How would you simplify the fraction 4/28
The Correct Answer and Explanation is :
To simplify the fraction ( \frac{4}{28} ), we need to find the greatest common divisor (GCD) of the numerator (4) and the denominator (28) and then divide both by that number.
Step 1: Identify the GCD
The GCD of two numbers is the largest number that divides both of them without leaving a remainder.
Finding the GCD:
- The factors of 4 are: 1, 2, 4.
- The factors of 28 are: 1, 2, 4, 7, 14, 28.
The common factors of 4 and 28 are 1, 2, and 4. The largest of these is 4, so:
[
\text{GCD}(4, 28) = 4
]
Step 2: Divide the Numerator and Denominator by the GCD
Now that we have the GCD, we divide both the numerator and the denominator by 4:
[
\frac{4 \div 4}{28 \div 4} = \frac{1}{7}
]
Step 3: Conclusion
Thus, the simplified form of ( \frac{4}{28} ) is ( \frac{1}{7} ).
Explanation
Simplifying fractions is an important mathematical skill because it helps us express values in their simplest form, making them easier to work with in calculations. A simplified fraction can often reveal a clearer understanding of the relationship between numbers.
For example, ( \frac{4}{28} ) essentially represents the same quantity as ( \frac{1}{7} ) but in a simpler manner. Fractions can often appear more complicated than they are, and simplifying them can help reduce potential errors in mathematical operations like addition, subtraction, multiplication, or division.
In practical applications, understanding how to simplify fractions is essential in many fields, including cooking, finance, and engineering. For instance, if a recipe calls for ( \frac{4}{28} ) of a cup of an ingredient, knowing it can be simplified to ( \frac{1}{7} ) can make measuring ingredients more manageable.
Therefore, simplifying fractions not only aids in clarity but also enhances the efficiency of mathematical operations.