Refer to Example 1. Find the sum visually.−2 + (−2)EXAMPLE 1 Adding integers visuallyAdd v...

Refer to Example 1. Find the sum visually.

−2 + (−2)

EXAMPLE 1 Adding integers visually

Add visually, using the symbols and .

(a) 3 + 2

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(b) −6 + 4

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(c) 2 + (−3)

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(d) −5 + (−2)

Solution

(a) Draw three positive units and then draw two more positive units.

 

Because no zeros were formed, the sum is five positive units, or 5.

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(b) Draw six negative units and then draw four positive units.

 

Ignoring the zeros that were formed, the sum is two negative units, or −2.

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(c) Draw two positive and three negative units.

 

The sum is −1.

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(d)

The sum is −7.

Another way to add integers visually is to use a number line. For example, to add 4 + (−3) start at 0 (the origin) and draw an arrow to the right 4 units long from 0 to 4. The number −3 is a negative number, so draw an arrow 3 units long to the left, starting at the tip of the first arrow. See Figure 1. The tip of the second arrow is at 1, which equals the sum of 4 and −3.

Figure 1

To find the sum −2 + (−3), draw an arrow 2 units long to the left, starting at the origin. Then draw an arrow 3 units long to the left, starting at the tip of the first arrow, which is located at −2. See Figure 1. Because the tip of the second arrow coincides with −5 on the number line, the sum of −2 and −3 is −5.