Divide ^{2}/_{9} with 1 ^{3}/_{7}. Give the answer in the simplest form.

Let's write down these fractions:

Notice that 1 ^{3}/_{7} is a mixed fraction. We need to convert it into an improper fraction before we can start dividing.

The conversion is shown below:

After the conversion, we have:

Now, we can divide these fractions. To do so, we change the division to multiplication, provided that we also change the divisor to its reciprocal.

After these changes, we can just multiply the fractions together.

Here, we have the resulting fraction as ^{7}/_{45}. Clearly, the answer is A.

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