positive counter (blue circle) and one negative counter (red circle) is 0.

After cancelling two blue circles with two red circles, there remains three blue circles.

Since the blue color is used to represent positive numbers, the above diagram implies that the result is 3. So, the value is $-2+5=3$.

Part (c). Step 1. Given Information: 

Consider the given expression$2+\left(-5\right)$.

Part (c). Step 2. Perform addition using drawings.  

The first number is 2 and the second number is $-5$. Draw 2 blue circles to represent the number 2 and 5 red circles to represent the number $-5$.

Note that each red circles cancels one blue circle so the value of the pair having one positive counter (blue circle) and one negative counter (red circle) is 0.

After cancelling two red circles by blue circles, there remains three red circles.

Since the red color is used represent negative numbers, the above diagram implies the result is $-3$. So, the result is $2+\left(-5\right)=-3$.