Question

Which shows the fractions in increasing order?

seven-ninths, one-sixth, two-ninths, five-sixths

one-sixth, two-ninths, seven-ninths, five-sixths

one-sixth, two-ninths, five-sixths, seven-ninths

one-sixth, five-sixths, two-ninths, seven-ninths

Answer 1

are you allowed to use a calculator?

Answer 2

there are several ways this question can be approached,
One is you can put each in the calculator, find out the decimal and then arrange it.. in this case,
7/9 = 0.78
1/6 = 0.17
2/9 = 0.22
5/6 = 0.83

can you arrange it from here?
1/6 > 2/9 > ....

Answer 3

you can also multiply the denominators with 6 or 9.. for example,
\[\frac{ 7 * 6 }{ 9*6} = \frac{ 42 }{ 54 }\and \frac{ 1 * 9 }{ 9*6} = \frac{ 9 }{ 54 }\]

Answer 4

do those respectively, then you should get 42/54, 9/54, 12/54, 45/54...
Then arrange in increasing order by looking at the numerators. Because we are dealing with fractions, the highest numerator yields the lowest decimal.