Simplify the fraction whose numerator is 7(4 - 3)/5 minus (2(2 - 8) - 3(8 + 1))/15, all divided by 3.

Step-by-step solution

1. 1

   Work from the innermost brackets outward. A nested fraction is evaluated like any expression: finish the numerator completely, finish the denominator, then divide.

   $4-3=1,\qquad 2-8=-6,\qquad 8+1=9.$

2. 2

   Simplify the first term of the numerator.

   $\frac{7(1)}{5}=\frac{7}{5}.$

3. 3

   Simplify the second term's numerator. Multiply before subtracting, and mind that both products are negative contributions:

   $2(-6)-3(9)=-12-27=-39,$

   so the second fraction is $\dfrac{-39}{15}=-\dfrac{13}{5}$.

4. 4

   Subtract the two fractions. Subtracting a negative adds:

   $\frac{7}{5}-\left(-\frac{13}{5}\right)=\frac{7+13}{5}=\frac{20}{5}=4.$

   The common denominator $5$ makes this immediate — a strong hint that the numerator was designed to come out whole.

5. 5

   Divide by the outer 3.

   $\frac{4}{3}.$

   As a decimal this is $1.3\overline{3}$; as a mixed number, $1\tfrac13$.