Ratio and Proportion

On a social network, an influencer's video has received $450$ "likes" after being viewed by $3000$ people. Calculate the ratio of the number of "likes" to the number of views, simplify the result, and interpret what the value obtained means.

In a math exam of $20$ questions, Lucía answered $15$ correctly and got $5$ wrong. Write down the ratio of:

1. a) The number of correct answers to the number of incorrect answers.
2. b) The number of correct answers to the total number of questions.

State in each case which is the antecedent and which is the consequent.

Given the ratio $\frac{4}{5}$, invent a real-life context for teenagers (for example, related to cinema, clothes or sports) where these quantities are used and explain its meaning. Indicate which quantities you are comparing.

An electric scooter travels $12$ kilometers in $30$ minutes. Calculate the ratio of the distance travelled to the time taken (expressed in hours). What physical quantity does this ratio represent?

For an end-of-term party, students are comparing two offers on bags of chips to see which is more economical. The "Crunch" brand offers a $250$ g bag for $105$ pesos, while the "Snack" brand sells a $400$ g bag for $156$ pesos.

1. a) Calculate the ratio of price to weight (in pesos per gram) for each brand.
2. b) Using the ratios obtained, state which of the two brands is cheaper.

In a basketball training session, Lucía scored $18$ of her $30$ shots, while Marcos scored $14$ of his $20$ shots.

1. a) Calculate each player's success ratio (shots scored to total shots) as a decimal.
2. b) Which of the two players had a better performance in the training session?

In an archery competition, an archer's score is analyzed using the ratio of "arrows in the center" to "total arrows shot".

• Archer A achieved a ratio of $7:12$ in $48$ shots.

• Archer B achieved a ratio of $5:8$ in $40$ shots.

1. a) Which of the two archers was more effective? Justify your answer by comparing the ratios using a common denominator.

1. b) If Archer A wants to match Archer B's success ratio in their next round of $24$ arrows, how many of those new arrows must hit the center?

Calculate the ratio of the width to the height of the screen of the following tablet, and explain whether the result would be the same if the tablet were twice as large while maintaining the same shape.

A graphic designer is working with two image formats. The first format has dimensions of $12$ cm wide by $18$ cm high. The second format is $20$ cm wide by $30$ cm high.

1. a) Calculate the ratio of width to height for each of the formats.
2. b) Are these dimensions proportional? Justify your answer by comparing the ratios.

A video game designer is comparing two monitors for their new workstation. The first monitor has a "standard widescreen" format with a ratio of its width to its height of $16:9$. The second is an "ultrawide" monitor with a ratio of $21:9$.

1. a) If both monitors have exactly the same height of $36$ cm, what is the difference between their widths?

1. b) Calculate the ratio of the area of the ultrawide monitor to the area of the standard monitor. Express the result as an irreducible fraction.

To prepare an orange paint mixture, an artist uses $3$ tins of red paint for every $2$ tins of yellow paint.

1. a) Express the ratio of red paint to yellow paint.
2. b) If they want to keep the same shade and use $6$ tins of yellow paint, how many tins of red paint will they need?

In a basketball practice, Marc has scored $8$ shots out of $12$ attempts, while Paula has scored $6$ out of $9$ attempts.

1. a) Write the ratio of successful shots for each of them.

1. b) Check whether the two ratios form a proportion. Who has better aim?

On a streaming platform, a moderator counted $1350$ messages in the stream's chat over the last $45$ minutes.

1. a) Calculate the ratio of the number of messages to the time elapsed in minutes.
2. b) Explain what the result obtained means in the context of the problem.
3. c) If the ratio remains constant, how many messages will be received in a full hour?

In a secondary school, the ratio of the number of students to the number of teachers is $18$.

1. a) Explain in one sentence what this ratio value means.
2. b) If there are currently $32$ teachers in the school, how many students are enrolled?
3. c) If for next year the number of students is expected to increase to $630$, how many teachers should there be to maintain the same ratio?

A scale model of a new municipal sports center has been built. The real building has a total length of $75$ meters, while on the model that same distance measures $30$ centimeters.

1. a) Calculate the ratio of the model measurement to the actual measurement (remember to express both in the same unit).
2. b) What is the scale of the plan used for the model?

Population density is the ratio of the number of inhabitants of a territory to its area expressed in $km^2$. Observe the data for these two fictional provinces:

• Province A: $450\,000$ inhabitants and $15\,000$ $km^2$.

• Province B: $280\,000$ inhabitants and $7\,000$ $km^2$.

1. a) Calculate the population density of each province and interpret the result.
2. b) Which of the two provinces is more "populated" relative to its size?

To get an olive green shade of paint, a painter mixes cans of white, yellow, and black paint. The ratio of yellow paint to white paint is $3/4$, and the ratio of black paint to yellow paint is $1/5$.

If they used $2$ liters of white paint for a room:

1. a) How many liters of yellow paint did they need?
2. b) What is the ratio of black paint to white paint in this mixture?

On a high-precision map of the Pyrenees, the scale is given as a ratio of $1:50\thinspace000$. A hiker measures the distance between two mountain huts on the map and gets $14.2$ cm. However, when checking a digital app, they notice that the actual distance is $7.5$ km.

1. a) Calculate the actual ratio (scale) between the measurement on the map and the measurement from the digital app.

1. b) What is the error in centimeters that the map shows compared to the distance on the app?

A scale model of a skyscraper is to be built. The similarity ratio between the model and the actual building is $1:250$.

1. a) If the base area of the real building is $1\thinspace200$ $m^2$, what is the ratio of the base area of the model to that of the real skyscraper?

1. b) Calculate the base area of the model in square centimeters. (Be careful: remember that the ratio of the areas is the square of the ratio of the lengths).