Change 4 3/5 to a improper fraction
The Correct Answer and Explanation is:
To convert the mixed number (4 \frac{3}{5}) into an improper fraction, you follow a specific process that involves a few simple steps. A mixed number consists of a whole number and a proper fraction. In this case, the whole number is 4, and the proper fraction is (\frac{3}{5}).
Step 1: Convert the Whole Number to a Fraction
First, we need to express the whole number (4) as a fraction. Since we are working with fifths (as indicated by the denominator of the proper fraction), we can express (4) as a fraction by giving it the same denominator.
To do this, multiply the whole number (4) by the denominator (5):
[
4 = \frac{4 \times 5}{5} = \frac{20}{5}
]
Step 2: Add the Proper Fraction
Now that we have expressed the whole number as a fraction, we can add it to the proper fraction (\frac{3}{5}):
[
\frac{20}{5} + \frac{3}{5} = \frac{20 + 3}{5} = \frac{23}{5}
]
Step 3: Result
Thus, the improper fraction equivalent of the mixed number (4 \frac{3}{5}) is (\frac{23}{5}).
Explanation
The reason we convert mixed numbers to improper fractions is that it simplifies calculations, particularly in operations like addition, subtraction, multiplication, or division involving fractions. Working with improper fractions can make the process more straightforward because it eliminates the need to deal with the whole number separately.
An improper fraction is one where the numerator (the top number) is greater than or equal to the denominator (the bottom number), while a proper fraction has a numerator that is less than the denominator. In this case, (\frac{23}{5}) is an improper fraction because (23) is greater than (5).
Understanding how to convert between mixed numbers and improper fractions is crucial in mathematics, as it enhances flexibility in working with different types of numbers. It also lays the foundation for more complex operations, making it essential for learners to master this concept early on in their studies.