Ratios and proportions

Calculate the value of the ratio of each pair of quantities and interpret the result:

1. a) $3\ \text{kg}$ of cherries cost $10,50\ \text{€}$.

1. b) A gravel cyclist covers $95\ \text{km}$ in $4\ \text{h}$.

1. c) A bottle contains $2\ \text{L}$ and a drum, $25\ \text{L}$.

Two metal rods measure $8\ \text{dm}$ and $12\ \text{dm}$.

1. a) Calculate the ratio of the length of the first to the second, and simplify it.

1. b) Calculate the ratio of the second to the first.

1. c) How are the two ratios obtained related to each other? Does this always happen?

A road map is drawn to a scale of $1 : 300.000$.

1. a) Explain the meaning of this ratio.

1. b) What real-life distance is represented by $5\ \text{cm}$ on the map?

1. c) Two towns are $21\ \text{km}$ apart in reality. How far apart are they on the map?

Check, by calculating the product of the extremes and the product of the means, whether the following pairs of ratios form a proportion:

1. a) $\frac{6}{4}$ and $\frac{15}{10}$

1. b) $\frac{5}{8}$ and $\frac{7}{12}$

1. c) $\frac{2,5}{4}$ and $\frac{5}{8}$

Find the fourth proportional in each case:

1. a) $\frac{x}{4} = \frac{9}{12}$

1. b) $\frac{5}{x} = \frac{15}{21}$

1. c) $\frac{8}{6} = \frac{20}{x}$

Find the mean proportional in each case, that is, the positive value of $x$ that satisfies the continuous proportion:

1. a) $\frac{x}{4} = \frac{25}{x}$

1. b) $\frac{3}{x} = \frac{x}{27}$

1. c) $\frac{x}{2} = \frac{50}{x}$