Exercise 11 Page 45

We want to find the distance between us and our friend. We know that we are 1.237 miles to the west of school and that our friend is 0.56 miles to the east of school. We can visualize this situation on the number line if we place the school at 0. This means that the negative numbers represent moving to the west and the positive numbers represent moving to the east.

As we can see on the number line, we are located at -1.237 and our friend is at 0.56. We want to find how far we are from our friend. Recall that the distance between any two numbers on a number line is the absolute value of the difference of the two numbers.

Alternative Solution

We want to find the distance between us and our friend. We know that our friend is at 0.56 miles, the school is at 0 miles, and we are at -1.237 miles. To find the distance, we will start by recalling some facts about distance and absolute value.

• The absolute value of a number is its distance from 0 on the number line.
• Since distance is always greater than or equal to 0, the absolute value of any number is greater than or equal to 0.

Let's consider the distance between different numbers and 0 on the number line.

The distance between our friend and the school is the absolute value of 0.56. This also means that the distance between the school and us is the absolute value of - 1.237. We can calculate how far away we are from our friend if we add the two distances. Let's do it! | 0.56|+| - 1.237|&=0.56+1.237 &=1.797 We found that we and our friend are 1.797 miles apart.