Question

3. Edward’s recipe for salad uses a ratio of cups of lettuce to lb of tomatoes. (a) Use a complex fraction to compare the amount of lettuce to the amount of tomatoes. (b) Determine how many cups of lettuce Edward needs to mix with 1 lb of tomatoes. Show your work.

Answer 1

(a) Complex fractions contain fractions as the numerator and denominator. For example, Edward's recipe for salad requires 3 3/4 cups of lettuce to 1 1/2 pounds of tomatoes.. Then the ratio would be

$\frac{3 \frac{3}{4} }{1 \frac{1}{2} }$

(b) We convert the complex fractions to improper fractions. The numerator would be (denominator*whole number)+numerator. The denominator remains as is.

3 3/4 = [(3*4)+3]/4 = 15/4
1 1/2 = [(2*1)+1]/2 = 3/2

So, if Edward has 1 lb of tomatoes,

$1 \ lb \ ( \frac{ \frac{15}{4} }{ \frac{3}{2} } )=1 \ lb \ ( \frac{15}{4} * \frac{2}{3})$

$= \frac{30}{12} = \frac{5}{2}$

Therefore, Edward needs 5/2 cups of lettuce.