August began working on a computer program. After 7 1/5 hours, he had completed 20 1/10 lines of code. What was his unit rate of programming in lines of code per hour?
You can do: 20 1/10 ÷ 7 1/5
Or: 20.1 ÷ 7.2
For unit rates you do quantity ÷ time
To find the unit rate of programming in lines of code per hour, we can divide the number of lines of code completed by the number of hours.
Number of lines of code completed = 20 1/10 lines
Number of hours = 7 1/5 hours
To add the mixed numbers, we need to convert them to improper fractions.
20 1/10 = (20 * 10 + 1) / 10 = 201/10
7 1/5 = (7 * 5 + 1) / 5 = 36/5
Now, let's divide the number of lines of code by the number of hours:
201/10 ÷ 36/5
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:
201/10 × 5/36
Simplify the fractions:
(201 * 5) / (10 * 36) = 1005 / 360
Divide the numerator by the denominator:
1005 ÷ 360 = 2.7916
The unit rate of programming in lines of code per hour is approximately 2.7916 lines of code per hour.
To find the unit rate of programming in lines of code per hour, we need to divide the total number of lines of code completed by the total number of hours worked.
August completed 20 1/10 lines of code in 7 1/5 hours.
Step 1: Convert the mixed numbers to improper fractions:
20 1/10 = 201/10
7 1/5 = 36/5
Step 2: Divide the total number of lines of code by the total number of hours:
(201/10) / (36/5)
Step 3: When dividing fractions, we multiply the first fraction by the reciprocal of the second fraction:
(201/10) * (5/36)
Step 4: Simplify the fractions if possible:
(201 * 5) / (10 * 36)
Step 5: Multiply the numerators and denominators:
1005 / 360
Step 6: Simplify the fraction if possible:
201 / 72
Therefore, August's unit rate of programming in lines of code per hour is 201/72.