Identify the property or rule that justifies each step in the calculation.
4/7k+(j+1/7k)
4/7k+(1/7k+j)
(4/7k+1/7k)+j
k(4/7+1/7)+j
5/7k+j
To identify the property or rule used in each step of the calculation, let's go through them one by one:
Step 1: 4/7k + (j + 1/7k)
In this step, we have a single expression consisting of two parts, 4/7k and (j + 1/7k). We are using the associativity property of addition, which states that the order in which numbers are added does not affect the sum. So we can rearrange the parentheses without changing the value.
Step 2: 4/7k + (1/7k + j)
In this step, we have rearranged the terms within the parentheses. Again, this is due to the associativity property of addition. We can move the terms around without changing the sum.
Step 3: (4/7k + 1/7k) + j
In this step, we have grouped the terms 4/7k and 1/7k together. This is because of the commutativity property of addition, which states that the order in which numbers are added does not affect the sum. We can add 4/7k and 1/7k in any order.
Step 4: k(4/7 + 1/7) + j
In this step, we have factored out the common term k from the grouped terms (4/7k + 1/7k). This is known as the distributive property, which states that the product of a number and a sum is equal to the sum of the products. Here, we are multiplying k by the sum (4/7 + 1/7).
Step 5: 5/7k + j
In this step, we have simplified the expression (4/7 + 1/7), which equals 5/7. This is simply an arithmetic calculation.
Overall, the properties and rules used in this calculation are the associativity of addition, the commutativity of addition, and the distributive property.