During weekdays, Richard is working as a part-time library assistant at a university. He needs to work for a total of 30 hours a week. For the first three days of the week, he worked 21 1/5 hours. Complete the working equation that represents the number of hours, h , Richard needs to work to reach 30 hours for the week and solve the equation.
The number of hours Richard needs to work to reach 30 hours for the week can be represented by the equation:
30 - 21 1/5 = h
Simplifying the right side of the equation:
30 - (21 + 1/5) = h
30 - 21 - 1/5 = h
30 - 105/5 - 1/5 = h
30 - 106/5 = h
30 - 21 1/5 = h
Converting 21 1/5 to improper fraction:
21 + 1/5 = 21(5/5) + 1/5 = (105/5) + 1/5 = 106/5
Simplifying the equation:
30 - 106/5 = h
(150/5) - (106/5) = h
44/5 = h
So, Richard needs to work 44/5 hours to reach 30 hours for the week.
Let's use "h" to represent the number of hours Richard needs to work to reach 30 hours for the week.
Richard has already worked for 21 1/5 hours for the first three days of the week.
To find the equation, we can subtract the hours Richard has already worked from the total number of hours he needs to work:
h = 30 - 21 1/5
To subtract a mixed number like 21 1/5, we can convert it to an improper fraction.
21 in improper fraction = 21/1
21 1/5 in improper fraction = 21/1 + 1/5 = 106/5
Now we can substitute the value and solve the equation:
h = 30 - 106/5
To simplify the equation further, we can convert 30 to a fraction with a denominator of 5.
30 in fraction form = 30/1 * 5/5 = 150/5
Now the equation becomes:
h = 150/5 - 106/5
To solve this equation, we subtract the numerators and keep the common denominator:
h = (150 - 106)/5
h = 44/5
Therefore, Richard needs to work 44/5 hours or 8 4/5 hours to reach 30 hours for the week.
To solve this problem, we need to find the number of hours Richard still needs to work to reach a total of 30 hours for the week.
Let's represent the number of hours Richard still needs to work as "h".
We already know that in the first three days of the week, Richard worked for 21 1/5 hours, which can be written as 21 + 1/5 hours.
To find the number of hours Richard still needs to work, we subtract the hours he has already worked from the total number of hours required:
h = 30 hours - (21 + 1/5 hours)
To simplify this equation, we need to convert the mixed number (21 1/5) to an improper fraction.
Step 1: Multiply the whole number (21) by the denominator (5) and add the numerator (1) to get the new numerator.
21 x 5 + 1 = 105 + 1 = 106
Step 2: The denominator remains the same.
Therefore, the mixed number 21 1/5 is equivalent to the improper fraction 106/5.
Now we can substitute the value of the hours Richard has already worked:
h = 30 hours - 106/5 hours
To subtract fractions, we need to find a common denominator. In this case, the common denominator is 5.
Step 3: Multiply the numerator (30) by the denominator (5) to get the new numerator.
30 x 5 = 150
Now we can subtract the fractions:
h = 150/5 - 106/5
= (150 - 106)/5
= 44/5
Therefore, Richard still needs to work for 44/5 hours to reach a total of 30 hours for the week.