To evaluate the expression 2/5 × 1/2 + 4/5 × 3/4, we can break it down into two separate parts and then combine the results.
Step 1: Evaluate 2/5 × 1/2
To multiply two fractions, multiply the numerators together and the denominators together:
Numerator: 2 × 1 = 2
Denominator: 5 × 2 = 10
So, 2/5 × 1/2 = 2/10. We can simplify this fraction:
2 ÷ 2 = 1 and 10 ÷ 2 = 5, thus 2/10 = 1/5.
Step 2: Evaluate 4/5 × 3/4
Again, we multiply the numerators and denominators:
Numerator: 4 × 3 = 12
Denominator: 5 × 4 = 20
So, 4/5 × 3/4 = 12/20. We can simplify this fraction:
12 ÷ 4 = 3 and 20 ÷ 4 = 5, thus 12/20 = 3/5.
Step 3: Add the two fractions
Now we need to add 1/5 + 3/5. Since they have the same denominator (5), we can simply add the numerators:
1 + 3 = 4
So, 1/5 + 3/5 = 4/5.
Final Answer
The result of the expression 2/5 × 1/2 + 4/5 × 3/4 is 4/5.