Evaluate 1 1/5 ÷ 2
Understand the Problem
The question asks to evaluate the expression (1 \frac{1}{5} \div 2). This involves converting the mixed fraction into an improper fraction and then performing the division.
Answer
$\frac{3}{5}$
Answer for screen readers
$\frac{3}{5}$
Steps to Solve
- Convert the mixed fraction to an improper fraction
To convert $1\frac{1}{5}$ to an improper fraction, multiply the whole number (1) by the denominator (5) and add the numerator (1). Then, place the result over the original denominator (5). $$1\frac{1}{5} = \frac{(1 \times 5) + 1}{5} = \frac{5 + 1}{5} = \frac{6}{5}$$
- Divide the improper fraction by 2
Dividing by 2 is the same as multiplying by $\frac{1}{2}$. $$\frac{6}{5} \div 2 = \frac{6}{5} \times \frac{1}{2} = \frac{6 \times 1}{5 \times 2} = \frac{6}{10}$$
- Simplify the fraction
Simplify $\frac{6}{10}$ by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 2. $$\frac{6}{10} = \frac{6 \div 2}{10 \div 2} = \frac{3}{5}$$
$\frac{3}{5}$
More Information
The result of $1 \frac{1}{5} \div 2$ is $\frac{3}{5}$, which is a proper fraction.
Tips
A common mistake is forgetting to convert the mixed fraction to an improper fraction before performing the division. Another mistake is incorrectly simplifying the resulting fraction.
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