Identify the property or rule that justifies each step in the calculation.
4/7k+(j+1/7k)
hint: distributive law
To identify the property or rule that justifies each step in the calculation of 4/7k + (j + 1/7k), we need to break down the calculation and explain each step:
Step 1: Add parentheses for clarity:
4/7k + (j + 1/7k)
Step 2: Distributive Property:
The distributive property states that a(b + c) = ab + ac. In this step, we apply the distributive property to distribute the 1/7k term:
4/7k + j + 1/7k
Step 3: Combine like terms:
Here, we combine the terms 4/7k and 1/7k. Since they have the same denominator, we can add their numerators and keep the denominator:
(4 + 1) / 7k + j
Step 4: Simplify the numerator:
The numerator 4 + 1 simplifies to 5, so we have:
5 / 7k + j
The justification for each step is as follows:
- Step 1: No property is applied; it is just a notation change for clarity.
- Step 2: The distributive property is used to distribute the 1/7k term.
- Step 3: The terms with the same denominator are combined by adding their numerators.
- Step 4: The numerator is simplified by adding 4 and 1.