Evaluate 2 divided by 3/5. Give your answer as a mixed number in its simplest form.
The Correct Answer and Explanation is :
To evaluate (2 \div \frac{3}{5}), we can convert the division of a fraction into multiplication by its reciprocal.
Step 1: Write the Expression
We start with the expression:
[
2 \div \frac{3}{5}
]
Step 2: Multiply by the Reciprocal
Instead of dividing, we multiply by the reciprocal of (\frac{3}{5}). The reciprocal is found by flipping the numerator and denominator:
[
\text{Reciprocal of } \frac{3}{5} = \frac{5}{3}
]
Now we rewrite the expression:
[
2 \times \frac{5}{3}
]
Step 3: Rewrite the Whole Number as a Fraction
To multiply a whole number by a fraction, we can express the whole number (2) as a fraction:
[
2 = \frac{2}{1}
]
Now we have:
[
\frac{2}{1} \times \frac{5}{3}
]
Step 4: Multiply the Numerators and Denominators
Next, we multiply the numerators and the denominators:
[
\frac{2 \times 5}{1 \times 3} = \frac{10}{3}
]
Step 5: Convert to Mixed Number
To convert (\frac{10}{3}) into a mixed number, we divide the numerator by the denominator:
[
10 \div 3 = 3 \quad \text{(whole number)} \quad \text{with a remainder of } 1.
]
Thus, we can express (\frac{10}{3}) as:
[
3 \frac{1}{3}
]
Conclusion
The final result of (2 \div \frac{3}{5}) is:
[
\boxed{3 \frac{1}{3}}
]
Explanation
Dividing by a fraction can seem tricky, but converting the division into multiplication by the reciprocal simplifies the process significantly. Understanding how to convert whole numbers to fractions is also crucial, especially when dealing with mixed numbers and ensuring that results are in their simplest form. Mixed numbers help express quantities in a way that is often easier to interpret, combining whole parts and fractional parts effectively.