Problem 35 - Elementary Algebra

Question

For the following problems, use the order of operations to find each value. $$0 \cdot 9+4 \cdot 0 \div 7+0[2(2-2)]$$

Step-by-Step Solution

Answer

Answer: The final value of the expression is 0.

Step 1: Handle parentheses first

We will start by evaluating any terms inside brackets and parenthesis. In this case, we have the term $$0[2(2-2)]$$. We should first evaluate the expression within the parentheses \((2-2)\). Which is: $$(2-2) = 0$$ Now, our expression becomes: $$0 \cdot 9 + 4 \cdot 0 \div 7 + 0[2(0)]$$ Step 2: Multiplication and Division

Step 2: Perform multiplication and division operations from left to right

In this step, we will perform all of the multiplication and division operations in the order from left to right. In our expression, we have the following multiplication and division operations: $$0 \cdot 9, \quad 4 \cdot 0, \quad 0 \div 7$$ Now, we'll apply these operations individually: $$(0 \cdot 9) = 0, \quad (4 \cdot 0) = 0, \quad (0 \div 7) = 0$$ Now substitute these results back into the expression: $$0 + 0 \div 7 + 0[2(0)]$$ Step 3: Simplify and Eliminate

Step 3: Simplify and eliminate unnecessary terms

In this step, we will try to simplify our expression by eliminating unnecessary terms. We have the following terms in our expression: $$0 + 0 \div 7 + 0[2(0)]$$ Since any number multiplied by 0 is 0, we can eliminate the term \(0[2(0)]\): $$0 + 0 \div 7$$ Step 4: Addition and Subtraction

Step 4: Perform addition and subtraction operations from left to right

Now, we can perform the addition and subtraction operations in the expression from left to right. Our expression now looks like: $$0 + 0 \div 7$$ Since the division operation has been simplified to 0 in step 2, the expression becomes: $$0+0$$ This results in a final value of: $$0$$ The final value of the expression is 0.