To evaluate the expression 3/4 × 4/5 - 1/2, follow these steps:
Step 1: Multiply the fractions
First, we multiply 3/4 by 4/5:
(3/4) × (4/5) = (3 × 4) / (4 × 5) = 12/20
Step 2: Simplify the result
Now we can simplify 12/20:
Both the numerator and the denominator can be divided by 4:
12 ÷ 4 = 3 and 20 ÷ 4 = 5.
So, 12/20 = 3/5.
Step 3: Convert 1/2 to have a common denominator
Next, we need a common denominator to subtract 1/2 from 3/5. The least common multiple of 5 and 2 is 10.
Convert 3/5 and 1/2:
- 3/5 = (3 × 2) / (5 × 2) = 6/10
- 1/2 = (1 × 5) / (2 × 5) = 5/10
Step 4: Subtract the fractions
Now that we have a common denominator, we can subtract:
6/10 - 5/10 = 1/10
Step 5: Final answer
The expression 3/4 × 4/5 - 1/2 evaluates to 1/10.