Question

1. jodi decides to consolidate two leftover cans of paint into one container. the total amount in the container is greater than 1 gallon. which could be the amounts of paint in the two cans? choose the three correct answers. pick up to 6 answers. a $\frac{5}{9}$ gallon and $\frac{8}{15}$ gallon b $\frac{2}{4}$ gallon and $\frac{7}{14}$ gallon c $\frac{5}{10}$ gallon and $\frac{3}{7}$ gallon d $\frac{3}{5}$ gallon and $\frac{2}{3}$ gallon e $\frac{5}{8}$ gallon and $\frac{6}{12}$ gallon

Explanation:

Step1: Analyze Option A

To add \(\frac{5}{9}\) and \(\frac{8}{15}\), find a common denominator (45).
\(\frac{5}{9}=\frac{25}{45}\), \(\frac{8}{15}=\frac{24}{45}\).
Sum: \(\frac{25 + 24}{45}=\frac{49}{45}\approx1.09>1\). So A is valid.

Step2: Analyze Option B

Simplify \(\frac{2}{4}=\frac{1}{2}\), \(\frac{7}{14}=\frac{1}{2}\).
Sum: \(\frac{1}{2}+\frac{1}{2}=1\), which is not greater than 1. So B is invalid.

Step3: Analyze Option C

Simplify \(\frac{5}{10}=\frac{1}{2}\). Add \(\frac{1}{2}\) and \(\frac{3}{7}\). Common denominator (14): \(\frac{7}{14}+\frac{6}{14}=\frac{13}{14}\approx0.93<1\). So C is invalid.

Step4: Analyze Option D

Add \(\frac{3}{5}\) and \(\frac{2}{3}\). Common denominator (15): \(\frac{9}{15}+\frac{10}{15}=\frac{19}{15}\approx1.27>1\). So D is valid.

Step5: Analyze Option E

Simplify \(\frac{6}{12}=\frac{1}{2}\). Add \(\frac{5}{8}\) and \(\frac{1}{2}\). Common denominator (8): \(\frac{5}{8}+\frac{4}{8}=\frac{9}{8}=1.125>1\). So E is valid.

(Note: The last option is partially visible, but from A, D, E we have three valid ones as required.)

Answer:

A. \(\frac{5}{9}\) gallon and \(\frac{8}{15}\) gallon, D. \(\frac{3}{5}\) gallon and \(\frac{2}{3}\) gallon, E. \(\frac{5}{8}\) gallon and \(\frac{6}{12}\) gallon