Question

an ice cream shop took inventory of their ice cream at the end of a shift. the shop had 5/6 of a carton of chocolate ice cream, 1/2 of a carton of vanilla ice cream, 2/3 of a carton of strawberry ice cream, and 2/3 of a carton of pecan praline ice cream. how many cartons of ice cream did the shop have in all? cartons

Explanation:

Step1: Convert to common denominator

To add the fractions, find a common denominator. The denominators are 6, 2, 3. The least common denominator is 6.
Convert each fraction:

• $\frac{5}{6}$ remains $\frac{5}{6}$
• $\frac{1}{2} = \frac{1\times3}{2\times3} = \frac{3}{6}$
• $\frac{2}{3} = \frac{2\times2}{3\times2} = \frac{4}{6}$ (for strawberry)
• $\frac{2}{3} = \frac{4}{6}$ (for pecan praline)

Step2: Add the fractions

Now add the numerators: $\frac{5}{6} + \frac{3}{6} + \frac{4}{6} + \frac{4}{6} = \frac{5 + 3 + 4 + 4}{6} = \frac{16}{6}$

Step3: Simplify the fraction

Simplify $\frac{16}{6}$ by dividing numerator and denominator by 2: $\frac{8}{3}$ or $2\frac{2}{3}$

Answer:

$\frac{8}{3}$ (or $2\frac{2}{3}$)