Question

Which of the following is the smallest fraction?

4/16
2/9
1/3
7/6
7/11

Answer 1

2/9 seems to yield the smallest decimal.

Answer 2

If you want to actually prove this (without computing the decimals), you can compare each fraction as follows:
4/16 and 2/9
multiply both by 16
4 and 32/9
or,
4 and 3+5/9
since 4>3+5/9 it follows that
4/16>2/9

Next,
2/9 and 1/3
multiply both by 9
2 and 3
since 2<3
2/9<1/3

Now compare
1/3 and 4/16. multiply both by 3
1 and 3/4
so,
1/3>4/16

We have,
2/9<4/16<1/3
so far.

now, 7/6 is greater than 1 and 2/9 is less than one so, 2/9<7/6.
comparing 2/9 with 7/11; multiply both by 9:
2 and 5+8/11
so,
2/9<7/11

In all cases 2/9 is the smallest.