Ratio and proportion
In a five-a-side football team there are 5 boys and 7 girls. In a recipe, for every 2 cups of rice, 3 cups of water are used. In both cases we compare two quantities by dividing: that is a ratio, and if two ratios are equal, they form a proportion.
Ratio between two quantities
In a video game tournament there are 16 strategy players and 24 sports players. The strategy-to-sports ratio is $\frac{16}{24} = \frac{2}{3}$: for every 2 strategy players, there are 3 sports players.
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…
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.
A video game shop offers a pack of $3$ controller covers for $12,60$ €. Express the ratio of the price to the number of covers. What would we usually call this result in…
A video game shop offers a pack of $3$ controller covers for $12,60$ €. Express the ratio of the price to the number of covers. What would we usually call this result in everyday language?
Simplifying a ratio
A ratio is simplified in the same way as a fraction: by dividing both terms by their highest common factor, until it cannot be simplified any further.
In a Maths exam of $20$ questions, Nerea answered $15$ correctly and got $5$ wrong. Write down the ratio of: a) The number of correct answers to the number of incorrect…
In a Maths exam of $20$ questions, Nerea answered $15$ correctly and got $5$ wrong. Write down the ratio of:
- a) The number of correct answers to the number of incorrect answers.
- 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.
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.…
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.
- a) Calculate the ratio of width to height for each of the formats.
- b) Are these dimensions proportional? Justify your answer by comparing the ratios.
Proportions: the equality of ratios
If you know three terms of the proportion, you can find the fourth by solving for it:
$$\frac{3}{8} = \frac{15}{x} \ \Rightarrow\ 3x = 120 \ \Rightarrow\ x = 40$$On a streaming platform, a moderator counted $1350$ messages in the stream's chat over the last $45$ minutes. a) Calculate the ratio of the number of messages to the…
On a streaming platform, a moderator counted $1350$ messages in the stream's chat over the last $45$ minutes.
- a) Calculate the ratio of the number of messages to the time elapsed in minutes.
- b) Explain what the result obtained means in the context of the problem.
- c) If the ratio remains constant, how many messages will be received in a full hour?
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…
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 $7\,000$ $km^2$.
- a) Calculate the population density of each province and interpret the result.
- b) Which of the two provinces is more "populated" relative to its size?
Back to the beginning: In the five-a-side football team the ratio of boys to girls is $\frac{5}{7}$ (whereas boys make up $\frac{5}{12}$ of the total); in the recipe, the rice-to-water ratio is $\frac{2}{3}$, so for 6 cups of rice you would need 9 cups of water because $\frac{2}{3} = \frac{6}{9}$.