Question

Suppose p/q, r/s, and t/u represent three rational numbers. If p/q is greater than r/s, and r/s is greater than t/u, compare p/q and t/u. Explain your reasoning.

p/q (< or >) t/u. On a number line, p/q is to the (right or left) of r/s, and r/s is to the (right or left) of t/u. So, p/q is to the (right or left) of t/u. ​

Answer 1

left to right, we have t/u < r/s < p/q.

Explanation:

The properties of ordering tell you ...

if a > b and b > c, then a > c

Here, we have a = p/q, b = r/s, c = t/u. The same property still applies:

if p/q > r/s and r/s > t/u, then p/q > t/u

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On a number line, the largest value is on the right:

p/q is right of r/s

r/s is right of t/u

therefore, ...

p/q is right of t/u