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When studying mathematics at the GCSE level, understanding how to interpret and work with ratios is an essential skill. Ratios are used to compare quantities and are commonly seen in everyday contexts, such as recipes, map scales, and, as in this case, student attendance.
Let’s look at a typical exam question you might encounter:
A maths class has 28 students. On Monday, 20 of the students were on time to a lesson and 8 students were late.
Number of students who were on time : number of students who were late = n : 1
(a) Work out the value of n.
Breaking Down the Problem
First, we are told that out of 28 students, 20 were on time and 8 were late. We are asked to express the ratio of students who were on time to those who were late in the form n : 1.
Step-by-Step Solution
Write the ratio:
The number of students who were on time to those who were late is 20 : 8
Simplify the ratio:
To simplify, divide both numbers by the highest common factor, which is 8 and 20 both divisible by 4: \frac{20}{4} : \frac{8}{4} = 5 : 2. But we are asked to write the ratio in the form n : 1.
Convert the ratio n : 1 to form:
To do this, divide both sides of the ratio by the number of students who were late (which is 2 in the simplified ratio):
So, n = 2.5
Final Answer
The value of n is 2.5.
Why is this important?
Understanding ratios is crucial not just for exams, but for real-life problem-solving. Questions like this one test your ability to read information, simplify ratios, and express them in the required form. If you find such problems challenging, working with a GCSE Online Tutor for Maths can provide you with targeted practice and expert guidance.
Conclusion
Always remember to:
- Simplify ratios to their lowest terms,
- Convert them to the required form,
- Check your calculations.
With steady practice, ratio problems will become second nature and help you in various aspects of your mathematics journey.
