- Identify the number of students in the 79-70 range as the 'part', which is 27.
- Calculate the 'whole' by summing the students in all ranges: \(32 + 65 + 27 = 124\).
- Write the ratio as Part:Whole, which is 27:124.
- Conclude that the simplest form of the ratio is \(\boxed{27:124}\).
Explanation
- Determine the whole number of students
To determine the part-to-whole ratio for the 6th-grade average range of 79-70, we first need to identify the total number of students represented in the table. The table provides three distinct grade ranges and the corresponding number of students in each:
- 100-90: 32 students
- 89-80: 65 students
- 79-70: 27 students
The 'whole' is the sum of all these students, which we calculate as:
\[32 + 65 + 27 = 124\]
So, the total number of students in all three ranges is 124.
- Identify the part and write the ratio
We are specifically interested in the grade range of 79-70. From the table, the 'part' corresponding to this specific range is 27 students. Thus, we have:
- Part (79-70 range) = 27
- Whole (Total students) = 124
The part-to-whole ratio is therefore written as:
\[27:124\]
- Simplify the ratio and conclude
To ensure the ratio is in its simplest form, we look for the greatest common divisor (GCD) of 27 and 124. The divisors of 27 are 1, 3, 9, and 27. Checking these against 124, we find that none of them (other than 1) divide 124 evenly (for example, 124 divided by 3 is approximately 41.33). Since the GCD is 1, the ratio 27:124 is already in its simplest form. Thus, the final part-to-whole ratio is \(\boxed{27:124}\).
Examples
Understanding ratios is essential for interpreting data distributions in various fields, such as education or marketing. For instance, if you want to know the proportion of students scoring in a specific grade bracket compared to the entire class size, you can express it as a part-to-whole ratio. This simple mathematical tool helps turn raw numbers into clear, comparative insights. For example, if a teacher has a class of 25 students and 5 scored an A, the ratio of A-graders to total students is \(5:25\), which simplifies to \(\frac{1}{5}\) or 1:5.