Question

2) Determine an inequality (<, >, or =) for each pair of fractions.

a. 4/11 and 5/14
b. -3/7 and -4/9

On number 2 I don’t know where to start but I need help showing full work!
And then knowing which answers go on 2a) & 2b) blanks I need help On my college math!

Answer 1

2) a.
`(4)/(11) > (5)/(14)`

2) b.
`-(3)/(7) >-(4)/(9)`

Explanation:

2) a. Fraction
`(4)/(11)` can be written as
`(4 * 14)/(11* 14) = (56)/(11* 14)` ....... (1)

Again, fraction
`(5)/(14)` can be written as
`(5 * 11)/(14 * 11)= (55)/(14 * 11)` ........ (2)

Now, comparing expressions (1) and (2) we can say

`(56)/(11* 14)>(55)/(14 * 11)`

i.e.
`(4)/(11) > (5)/(14)`

2) b. Fraction
`(3)/(17)` can be written as
`(3 * 9)/(7* 9) = (27)/(7* 9)` ....... (3)

Again, fraction
`(4)/(9)` can be written as
`(4 * 7)/(9 * 7)= (28)/(9 * 7)` ........ (4)

Now, comparing expressions (3) and (4) we can say

`(28)/(9* 7)>(27)/(7 * 9)`

i.e.
`(4)/(9) > (3)/(7)`

i.e.
`-(4)/(9) < -(3)/(7)` {Since multiplication with a negative number on both sides of an inequality will change sign of the inequality.}

i.e.
`-(3)/(7) >-(4)/(9)`

(Answer)