Calculate each of the following products.

• 1. $\frac { 1 } { 8 } \cdot \frac { 8 } { 1 }$

     Hint (a):

     When multiplying fractions together, the answer has a numerator equal to the product of the numerators and a denominator equal to the product of the denominators.

  2. $\frac { 3 } { 4 } \cdot \frac { 4 } { 3 }$ 

     Steps 1 (b):

     $\frac{3}{4}\cdot\frac{4}{3}= \frac{3 \cdot\ 4}{4 \cdot\ 3}$

     Step 2 (b):

     $\frac{3 \cdot\ 4}{4 \cdot\ 3}= \frac{12}{12}$

     Step 3 (b):

     $\frac{12}{12}=1$

  3. $\frac { 2 } { 3 } \cdot \frac { 3 } { 2 }$ 

     Answer (c):

     1

  4. $7 ·\frac { 1 } { 7 }$ 

     Hint (d):

     $7=\frac{7}{1}$

  5. What do the products in parts (a) through (d) have in common?

     Hint (e):

     Check the relationship between the products of the problems above.