Question

How can you use a bar diagram to check the accuracy of the solution to a ratio or rate problem?

Answer 1

You could potentially use a composite bar graph to show a ratio. Alternatively, if you have a total, say $5, shared out in the ratio 2:3, you could see if 2 of the 5 parts were represented by the 2 bar and 3 parts by the 3 bar by checking the scale on the y axis.

Answer 2

We use the concept of ratios to show the relative sizes of two or more values. Suppose we have three variables, say, x, y and z, where:

x: Represents the number of boys at a school

y: Represents the number of girls at a school

z: Represents all the students

So, we can get the following ratios:

$\frac{x}{z}=\frac{boys}{all \ students}=\frac{3}{8} \\ \\ \frac{y}{z}= \frac{girls}{all \ students}=\frac{5}{8} \\ \\ \frac{y}{x}= \frac{girls}{boys}=\frac{5}{3} \\ \\ \frac{x}{y}= \frac{boys}{girls}=\frac{3}{5}$

The representation of these ratios are shown in the Figure below. Note that the squares in pink (5 squares) represents the girls and the ones in blue (3 squares) represents the boys. The total number of squares is 8. So, we can verify that the previous ratios are correct.