7 2/3 as a improper fraction ?
The Correct Answer and Explanation is:
To convert the mixed number 7 2/3 into an improper fraction, follow these steps:
Step 1: Understand the structure of a mixed number
A mixed number consists of a whole number and a fraction. In this case, 7 2/3 means 7 whole parts and an additional 2/3 of a part.
Step 2: Multiply the whole number by the denominator of the fraction
The whole number is 7, and the denominator of the fraction is 3 (from 2/3). To begin converting, we multiply the whole number by the denominator:
[
7 \times 3 = 21
]
This step gives us the equivalent fraction form of the whole number 7.
Step 3: Add the numerator of the fractional part
The fraction part of the mixed number is 2/3, so we add the numerator (which is 2) to the result from Step 2:
[
21 + 2 = 23
]
Thus, the improper fraction’s numerator is 23.
Step 4: Keep the same denominator
The denominator of the improper fraction remains the same as the denominator of the fractional part, which is 3.
Step 5: Write the improper fraction
Now, combine the result from Step 3 with the denominator from Step 4 to form the improper fraction:
[
\frac{23}{3}
]
Thus, 7 2/3 as an improper fraction is 23/3.
Explanation
An improper fraction is one where the numerator is greater than or equal to the denominator. In this case, by converting the mixed number into an improper fraction, we express the entire value (the whole number plus the fractional part) as a single fraction, making it easier to perform mathematical operations like addition, subtraction, multiplication, or division involving fractions.
The process involves taking the whole number, multiplying it by the denominator of the fractional part, and then adding the numerator of the fraction. This provides a complete fraction representation of the mixed number, and in this case, 7 2/3 becomes 23/3. This improper fraction can be left as is or converted back into a mixed number if necessary.