What the improper fraction of 9 1/3
The Correct Answer and Explanation is:
To convert the mixed number 9 1/3 into an improper fraction, follow these steps:
- Understand the components of a mixed number:
- A mixed number consists of a whole number (9) and a fraction (1/3).
- In this case, the whole number is 9 and the fractional part is 1/3.
- Convert the whole number to a fraction:
- Every whole number can be expressed as a fraction with the denominator of 1. For example, the whole number 9 can be written as:
[
9 = \frac{9}{1}
]
- Express the mixed number as a sum of the whole number and the fraction:
- The mixed number 9 1/3 can be written as:
[
9 1/3 = 9 + \frac{1}{3}
]
- Convert the whole number into a fraction with the same denominator as the fractional part:
- To add the whole number 9 and the fraction 1/3, they need a common denominator. Since the fractional part is already expressed with the denominator 3, convert 9 to a fraction with 3 as the denominator:
[
9 = \frac{9}{1} = \frac{9 \times 3}{1 \times 3} = \frac{27}{3}
]
- Add the fractions:
- Now that both parts are fractions with the same denominator, you can add them:
[
9 + \frac{1}{3} = \frac{27}{3} + \frac{1}{3} = \frac{27 + 1}{3} = \frac{28}{3}
]
Thus, the improper fraction equivalent of the mixed number 9 1/3 is 28/3.
Why does this work?
This process works because a mixed number represents the sum of a whole number and a fraction. To combine these into a single fraction, we rewrite the whole number as a fraction with the same denominator as the fractional part, then add them together. By multiplying the whole number by the denominator of the fraction, we align both parts under the same denominator, making it possible to combine them into a single improper fraction.