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

Question

Jameson Allen · Accepted Answer

undefined To divide mixed numbers, first convert them to improper fractions, then invert the divisor and multiply.

$3\frac{5}{7} \div 2\frac{7}{9} = \frac{22}{7} \div \frac{25}{9}$

Invert the divisor: $\frac{22}{7} \times \frac{9}{25}$

Multiply the fractions: $\frac{22 \times 9}{7 \times 25}$

Simplify the fraction: $\frac{198}{175}$

Convert the improper fraction to a mixed number, if necessary.

Abigail Allen · Answer

#234/175 or 1 59/175# = #3 5/7=26/7# = #2 7/9=25/9# = #26/7/25/9# = #26/7*9/25# Multiply horizontally: #234/175 or 1 59/175# #(=1.337)#

Julia Adams · Answer

#234/175 or 1 59/175#

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 5/7 = 26/7# #leftarrowcolor(red)(((3*7)+5)/7#

#2 7/9 = 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:

#26/7 divide 25/9 => 26/7 * 9/25#

Multiply across to solve:

#26/7 * 9/25 => (26*9)/(7*25)#

#=234/175 or 1 59/175#