# How do you divide 3\frac { 5} { 7} \div 2\frac { 7} { 9}?

Mar 28, 2018

$\frac{234}{175} \mathmr{and} 1 \frac{59}{175}$

#### Explanation:

= $3 \frac{5}{7} = \frac{26}{7}$

= $2 \frac{7}{9} = \frac{25}{9}$

= $\frac{26}{7} / \frac{25}{9}$

= $\frac{26}{7} \cdot \frac{9}{25}$

Multiply straight across:

$\frac{234}{175} \mathmr{and} 1 \frac{59}{175}$

$\left(= 1.337\right)$

Mar 28, 2018

$\frac{234}{175} \mathmr{and} 1 \frac{59}{175}$

#### Explanation:

The first we thing we need to do to make it easier on us in dividing these mixed-number fractions, it to make them into improper fractions.

The way to make any mixed number into an improper fraction is to follow three easy steps:

• Multiply the whole number by the denominator

• Take that number and add it to the numerator

• Set that number over the original denominator

Knowing this, we can start to find our improper fractions:

$3 \frac{5}{7} = \frac{26}{7}$ leftarrowcolor(red)(((3*7)+5)/7

$2 \frac{7}{9} = \frac{25}{9}$ leftarrowcolor(red)(((2*9)+7)/9

When dividing fractions, we need to remember that we have to change the second fraction into its reciprocal and then multiply.

So, we should now have:

$\frac{26}{7} \div i \mathrm{de} \frac{25}{9} \implies \frac{26}{7} \cdot \frac{9}{25}$

Multiply across to solve:

$\frac{26}{7} \cdot \frac{9}{25} \implies \frac{26 \cdot 9}{7 \cdot 25}$

$= \frac{234}{175} \mathmr{and} 1 \frac{59}{175}$