Identify the property or rule that justifies each step in the calculation.
4/7k+(j+1/7k) ________
(4/7k+1/7k)+j ________
k(4/7+1/7)+j _________
(4/7k+1/7k)+j ________
5/7k+j _______
Hint: you cannot say that 5/7k+j is the answer
from the first step to the second
You used the Commutative Law and the Associative law.
from the second step to the first step you factored out the common K.
It looks like it was put back in for the next step.
Last step.. combined like terms.
To identify the property or rule that justifies each step in the calculation, let's walk through each step one by one:
Step 1:
4/7k + (j + 1/7k)
To simplify the expression in parentheses, we can apply the Commutative Property of Addition, which states that the order of adding numbers can be changed without affecting the result. So, we can rearrange the terms inside the parentheses:
(j + 1/7k) + 4/7k
Step 2:
(j + 1/7k) + 4/7k
Next, we can use the Associative Property of Addition, which states that the grouping of numbers being added can be changed without affecting the result. So, we can rearrange the terms inside the parentheses:
j + (1/7k + 4/7k)
Step 3:
j + (1/7k + 4/7k)
To simplify 1/7k + 4/7k, we add the numerators (1 + 4) while keeping the denominator the same:
j + (5/7k)
Step 4:
j + (5/7k)
Now, we can apply the Commutative Property of Addition to rearrange the terms in any order:
(5/7k) + j
Step 5:
(5/7k) + j
Finally, we have the terms in the desired order. However, if you're looking for the answer in simplest form, you cannot combine the terms further because they have different variables (k and j).
So, the final simplified expression is (5/7k) + j.