Convert to fractional notation (improper fraction): 6 5/8
The Correct Answer and Explanation is:
To convert the mixed number (6 \frac{5}{8}) into an improper fraction, follow these steps:
- Understand Mixed Numbers: A mixed number consists of a whole number and a fractional part. In this case, (6) is the whole number and (\frac{5}{8}) is the fractional part.
- Convert the Whole Number to a Fraction: Any whole number can be represented as a fraction by placing it over (1). Thus, (6) can be written as (\frac{6}{1}).
- Find a Common Denominator: The fractional part (\frac{5}{8}) has a denominator of (8). To combine the whole number and the fraction, we need to express (\frac{6}{1}) with a denominator of (8). This is done by multiplying the numerator and denominator of (\frac{6}{1}) by (8): [
\frac{6}{1} = \frac{6 \times 8}{1 \times 8} = \frac{48}{8}
] - Add the Fractions: Now that both parts have the same denominator, we can add them together. The next step is to add (\frac{48}{8}) and (\frac{5}{8}): [
\frac{48}{8} + \frac{5}{8} = \frac{48 + 5}{8} = \frac{53}{8}
] - Final Answer: The improper fraction that represents the mixed number (6 \frac{5}{8}) is (\frac{53}{8}).
Summary
The conversion of the mixed number (6 \frac{5}{8}) to an improper fraction involves several key steps. First, we express the whole number as a fraction with a denominator that matches the fractional part. Next, we convert the whole number (6) into an equivalent fraction of (\frac{48}{8}) to ensure the denominators align. Finally, we add the two fractions to obtain the improper fraction (\frac{53}{8}). This process is essential for operations involving fractions, such as addition, subtraction, or comparison, as improper fractions can simplify calculations, especially in algebraic expressions or when further operations are needed. Understanding this conversion is a fundamental skill in mathematics that applies to many areas, including measurement, geometry, and data analysis.