Question

1 7/9÷ 4/5What is one and seven ninths divided by four fifths?

Answer 1

The operation we have to solve is:

$1\frac{7}{9}\div\frac{4}{5}$

The steps to solve are the following:

Step 1. Convert the first mixed number 1 7/9 to a fraction.

We convert 1 7/9 to a fraction following the general rule:

$A\frac{b}{c}=\frac{A\times c+b}{c}$

Applying this to 1 7/9:

$1\frac{7}{9}=\frac{1\times9+7}{9}$

which is equal to:

$1\frac{7}{9}=\frac{16}{9}$

Substituting this, the operation we have to solve is:

$\frac{17}{9}\div\frac{4}{5}$

Step 2. Now we apply the following rule to divide fractions:

$\frac{a}{b}\div\frac{d}{c}=\frac{a\times c}{b\times d}$

And the result is:

$\frac{17}{9}\div\frac{4}{5}=\frac{17\times5}{9\times4}$

which is equal to:

$\frac{17}{9}\div\frac{4}{5}=\frac{85}{36}$

Step 3. Convert the result to a mixed number.

In step 2 we got 85/36 as a result, but we can convert that fraction to a mixed number considering that 36 fits two times in the number 85 (because 36x2=72) and we have 85-72=13 out 36 left:

$\frac{85}{36}=2\frac{13}{36}$

Answer:

$2\frac{13}{36}$