How do you divide #\frac { 6} { 13} \div \frac { 8} { 9}#?

Question

Gabriel Agustin · Accepted Answer

#27/52# The method for #color(blue)"division of fractions"# is. #•" Leave the first fraction"# #•" Change division to multiplication"# #•" Invert (turn upside down) the second fraction"# #•" Cancel factors between numerator/denominator if poss."# #rArr6/13÷8/9# #=6/13xx9/8larr" multiply and invert"# #=cancel(6)^3/13xx9/cancel(8)^4larr" cancelling"# #=(3xx9)/(13xx4)=27/52larr" in simplest form"# A fraction is in #color(blue)"simplest form"# when no other factor, apart from 1 will divide into the numerator/denominator.

Cameron Arnold · Answer

undefined To divide $\frac{6}{13}$ by $\frac{8}{9}$, you multiply the first fraction by the reciprocal of the second fraction. So it becomes:

$$
\frac{6}{13} \div \frac{8}{9} = \frac{6}{13} \times \frac{9}{8}
$$

Then you multiply the numerators together and the denominators together:

$$
\frac{6}{13} \times \frac{9}{8} = \frac{6 \times 9}{13 \times 8}
$$

Which simplifies to:

$$
\frac{54}{104}
$$

And finally, you simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2:

$$
\frac{54}{104} = \frac{27}{52}
$$

So, $\frac{6}{13} \div \frac{8}{9} = \frac{27}{52}$.