Evaluating the Expression: 1/2 ÷ 2/3 × 2/5
To evaluate the expression 1/2 ÷ 2/3 × 2/5, we will follow these steps:
- Convert Division to Multiplication:
When dividing by a fraction, we can multiply by its reciprocal. Thus, we can rewrite the expression: - 1/2 ÷ 2/3 becomes 1/2 × 3/2
- Perform the Multiplication:
Now, we multiply: - (1 × 3) / (2 × 2) = 3/4
- Multiply the Result by 2/5:
Now take the result (3/4) and multiply it by (2/5): - (3/4) × (2/5) = (3 × 2) / (4 × 5) = 6/20
- Simplify the Result:
We can simplify 6/20 by finding the greatest common divisor (GCD), which is 2: - (6 ÷ 2) / (20 ÷ 2) = 3/10
Therefore, the final answer is 3/10.
If you want to express this as a mixed number, since the numerator (3) is less than the denominator (10), it remains:
3/10