Question

1. Consider the rational numbers 4/13 and 3/10 .

A. Which number is the larger number? Explain.
B. What is a rational number between the two given numbers?

Answer 1

There are infinite rational numbers between the two numbers you have given
Why not start with the one midway between the two?
Since 3/10 = 39/130 < 4/13 = 40/130
a = (39 + 40)/260 = 79/260
will do for a start.

Answer 2

A. 4/13 3/10

find a common denominator which is 130

mult. by 10/10 and the second one by 13/13

40/130 and 39/130

so, that means 4/13 is larger because after you find a common denominator, compare the top numbers to find the larger and 40 is larger than 39.

B. a rational number between them would be 39.5/130