Recapping Ratios and Percentages
In Section 7.1, we explore the fundamental concepts of ratios and percentages as tools for comparing quantities. A ratio is defined as a relationship between two numbers that indicates how many times the first number contains the second. For example, if you have 20 apples and 5 oranges, the ratios of oranges to apples is given as 5:20, which can be simplified to 1:4. This relationship can also be represented as a fraction:
$$\frac{5}{20} = \frac{1}{4}$$
Conversions from ratios to percentages help to visualize relationships better. For instance, in a basket containing only apples and oranges, if 5 out of 25 fruits are oranges, then:
$$\text{Percentage of oranges} = \frac{5}{25} \times 100 = 20\%$$
Conversely, the percentage of apples will be 100% - 20% = 80%. The concept is practical, illustrated with examples including calculating the ratio of girls to boys in a class and determining transport costs for an upcoming school picnic. Exercises reinforce these ideas, inviting students to convert ratios to percentages and explore various contextual problems. By understanding these concepts, students gain essential skills for mathematical and everyday problem solving.