In a class consisting of boys and girls, there are 45 students. If three fifth of the students are boys, find the number of boys in the class.
27
Calculating the Number of Boys in a Class
This problem involves calculating a fraction of a whole number to find the number of boys in a class. We are given the total number of students in the class and the fraction of students who are boys.
Problem Details
- Total number of students in the class: 45
- Fraction of students who are boys: three fifths ($\frac{3}{5}$)
Step-by-Step Calculation of Boys
To find the number of boys, we need to multiply the total number of students by the fraction of students who are boys. The calculation is as follows:
Number of boys = (Fraction of boys) $\times$ (Total number of students)
Number of boys = $\frac{3}{5} \times 45$
We can perform this calculation by first dividing the total number of students (45) by the denominator of the fraction (5), and then multiplying the result by the numerator of the fraction (3).
Step 1: Divide the total students by the denominator:
$\frac{45}{5} = 9$
Step 2: Multiply the result by the numerator:
$3 \times 9 = 27$
So, the number of boys in the class is 27.
Finding the Number of Girls (Optional)
Although the question only asks for the number of boys, we can also find the number of girls for a complete understanding of the class composition.
Number of girls = Total number of students - Number of boys
Number of girls = $45 - 27 = 18$
There are 18 girls in the class.
Summary of Class Composition
| Category | Number |
|---|---|
| Total Students | 45 |
| Boys ($\frac{3}{5}$ of total) | 27 |
| Girls | 18 |
The calculation shows that three fifths of the 45 students is equal to 27. Therefore, the number of boys in the class is 27.
Revision Table: Understanding Fractions
Understanding how to calculate a fraction of a whole number is key to solving this type of problem. Here's a quick revision:
| Concept | Explanation | Example |
|---|---|---|
| Fraction | Represents a part of a whole. It has a numerator (top number) and a denominator (bottom number). | $\frac{3}{5}$ (3 parts out of 5 equal parts) |
| Calculating Fraction of a Whole | Multiply the fraction by the whole number. Whole number can be divided by denominator first, then multiplied by numerator, or vice-versa. | $\frac{3}{5}$ of 45 = $\frac{3}{5} \times 45$ |
Additional Information: Fraction Word Problems
Word problems involving fractions often require identifying the total quantity and the fraction that applies to a specific part of that quantity. Practice is essential to become comfortable with these types of problems.
- Always identify the total value or quantity.
- Identify the fraction given in the problem that relates to the part you need to find.
- Multiply the fraction by the total to find the value of the part.
- Remember that "of" in mathematics often means multiplication when dealing with fractions or percentages.
This problem is a straightforward example of finding a part when the fraction and the whole are known.
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