Question

1 three brothers share one video game system at their home. in total, they are allowed to play games on the system for one half hour each day. if each brother plays an equal amount of time, which shows the amount of time each brother plays each day? a $\frac{1}{3}$ hour c $\frac{1}{4}$ hour b $\frac{1}{6}$ hour d $\frac{1}{10}$ hour 2 jovita has 9 full sheets of rice paper. she can make an origami animal with $\frac{1}{6}$ sheet. what is the greatest number of origami animals jovita can make using all of the paper she has? f 54 g 15 h $\frac{1}{54}$ j $\frac{1}{15}$ 3 jeremiah has a piece of licorice that is $\frac{1}{4}$ foot long. if he cuts it into 2 pieces of equal length, how long will each piece be? a $\frac{1}{2}$ foot c $\frac{1}{6}$ foot b $\frac{1}{4}$ foot d $\frac{1}{8}$ foot 4 latoyas goal is to write a short novel that has 6 chapters. if she writes $\frac{1}{3}$ chapter each month, how long will it take her to reach her goal? f 9 months g 1 year 6 months h 1 year 8 months j 2 years

Explanation:

Question 1

Step1: Total time and number of brothers

Total time is $\frac{1}{2}$ hour, 3 brothers.

Step2: Divide total time by number of brothers

Time per brother = $\frac{1}{2} \div 3 = \frac{1}{2} \times \frac{1}{3} = \frac{1}{6}$ hour? Wait, no, wait the options: Wait, maybe I misread. Wait the problem says "one half hour" total? Wait no, maybe "one half hour" is $\frac{1}{2}$ hour? Wait no, the options have A $\frac{1}{3}$, B $\frac{1}{6}$, etc. Wait, maybe the total time is 1 hour? No, the problem says "in total, they are allowed to play games on the system for one half hour each day". So total time is $\frac{1}{2}$ hour? Wait no, "one half hour" is 30 minutes, which is $\frac{1}{2}$ hour. But 3 brothers, so each gets $\frac{1}{2} \div 3 = \frac{1}{6}$? But the options: A $\frac{1}{3}$, B $\frac{1}{6}$, C $\frac{1}{4}$, D $\frac{1}{10}$. Wait maybe the total time is 1 hour? Wait the problem says "one half hour" – maybe it's a typo, and it's "one hour"? No, "one half hour" is 30 minutes. Wait, maybe I misread: "in total, they are allowed to play games on the system for one half hour each day" – so total time per day is $\frac{1}{2}$ hour, 3 brothers. So each plays $\frac{1}{2} \div 3 = \frac{1}{6}$? But option B is $\frac{1}{6}$? Wait the options: A $\frac{1}{3}$, B $\frac{1}{6}$, C $\frac{1}{4}$, D $\frac{1}{10}$. So the answer would be B. $\frac{1}{6}$ hour. Wait but let's check again. Wait maybe the total time is 1 hour? No, "one half hour" is 30 minutes. Wait, maybe the problem is "one hour" total? Then $\frac{1}{3}$ hour. But the options have A $\frac{1}{3}$. Wait, maybe the original problem has "one hour" instead of "one half hour"? Because if total time is 1 hour, 3 brothers, each gets $\frac{1}{3}$ hour. But the problem says "one half hour". Hmm. Wait maybe I made a mistake. Wait the problem: "in total, they are allowed to play games on the system for one half hour each day". So total time is $\frac{1}{2}$ hour, 3 brothers. So each plays $\frac{1}{2} \div 3 = \frac{1}{6}$ hour. So option B is $\frac{1}{6}$ hour. So answer B.

Step1: Number of sheets and sheets per animal

Jovita has 9 full sheets, each animal needs $\frac{1}{6}$ sheet.

Step2: Divide total sheets by sheets per animal

Number of animals = $9 \div \frac{1}{6} = 9 \times 6 = 54$

Step1: Length of licorice and number of pieces

Length is $\frac{1}{4}$ foot, cut into 2 equal pieces.

Step2: Divide length by number of pieces

Length per piece = $\frac{1}{4} \div 2 = \frac{1}{4} \times \frac{1}{2} = \frac{1}{8}$ foot? Wait no, the options: A $\frac{1}{2}$, B $\frac{1}{4}$, C $\frac{1}{6}$, D $\frac{1}{8}$. Wait, $\frac{1}{4} \div 2 = \frac{1}{8}$? Wait no, $\frac{1}{4}$ divided by 2 is $\frac{1}{8}$? Wait, $\frac{1}{4} \div 2 = \frac{1}{4} \times \frac{1}{2} = \frac{1}{8}$. But the options: D is $\frac{1}{8}$? Wait the options are A $\frac{1}{2}$, B $\frac{1}{4}$, C $\frac{1}{6}$, D $\frac{1}{8}$. So answer D.

Answer:

B. $\frac{1}{6}$ hour

Question 2