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

Question

Julia Adams · Accepted Answer

See the entire simplification process below:

First, we must convert these mixed fractions into improper fractions by multiplying the integer portion by the correct form of #1# and then adding the result to the fraction: #(2 1/3)/(1 2/5) = ((3/3 xx 2) + 1/3)/((5/5 xx 1)+ 2/5) = (6/3 + 1/3)/(5/5 + 2/5) = (7/3)/(7/5)# We can now divide this expression using this rule for dividing fractions: #(color(red)(a)/color(blue)(b))/(color(green)(c)/color(purple)(d)) = (color(red)(a) xx color(purple)(d))/(color(blue)(b) xx color(green)(c))# Substituting the values from our previous calculation gives: #(color(red)(7)/color(blue)(3))/(color(green)(7)/color(purple)(5)) = (color(red)(7) xx color(purple)(5))/(color(blue)(3) xx color(green)(7))= (cancel(color(red)(7)) xx color(purple)(5))/(color(blue)(3) xx cancel(color(green)(7))) = 5/3# Or #5/3 = (3 +2)/3 = 3/3 + 2/3 = 1 + 2/3 = 1 2/3#

Abigail Allen · Answer

undefined To simplify (2 1/3)/(1 2/5), we first convert the mixed numbers to improper fractions.

2 1/3 can be written as (2 * 3 + 1)/3 = 7/3. 
1 2/5 can be written as (1 * 5 + 2)/5 = 7/5.

Now, we can rewrite the expression as (7/3)/(7/5).

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.

So, (7/3)/(7/5) = (7/3) * (5/7).

Multiplying the numerators and denominators, we get (7 * 5)/(3 * 7) = 35/21.

Therefore, (2 1/3)/(1 2/5) simplifies to 35/21.