Question

Calculate the exact value of ( 4 1/3 - 1 2/5 ) ÷ 4/15

Answer 1

the answer is 11.

use BEDMAS, and calculate the equation inside the brackets (answer to that is 44/15)

then divide it by 4/15 and you get 11

Answer 2

let's firstly convert the mixed fractions to improper fractions and proceed.

`\bf \stackrel{mixed}{4(1)/(3)}\implies \cfrac{4\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{13}{3}}~\hfill \stackrel{mixed}{1(2)/(5)}\implies \cfrac{1\cdot 5+2}{5}\implies \stackrel{improper}{\cfrac{7}{5}} \\\\[-0.35em] ~\dotfill`

`\bf \stackrel{\textit{recall that by PEMDAS, parenthesis first}~\hfill }{\left(\cfrac{13}{3}-\cfrac{7}{5} \right)/ \cfrac{4}{15}\implies \left(\stackrel{\textit{using an LCD of 15}}{\cfrac{(5)13-(3)7}{15}} \right)/ \cfrac{4}{15}\implies \left(\cfrac{65-21}{15} \right)/ \cfrac{4}{15}} \\\\\\ \left(\cfrac{44}{15}\right)/ \cfrac{4}{15}\implies \cfrac{44}{15}* \cfrac{15}{4}\implies \cfrac{44}{4}\cdot \cfrac{15}{15}\implies 11\cdot 1\implies 11`