What mixed number has the same value as 23/3? A) 7 1/3 B) 7 2/3 C) 6 1/3 D) 6 2/3
The Correct Answer and Explanation is:
To convert the improper fraction 233\frac{23}{3}323 to a mixed number, follow these steps:
Step 1: Divide the numerator by the denominator
Divide 23 by 3:23÷3=7 with a remainder of 223 \div 3 = 7 \text{ with a remainder of } 223÷3=7 with a remainder of 2
This means that:
- 3 goes into 23 exactly 7 whole times
- 2 is left over after subtracting 3×7=213 \times 7 = 213×7=21 from 23
Step 2: Write as a mixed number
The quotient becomes the whole number part, and the remainder becomes the numerator of the fractional part. The denominator stays the same:233=723\frac{23}{3} = 7 \frac{2}{3}323=732
Final Answer:
B) 7 2/3
Explanation:
An improper fraction has a numerator larger than its denominator. In this case, 23 is larger than 3, making 233\frac{23}{3}323 improper. To make it easier to understand and work with, especially in everyday contexts like measuring or cooking, we convert it to a mixed number, which includes a whole number and a proper fraction.
The whole number represents how many full groups of 3 can be taken from 23, while the fraction shows what is left over. Since 3 fits into 23 exactly 7 full times, and 2 remain, we express this as 7 wholes and 23\frac{2}{3}32 of another group.
This is a useful skill in math because mixed numbers often make more sense when describing quantities in real-life situations, like 7 and two-thirds of a pizza or 7 and two-thirds of an hour.
So the mixed number that has the same value as 233\frac{23}{3}323 is 7 23\frac{2}{3}32.
Correct answer: B) 7 2/3.
