What is 1 1/8 as a improper fraction
The Correct Answer and Explanation is :
To convert the mixed number (1 \frac{1}{8}) into an improper fraction, follow these steps:
- Understand the Components: A mixed number consists of a whole number and a proper fraction. In (1 \frac{1}{8}), the whole number is (1), and the proper fraction is (\frac{1}{8}).
- Convert the Whole Number: To convert the whole number into a fraction, multiply it by the denominator of the fractional part. In this case, the denominator is (8). Therefore, (1) can be expressed as: [
1 = \frac{1 \times 8}{8} = \frac{8}{8}
] - Add the Proper Fraction: Now, add the improper fraction from the whole number to the proper fraction: [
\frac{8}{8} + \frac{1}{8} = \frac{8 + 1}{8} = \frac{9}{8}
]
So, (1 \frac{1}{8}) as an improper fraction is (\frac{9}{8}).
Explanation
An improper fraction is a fraction where the numerator (the top number) is greater than or equal to the denominator (the bottom number). In our case, the numerator (9) is greater than the denominator (8), making (\frac{9}{8}) an improper fraction.
Converting mixed numbers to improper fractions is useful in various mathematical operations, particularly in addition, subtraction, and algebraic problems. It simplifies the process, as working with a single fraction instead of a mixed number can reduce confusion and errors.
This method can be applied to any mixed number. First, convert the whole number into an equivalent fraction using the denominator of the fractional part. Then, simply add the two fractions together. This technique can also aid in understanding the relationships between numbers, as mixed numbers often represent quantities, such as measurements in cooking or construction, where fractions are commonly used.
In summary, the conversion of mixed numbers like (1 \frac{1}{8}) to improper fractions, such as (\frac{9}{8}), is a fundamental skill in mathematics that facilitates easier calculations and clearer representation of numbers.