Question

Write the ratio 21 students to 28 students as a fraction in lowest terms. Write your answer in the box.

Short answer

\( \frac{3}{4} \)

Step-by-step solution

Identify the Given Values

The problem provides two values: 21 students and 28 students. These values will be used to form the ratio.

Write the Ratio as a Fraction

Express the given ratio as a fraction: \[ \frac{21}{28} \]

Find the Greatest Common Divisor (GCD)

Determine the greatest common divisor of 21 and 28. The GCD of 21 and 28 is 7.

Simplify the Fraction

Divide both the numerator and the denominator by their GCD: \[ \frac{21 \div 7}{28 \div 7} = \frac{3}{4} \]

Key concepts

ratios

Ratios are a way to compare two or more quantities. They tell us how much of one thing there is compared to another. In this exercise, we are comparing the number of students in two groups.
For example, if there are 21 students in one group and 28 in another, we can write the ratio as 21:28. Ratios can also be expressed as fractions, which helps in simplifying them.
Understanding ratios helps in many real-life situations, like mixing ingredients or splitting a bill among friends. It is important to know how to convert and simplify ratios for these purposes.

fractions

A fraction represents a part of a whole. It has a numerator (top number) and a denominator (bottom number). In our exercise, we are working with the fraction \( \frac{21}{28} \) to express the ratio of 21 students to 28 students.
Fractions can be simplified by dividing both the numerator and denominator by their greatest common divisor (GCD). This helps in finding the simplest form of the fraction, making it easier to understand and use.
The concept of fractions is widely used in mathematics and everyday life, such as in cooking, budgeting, and measuring.

greatest common divisor

The greatest common divisor (GCD) is the largest number that divides both the numerator and the denominator without leaving a remainder. In our exercise, we need the GCD of 21 and 28 to simplify the fraction.
To find the GCD of 21 and 28, we can list the factors of each number:

• Factors of 21: 1, 3, 7, 21
• Factors of 28: 1, 2, 4, 7, 14, 28

The largest common factor is 7. So, the GCD is 7. Using the GCD helps to simplify fractions accurately and efficiently.

simplification

Simplification is the process of reducing fractions to their simplest form. After finding the GCD, we divide both the numerator and the denominator by this number.
In our example, we simplify the fraction \( \frac{21}{28} \) as follows:

• Divide 21 by 7 to get 3
• Divide 28 by 7 to get 4

So, \( \frac{21}{28} \) simplifies to \( \frac{3}{4} \). Simplifying fractions makes them easier to work with and understand. This skill is essential in various mathematical operations and problem-solving scenarios.