How do you simplify #2/9 * 3/5 / (1/2 + 2/3)#?

1 Answer
Jan 12, 2016

Answer:

# 4 / 35#

Explanation:

You need to solve the expression in the brackets first:

# 1/2 + 2/3#

To do so, you must find the least common multiple (for #2# and #3#, this is #6#) and extend the fractions to it:

# 1/2 + 2/3 = (1 * 3) / (2 * 3) + (2 * 2) / (3 * 2) = 3 / 6 + 4 / 6 = 7 / 6#

So, now you have the following:

# 2 / 9 * 3 / 5 -: 7/6 #

To divide by a fraction you need to multiply by its reciprocal, so basically, you "turn" the fraction #7/6# and replace the division ("#/# or #-:#) by multiplication (#*#):

# 2 / 9 * 3 / 5 -: 7/6 = 2 / 9 * 3 / 5 * 6 / 7 = (2 * 3 * 6) / (9 * 5 * 7) = (2 * cancel(color(blue)(3)) * 6) / (cancel(color(blue)(9)) color(blue)(3) * 5 * 7)#

#= (2 * cancel(color(green)(6)) color(green)(2)) / (cancel(color(green)(3)) * 5 * 7) = 4 / 35#