Question

For each of the following pairs of rational numbers, place a greater than symbol, >, a less than symbol, <, or an equality symbol, =, in the square to make the statement true.

Answer 1

I chow you how to solve for (d) and (i) and you could do the rest by yourself:

The best way to solve this operations is convert the numbers to a one form and then compare.

For (d)

`\begin{gathered} (7)/(3)=(6+1)/(3)=(6)/(3)+(1)/(3)=2+(1)/(3)=2(1)/(3)=2.333 \\ (13)/(5)=(10+3)/(5)=(10)/(5)+(3)/(5)=2+(3)/(5)=2(3)/(5)=2.6 \\ So, \\ (7)/(3)<(13)/(5) \end{gathered}`

Now for (i), take into account that this numbers are negative:

`\begin{gathered} -11.5=-11.5\cdot(4)/(4)=-(11.5\cdot4)/(4)=-(46)/(4) \\ So,\text{ } \\ -(46)/(4)<-(31)/(4) \end{gathered}`

Note that 46/4 is greater than 31/4, but -46/4 is lower than -31/4.

Also note that in this example I find to equalize the denominator of the numbers adn then you can compare the numerators.