Ratio and Proportion

In a 7th grade class, there are $12$ students who play basketball and $18$ students who play soccer. Write the ratio of the number of basketball players to soccer players. Explain in your own words what the result means after simplifying the fraction.

Look at the following drawing representing the pieces of fruit in a fruit bowl. Calculate the ratio of the number of apples (orange) to the number of pears (soft white).

In an adventure video game, your character has obtained $24$ health potions after opening $6$ magic chests. Calculate the ratio of the number of potions to the number of chests. On average, how many health potions are there in each chest?

A radio-controlled car travels a distance of $45$ meters in $15$ seconds. Calculate the ratio of distance to time. What physical quantity does this result represent?

Un paquete de $500$ gramos de cereales cuesta $210$ pesos. Expresa la razón entre el precio y el peso en gramos. Después, calcula el valor decimal de esa razón para saber cuánto cuesta $1$ solo gramo de cereales.

In a basketball training session, Lucía scored $18$ three-pointers out of $30$ shots taken, while her teammate Marcos scored $14$ three-pointers out of $20$ shots.

1. a) Express the success ratio of each player as a decimal number.
2. b) Which of the two has a better success ratio? Justify your answer by comparing both values.

Marta has read $60$ pages of a novel in $2$ hours, while her brother Javier has read $45$ pages in $1.5$ hours.

• Calculate the ratio of pages to hours for Marta.

• Calculate the ratio of pages to hours for Javier.

• Do they both read at the same speed? Justify your answer.

A travel influencer has reviewed her Instagram statistics. In her latest post, she got $4,500$ likes after receiving a total of $60,000$ views.

1. a) Calculate the ratio of the number of likes to the number of views.
2. b) If in the next photo the ratio is $0.1$, which of the two photos was proportionally more successful among her followers?

A sweet shop offers two types of bags of gummy sweets:

• Bag A: contains $250\text{ g}$ and costs $\text{RD\$}\ 210$.

• Bag B: contains $400\text{ g}$ and costs $\text{RD\$}\ 312$.

1. a) Calculate the price-to-weight ratio for each bag.
2. b) Which of the two bags is cheaper value for money? Justify your answer using the values obtained.

An influencer's "engagement rate" is calculated by comparing the number of interactions (likes and comments) with their total number of followers.

• User A has $12,500$ followers and received $625$ interactions on their latest photo.

• User B has $45,000$ followers and received $2,160$ interactions.

Calculate the ratio of interactions per follower for each one. Which of the two has a proportionally more active audience? Express the result as a decimal and explain what that value means in this context.

On a treasure island map from a movie, the distance between "Pirate Harbor" and "Skull Mountain" is $15\text{ cm}$. In reality, that distance is $4.5\text{ km}$.

1. a) Calculate the ratio of the map measurement to the real-life measurement (remember to convert both to the same unit, for example, centimeters).
2. b) What is the name of this special ratio used on maps?

In your 7th grade class there are $32$ students in total. It is known that for every $3$ students who prefer PE classes, there are $5$ students who prefer Art.

1. a) Write the ratio of those who prefer PE to those who prefer Art.
2. b) If these are the only two options and everyone has chosen one, how many students prefer each subject? (Hint: notice that the sum of the terms in the simplified ratio is $3 + 5 = 8$).

The ratio of the length of the base to the height of old cinema screens was $4:3$ (almost square aspect ratio), whereas in modern cinemas the ratio is usually $21:9$ (widescreen format).

If a modern cinema screen has a height of $6.3$ meters, how long is its base? What would the base of an old screen be with that same height of $6.3$ meters? Compare both results and explain which of the two screens is more "elongated".

To prepare a pink paint mixture, an artist uses $3$ tins of white paint for every $2$ tins of red paint.

• Write the ratio of white paint to red paint.

• If the artist decided to use $6$ tins of red paint, how many tins of white paint should he use to keep the same shade of pink?

Look at these two mixtures of water and strawberry syrup. Mixture $A$ has $2$ glasses of syrup for every $5$ glasses of water. Mixture $B$ has $4$ glasses of syrup for every $10$ glasses of water.

• Write the ratio for each mixture.

• Are these mixtures proportional? That is, will they taste the same?

In a strategy video game, to craft a "Super Speed" potion, the alchemist uses $150\text{ mg}$ of stardust for every $250\text{ ml}$ of magic water.

1. a) Express the ratio of stardust to magic water. Simplify the result and interpret what this value means.
2. b) Calculate the inverse ratio (magic water to stardust) and explain what information it gives us.

To prepare a very special shade of orange, a graffiti artist mixes $1.2\text{ liters}$ of red paint with $0.8\text{ liters}$ of yellow paint.

1. a) Write the ratio of the amount of red paint to yellow paint. Express it as an irreducible fraction.
2. b) If he wants to keep the same shade but only has $0.5\text{ liters}$ of yellow paint, what amount of red paint should he use? (Use the ratio obtained in the previous part).

A street artist is creating a new color "Cyber Green" by mixing blue paint and yellow paint. In her first tin, she mixed $0.75$ liters of blue with $1.2$ liters of yellow. Running out of paint, she decides to prepare a second mixture in a larger tin using $2.5$ liters of blue. How many liters of yellow must she add so that the ratio of blue to yellow is exactly the same as in the first mixture? Express the initial ratio as a simplified fraction.

In a basketball practice, Lucía scored $18$ shots out of $25$ attempts, while Marcos scored $24$ out of $32$ attempts.

1. a) Write the success ratio for each player.
2. b) Calculate the decimal value of each ratio.
3. c) If both maintain their efficiency and shoot $100$ times, how many baskets will each one score? Are these ratios equivalent? Justify your answer using the cross-multiplication of extremes and means.

A hummingbird can flap its wings about $4,800$ times in one minute. On the other hand, a griffon vulture flaps them about $120$ times every minute.

1. a) Calculate the ratio between the hummingbird's wingbeats and the vulture's. What does that number mean?

1. b) If we compare the hummingbird's weight ($3\text{ g}$) with its length ($10\text{ cm}$), calculate the weight/length ratio. What units would that ratio have?

A hybrid car consumes $4.2$ liters of petrol to travel $100$ km, whereas a motorcycle consumes $1.5$ liters to travel $40$ km.

1. a) Calculate the consumption ratio (liters per kilometer) for each vehicle.
2. b) Which of the two vehicles consumes less proportionally?
3. c) If the consumption-to-distance ratio of a third vehicle is $0.052$, how many liters will it use on a journey of $250$ km?

In a nutrition study, the ratio of the amount of sugar to the total weight of two types of cereal is analysed.

• "Energy" cereal has $12$ g of sugar in a $40$ g serving.

• "Health" cereal has $18$ g of sugar in a $75$ g box.

Calculate the ratio of sugar per gram of product for both. What percentage of sugar does each one have? (Remember that to convert a ratio to a percentage, you can multiply its decimal value by 100). Which of the two would you choose if you wanted to consume less sugar proportionally?

Population density is the ratio of the number of inhabitants to the area they occupy (inhabitants/km²).

• City X has a population of $1,250,000$ people and an area of $450.5$ km².

• City Y has $840,000$ inhabitants and occupies $120.2$ km².

Calculate the population density of both cities, rounding to the nearest whole number. If City X tripled its population while maintaining its area, what would its new density be? Would it still be less dense than City Y?