Problems with fractions

In a Year 9 class of 28 students, a survey was conducted about their leisure preferences and it was found that $\frac{3}{7}$ of the class prefers playing sports to watching series.

Calculate how many students prefer playing sports and how many prefer watching series, assuming that everyone chose one of the two options.

Salma has a music playlist with 120 songs.

• $\frac{1}{2}$ of the songs are Pop.

• $\frac{1}{3}$ of the songs are Rock.

• The rest are Electronic Music.

1. a) How many songs are Pop and how many are Rock?
2. b) What fraction of the total do the Electronic Music songs represent? (Remember to simplify your answer if possible).

Your mobile phone has a long-lasting battery. After using it all morning to listen to music, you notice that the battery indicator shows you have $25\%$ charge remaining, which is equivalent to the fraction $\frac{1}{4}$.

If the phone indicates that the remaining $\frac{1}{4}$ corresponds to 3 hours of use:

1. a) How many hours of use does the battery have when fully charged ($100\%$)?
2. b) How many hours have you been listening to music?

Use the following visual diagram to help work out the answer.

A water tank used for watering a school vegetable garden has a total capacity of 1 200 litres.

During a very hot week, $\frac{5}{6}$ of the water in the tank was used.

1. a) How many litres of water have been used?
2. b) Represent the situation graphically and calculate how many litres remain in the tank.

You can do it on paper and send a photo with your answer.

Imagine you have a monthly mobile data plan. During the first week of the month, you have used $\frac{1}{3}$ of your total data streaming videos. During the second week, you have spent $\frac{2}{5}$ of what you had left browsing social media.

1. a) What fraction of your total data have you consumed in these two weeks?
2. b) If you still have 2 GB left for the rest of the month, how many GB was your data plan initially?

You are downloading a new video game that takes up a lot of hard drive space. When the progress bar reaches $\frac{2}{7}$ completed, your internet connection drops. Upon reconnecting, the download continues and progresses $\frac{3}{5}$ of what was left to download.

1. a) What fraction of the total game has been downloaded after the second stage?
2. b) If there are still 4 GB left to complete the download, how much space does the video game take up in total?

A group of students is organising an end-of-year trip. To fund it, they decide to sell raffle tickets. The first month they sell $\frac{3}{8}$ of the total tickets. The second month, they make an effort and sell $\frac{2}{3}$ of the tickets they had left to sell.

1. a) What fraction of the total tickets do they still have left to sell after the second month?
2. b) If in the end they have 150 unsold tickets left over, how many tickets did they have at the start for the raffle?

For the end-of-year trip, students are selling raffle tickets.

• Group A has sold $\frac{1}{3}$ of the total tickets.

• Group B has sold $\frac{2}{5}$ of the total.

• Group C has sold the rest.

1. a) Calculate what fraction of the total tickets Group A and Group B have sold combined.
2. b) What fraction of the tickets did Group C have to sell?

A community allotment of $600 m^2$ is divided up to grow different vegetables. $\frac{1}{4}$ of the plot is dedicated to tomatoes and $\frac{2}{5}$ of the plot to peppers. The rest of the land is divided equally to plant lettuces and carrots.

1. a) What fraction of the total allotment is dedicated to lettuces?
2. b) How many square metres does the carrot crop occupy?

A cyclist is competing in a mountain stage. He has covered $\frac{3}{7}$ of the total route when he stops for refreshments. He continues his ride and covers $\frac{2}{5}$ of what was left until he reaches a mountain pass. At that point, he checks his GPS and sees that he still has $18$ km left to reach the finish line.

How many kilometres is the stage in total and how many kilometres did he cover in the first section before the refreshment stop?