Question

A teacher poses this problem: I am thinking of four numbers, a,b,c and d, where a < 0, b < 0, c > 0,and d > 0.What else do you need to know to plot the four numbers in the correct order on a number line? What two questions should you ask? Explain how the answers s would help you plot the numbers on a number line

Answer 1

1. Is a larger (more positive) than b?
2. Is c larger (more positive) than d?

Explanation:

Since a and b are less than zero, both are negative, but we don't know their order. We need to ask the order of a and b.

Since c and d are greater than zero, both are positive, but we don't know their order. We need to ask the order of c and d.

If you know a < b, then their order left to right on the number line will be a, b. Otherwise, it will be b, a.

If you know c < d, then their order left to right on the number line will be c, d. Otherwise it will be d, c.

Depending on the answers to the questions above, the order will be one of ...

• a, b, c, d
• b, a, c, d
• a, b, d, c
• b, a, d, c

As you can see, a and b will always be left of c and d.