Introduction to Integers

Example 3.1

Draw a number line. Mark 0 in the center and label several units to the left and right.

1. To plot 3, start at 0 and count three units to the right. Place a point as shown in Figure 3.7.

Figure 3.7

2. To plot −3, start at 0 and count three units to the left. Place a point as shown in Figure 3.8.

Figure 3.8

3. To plot −2, start at 0 and count two units to the left. Place a point as shown in Figure 3.9.

Figure 3.9

Example 3.2

Begin by plotting the numbers on a number line as shown in Figure 3.12.

Figure 3.12

1. Compare 14 and 6.                  14___6

   14 is to the right of 6 on the number line.    
   
   \(14 > 6\)

2. Compare −1 and 9.                 −1___9

   −1 is to the left of 9 on the number line.    
   
   \(−1 < 9 \)

3. Compare −1 and −4.              −1___−4

   −1 is to the right of −4 on the number line.

   \(−1 > −4\)

4. Compare 2 and −20.             −2___−20

   2 is to the right of −20 on the number line.

   \(2 > −20\)

Example 3.3

1. The number −7 is the same distance from 0 as 7, but on the opposite side of 0. So −7 is the opposite of 7 as shown in Figure 3.14.

Figure 3.14

2. The number 10 is the same distance from 0 as −10, but on the opposite side of 0. So 10 is the opposite of −10 as shown in Figure 3.15.

Figure 3.15

Example 3.4

−(−6) The opposite of −6 is 6. 

Example 3.5