To evaluate the expression: 1/2 ÷ 4/5 + 1/4 × 3/4, we will break it down into manageable steps.
Step 1: Evaluate the Division
1/2 ÷ 4/5
When dividing fractions, we multiply by the reciprocal of the second fraction:
1/2 ÷ 4/5 = 1/2 × 5/4
Now we multiply:
1 × 5 = 5 and 2 × 4 = 8
So, 1/2 ÷ 4/5 = 5/8
Step 2: Evaluate the Multiplication
1/4 × 3/4
Simply multiply the numerators and the denominators:
1 × 3 = 3 and 4 × 4 = 16
So, 1/4 × 3/4 = 3/16
Step 3: Combine the Results
Now we need to add the two results:
5/8 + 3/16
Before adding, we need a common denominator. The least common denominator of 8 and 16 is 16. Convert 5/8 into sixteenths:
5/8 = (5 × 2)/(8 × 2) = 10/16
Now, we can add:
10/16 + 3/16 = 13/16
Final Answer
The final answer is 13/16.