which mixed number is equivalent to the improper fraction? 23/3 A. 6 5/3 B. 8 1/3 C. 7 1/3 D. 7 2/3
The Correct Answer and Explanation is:
The correct answer is: C. 7 2/3
Explanation:
To convert an improper fraction like 23/3 into a mixed number, follow these steps:
1. Divide the numerator by the denominator.
We divide 23 by 3:
- 3 goes into 23 a total of 7 times without exceeding it.
- 3 × 7 = 21
- Subtract 21 from 23 to get the remainder: 23 − 21 = 2
So, we have:
- Quotient = 7 (this is the whole number part)
- Remainder = 2 (this becomes the numerator of the fractional part)
- The denominator remains the same = 3
Thus, 23/3 = 7 2/3
2. Understanding why this works:
Improper fractions have numerators greater than or equal to the denominators, meaning they represent values greater than one whole unit. Mixed numbers express this value as a combination of a whole number and a proper fraction.
The mixed number 7 2/3 means:
- Seven whole parts (each equal to 3/3),
- Plus an additional 2/3,
- So altogether:
7 × 3/3 = 21/3, and
21/3 + 2/3 = 23/3
Therefore, 7 2/3 is equivalent to 23/3.
3. Why other options are incorrect:
- A. 6 5/3: This is also an improper mixed number. 5/3 is greater than 1, making it incorrect as a simplified mixed number.
- B. 8 1/3: 8 × 3 + 1 = 24 + 1 = 25 → 25/3, not 23/3.
- D. 7 1/3: 7 × 3 + 1 = 21 + 1 = 22 → 22/3, not 23/3.
Final Answer: C. 7 2/3
