How do you solve 24÷3/8 ?
The Correct Answer and Explanation is:
To solve the expression ( 24 \div \frac{3}{8} ), you need to remember the rules of dividing fractions. When you divide by a fraction, it is equivalent to multiplying by its reciprocal. Therefore, the expression can be rewritten as:
[
24 \div \frac{3}{8} = 24 \times \frac{8}{3}
]
Step 1: Convert the Whole Number to a Fraction
First, we convert the whole number 24 into a fraction. This is done by expressing it as ( \frac{24}{1} ). So the expression becomes:
[
\frac{24}{1} \times \frac{8}{3}
]
Step 2: Multiply the Fractions
Next, multiply the numerators (the top parts) and the denominators (the bottom parts) of the fractions:
[
\frac{24 \times 8}{1 \times 3} = \frac{192}{3}
]
Step 3: Simplify the Resulting Fraction
Now, you need to simplify ( \frac{192}{3} ). You can do this by performing the division:
[
192 \div 3 = 64
]
So, ( \frac{192}{3} ) simplifies to 64.
Conclusion
Thus, the final answer to the expression ( 24 \div \frac{3}{8} ) is:
[
\boxed{64}
]
Additional Insights
This process illustrates a fundamental principle of arithmetic involving fractions. Dividing by a fraction can often be more intuitive when we consider it as multiplying by the reciprocal. Understanding this concept is essential in higher mathematics and helps in simplifying complex equations. The ability to manipulate fractions is crucial in many applications, such as in algebra, where variable manipulation often involves similar operations with fractions. The key takeaway is to remember that dividing by a fraction translates into multiplication by its reciprocal, which simplifies many calculations and helps in achieving the correct results efficiently.