What is 1 5/8 as an improper fraction?
The Correct Answer and Explanation is:
To convert the mixed number (1 \frac{5}{8}) into an improper fraction, follow these steps:
- Identify the whole number and the fraction: In the mixed number (1 \frac{5}{8}), the whole number is (1) and the fractional part is (\frac{5}{8}).
- Convert the whole number to a fraction: A whole number can be expressed as a fraction by putting it over (1). Therefore, (1) can be written as (\frac{1}{1}). To combine this with the fraction (\frac{5}{8}), we need a common denominator.
- Find a common denominator: The denominator of the fraction (\frac{5}{8}) is (8). To convert (1) into a fraction with a denominator of (8), we multiply both the numerator and the denominator of (1) by (8):
[
1 = \frac{1 \times 8}{1 \times 8} = \frac{8}{8}
] - Add the two fractions: Now, add the converted whole number fraction (\frac{8}{8}) to the fractional part (\frac{5}{8}):
[
\frac{8}{8} + \frac{5}{8} = \frac{8 + 5}{8} = \frac{13}{8}
]
Thus, the improper fraction representation of (1 \frac{5}{8}) is (\frac{13}{8}).
Explanation:
Improper fractions are fractions where the numerator (the top number) is greater than or equal to the denominator (the bottom number). In this case, (1 \frac{5}{8}) represents a value that is greater than (1), specifically (1.625) in decimal form. By converting it to an improper fraction, we can work with it more easily, especially in mathematical operations such as addition, subtraction, multiplication, or division involving other fractions.
The steps of conversion involve multiplying the whole number by the denominator of the fraction part, which helps to combine them into one fraction. Understanding how to convert mixed numbers to improper fractions is essential in arithmetic, particularly when solving equations or simplifying complex fractions. Recognizing how fractions can represent the same value in different forms allows for flexibility in problem-solving and enhances mathematical comprehension. Thus, converting (1 \frac{5}{8}) to (\frac{13}{8}) not only makes calculations simpler but also reinforces foundational concepts in fractions.