Evaluate the following rational expressions.

1.  $-3\frac{2}{9}+\ 8\frac{7}{9}$

• Step 1(a):

  Add the integer values together. Then, if necessary, use a giant 1 to make the denominators of the fractions the same.

  $−3+8=5$

  Step 2(a):

  Add the fractions together, reduce if possible, and change the sum into a mixed number if necessary. Then add the integer sum and the fraction sum together.

  $-\frac{2}{9}+\frac{7}{9}=\frac{5}{9}$

  Answer (a):

  $5+\frac{5}{9}=5\frac{5}{9}$

2.  $-7\frac{2}{7}-4\frac{1}{5}$

• Hint (b):

  Follow the steps for part (a). Remember, subtracting any number is like adding its opposite.

  Answer (b):

  $-11\frac{17}{35}$

3.  $1\frac{5}{7}\ \cdot3\frac{6}{7}$

• Hint (c):

  Convert the mixed numbers into fractions greater than $1$. Then simplify. Reduce if possible and convert the product into a mixed number if necessary.

4.  $-8\frac{1}{7}\div-5\frac{5}{9}$

• Hint (d):

  Follow the steps for part (c). Remember, dividing by a fraction is like multiplying by its reciprocal.

  Answer (d):

  $1\frac{163}{350}$