use the propertys of operation to add 9(k+1/3)+10(1/2k-1)
To simplify the expression 9(k + 1/3) + 10(1/2k - 1) using the properties of operations, we need to distribute the 9 and 10 to the terms inside the parentheses.
First, distribute the 9:
9(k + 1/3) = 9k + 9(1/3)
Next, distribute the 10:
10(1/2k - 1) = 10(1/2k) - 10(1)
Simplifying these expressions:
9k + 9(1/3) = 9k + 9/3 = 9k + 3
10(1/2k) - 10(1) = 10/2k - 10
Now, we can combine like terms:
9k + 3 + 10/2k - 10 = 9k + 10/2k + 3 - 10
To simplify further, we need to find a common denominator for 2k:
Common denominator = 2k
Rewriting 10 as 10 * (2k)/(2k):
9k + 10/2k + 3 - 10 = 9k + 10(2k)/(2k) + 3 - 10
Now, we can add the fractions with the same denominator:
9k + 10(2k)/(2k) + 3 - 10 = 9k + (20k)/(2k) + 3 - 10
Simplifying the addition of fractions:
9k + (20k)/(2k) + 3 - 10 = 9k + 10k + 3 - 10 = 19k + 3 - 10 = 19k - 7
Therefore, the simplified form of 9(k + 1/3) + 10(1/2k - 1) is 19k - 7.