Write the fraction 20/28 in the simplest form
The Correct Answer and Explanation is:
To simplify the fraction ( \frac{20}{28} ), we need to find the greatest common divisor (GCD) of the numerator (20) and the denominator (28). The GCD is the largest number that divides both numbers without leaving a remainder. Here’s how to simplify the fraction step by step:
- Identify the Factors:
- The factors of 20 are: ( 1, 2, 4, 5, 10, 20 ).
- The factors of 28 are: ( 1, 2, 4, 7, 14, 28 ).
- Find the GCD:
- The common factors of 20 and 28 are: ( 1, 2, 4 ).
- The greatest of these common factors is ( 4 ). Therefore, the GCD of 20 and 28 is ( 4 ).
- Divide the Numerator and Denominator by the GCD:
- To simplify the fraction, we divide both the numerator and the denominator by the GCD:
[
\frac{20 \div 4}{28 \div 4} = \frac{5}{7}
]
- Final Result:
- The simplified form of the fraction ( \frac{20}{28} ) is ( \frac{5}{7} ).
Explanation of the Process:
When simplifying fractions, it is essential to reduce them to their simplest form to make them easier to understand and work with. The simplest form of a fraction is achieved when the numerator and denominator are coprime, meaning they have no common factors other than 1.
Understanding how to find the GCD is crucial in simplifying fractions. It allows us to determine the largest factor that both the numerator and denominator share, ensuring that we are dividing by the maximum possible value. This not only simplifies the fraction but also provides a clearer representation of the ratio between the two numbers.
In real-life applications, simplified fractions are often easier to work with, whether in cooking, budgeting, or measurements. It helps prevent errors that could arise from working with more complex fractions. Thus, knowing how to reduce fractions, like ( \frac{20}{28} ) to ( \frac{5}{7} ), is an essential skill in mathematics and practical situations.