Question

1. which sum is equivalent to \\(\frac{3}{5} + \frac{1}{6}\\)?

a \\(\frac{6}{10} + \frac{2}{10}\\)
b \\(\frac{12}{30} + \frac{5}{30}\\)
c \\(\frac{18}{30} + \frac{5}{30}\\)
d \\(\frac{3}{11} + \frac{4}{11}\\)

1. which number is not a common denominator of the fractions being added?

\\(\frac{2}{9} + \frac{5}{12}\\)
a 108
b 72
c 36
d 24

1. a museum shows 3 - d movies 5 times a day. the cost is $3.50 per ticket. there are 45 seats in the theater. how much money will the museum receive in one day if all the seats are sold?

a $78.75
b $157.50
c $225.55
d $787.50

Explanation:

Question 1

Step1: Find a common denominator for \(\frac{3}{5}\) and \(\frac{1}{6}\). The least common denominator (LCD) of 5 and 6 is \(5\times6 = 30\).

Step2: Convert \(\frac{3}{5}\) to a fraction with denominator 30: \(\frac{3}{5}=\frac{3\times6}{5\times6}=\frac{18}{30}\).

Step3: Convert \(\frac{1}{6}\) to a fraction with denominator 30: \(\frac{1}{6}=\frac{1\times5}{6\times5}=\frac{5}{30}\).

Step4: So \(\frac{3}{5}+\frac{1}{6}=\frac{18}{30}+\frac{5}{30}\), which matches option C.

Step1: Find the least common denominator (LCD) of 9 and 12. Prime factorize 9 (\(3\times3\)) and 12 (\(2\times2\times3\)). The LCD is \(2\times2\times3\times3 = 36\).

Step2: Multiples of 36 are 36, 72, 108, etc. 24 is not a multiple of 36 (since \(36\div24 = 1.5\), not an integer), so 24 is not a common denominator.

Step1: First, find the total number of tickets sold in a day. The museum shows movies 5 times a day, and each showing has 45 seats. So total tickets = \(5\times45 = 225\) tickets.

Step2: Each ticket costs \$3.50. So total money = \(225\times3.50\).

Step3: Calculate \(225\times3.50\): \(225\times3 = 675\) and \(225\times0.5 = 112.5\), then \(675 + 112.5 = 787.5\). So the total money is \$787.50, which is option D.

Answer:

C. \(\frac{18}{30}+\frac{5}{30}\)

Question 2