Now, using the information about the breakfasts that some students have in the morning, find the ratio of students who ate cereal to those who ate yoghurt. Give your answer in its simplest form.
| | Porridge | Cereal | Toast | Yoghurt | Total |
| --------- | -------- | ------ | ----- | ------- | ----- |
| Class A | 6 | 13 | 4 | 6 | 29 |
| Class B | 2 | 8 | 7 | 11 | 28 |
| Class C | 4 | 6 | 6 | 7 | 23 |
| Total | 12 | 27 | 17 | 24 | 80 |
Answer (2)
Find the total number of students who ate cereal: 27.
Find the total number of students who ate yoghurt: 24.
Write the ratio of cereal eaters to yoghurt eaters: 24 27 .
Simplify the ratio: 8 9 .
The simplified ratio is 8 9 .
Explanation
Understand the problem We are given a table showing the breakfast choices of students from three classes. Our goal is to find the ratio of students who ate cereal to those who ate yoghurt, expressed in its simplest form.
Identify the numbers of cereal and yoghurt eaters From the table, we can see that the total number of students who ate cereal is 27, and the total number of students who ate yoghurt is 24.
Write the ratio The ratio of cereal eaters to yoghurt eaters is therefore 24 27 .
Find the greatest common divisor (GCD) To simplify this fraction, we need to find the greatest common divisor (GCD) of 27 and 24. The factors of 27 are 1, 3, 9, and 27. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. The greatest common divisor is 3.
Simplify the fraction Now, we divide both the numerator and the denominator by 3: 24 ÷ 3 27 ÷ 3 = 8 9 .
State the final answer Therefore, the simplified ratio of students who ate cereal to those who ate yoghurt is 8 9 .
Examples
Understanding ratios is useful in many real-life situations. For example, if you're baking a cake and the recipe calls for a ratio of 2 cups of flour to 1 cup of sugar, knowing ratios helps you scale the recipe up or down. Similarly, in sports, the win-loss ratio helps to understand a team's performance. In this case, the ratio of cereal to yoghurt eaters helps us understand breakfast preferences in the school.
The ratio of students who ate cereal to those who ate yoghurt is 8 9 in its simplest form. This means for every 9 students who chose cereal, there are 8 students who chose yoghurt. The solution involved identifying totals, writing a ratio, and simplifying it using the greatest common divisor.
;
