What is 24 divided by 23 1/3 equal in fraction form and simplified
The Correct Answer and Explanation is:
Answer: 242313=24703=24×370=7270=3635\frac{24}{23\frac{1}{3}} = \frac{24}{\frac{70}{3}} = \frac{24 \times 3}{70} = \frac{72}{70} = \frac{36}{35}233124=37024=7024×3=7072=3536
Explanation
To divide a whole number by a mixed number, we follow a systematic approach. First, we convert the mixed number into an improper fraction. Then we rewrite the division as multiplication by the reciprocal. Finally, we simplify the resulting fraction to its lowest terms.
In this problem, we are dividing 24 by 23⅓. The mixed number 23⅓ means 23 plus one-third. To convert this into an improper fraction, we multiply the whole number part (23) by the denominator of the fractional part (3), and then add the numerator (1). This gives: 23×3=69,69+1=7023 \times 3 = 69, \quad 69 + 1 = 7023×3=69,69+1=70
So, 23⅓ is equal to the improper fraction 703\frac{70}{3}370.
Now, the original problem becomes: 24703\frac{24}{\frac{70}{3}}37024
To divide by a fraction, we multiply by its reciprocal. The reciprocal of 703\frac{70}{3}370 is 370\frac{3}{70}703. So, we have: 24703=24×370\frac{24}{\frac{70}{3}} = 24 \times \frac{3}{70}37024=24×703
We multiply the numerators and the denominators: 24×3=72,1×70=70,so727024 \times 3 = 72, \quad 1 \times 70 = 70, \quad \text{so} \quad \frac{72}{70}24×3=72,1×70=70,so7072
This fraction can be simplified. Both 72 and 70 are divisible by 2: 72÷270÷2=3635\frac{72 \div 2}{70 \div 2} = \frac{36}{35}70÷272÷2=3536
This is the simplified form of the fraction. It is an improper fraction because the numerator (36) is larger than the denominator (35), but it is already in simplest terms since 36 and 35 have no common factors other than 1.
Thus, 24 divided by 23⅓ equals 3635\frac{36}{35}3536 in simplified fraction form.
