Problem 13 - Fundamentals of Mathematics

Question

Determine the value of each of the following. \(8+(32-7)\)

Step-by-Step Solution

Answer

The value is 33.

Step 1: Solve Inside the Parentheses

According to the order of operations, we first solve any expression inside parentheses. The expression inside the parentheses is \(32 - 7\). Subtract 7 from 32, which gives us 25.

Step 2: Add the Results

Now that we have solved the expression inside the parentheses to get 25, we add it to 8: \(8 + 25 = 33\).

Key Concepts

Parentheses

When tackling math problems, one of the first things to look for is parentheses. Parentheses are like the organizers; they tell you what to focus on first. In math, the order of operations means we deal with anything inside parentheses before doing other calculations. This is crucial because it ensures that everyone solves the problem in the same way and gets the same result.

For example, if you have the expression \(8 + (32 - 7)\), find what’s in parentheses first, \(32 - 7\). By figuring this part out first, we simplify the expression and make it easier to solve the rest. Always remember, what happens inside the parentheses stays inside until it's all worked out!

Addition

After solving any operations within parentheses, we move on to addition. Addition is very straightforward, involving combining numbers to find their total. Think of it like gathering items into a single pile to see how much you have.

In the expression \(8 + (32 - 7)\), once you’ve performed the subtraction inside the parentheses and have \(25\), it's time for addition. You add \(8\) and \(25\), giving you a total of \(33\).

Addition is generally the easiest operation because it doesn’t matter which order you add things in—\(a + b\) is the same as \(b + a\). So, if you prefer, you can think of \(25 + 8\) instead of \(8 + 25\), and the result will still be the same: \(33\).

Subtraction

Subtraction is about taking away, and it can be trickier than addition because the order matters. It’s the process of finding the difference between numbers. You might think of it like removing something from a group to see what’s left.

In the expression \(8 + (32 - 7)\), we focus on \(32 - 7\) first since it's in the parentheses. Subtract \(7\) from \(32\), leaving you with \(25\). This subtraction step is essential before any addition can occur, as it simplifies the problem and helps lead to the correct result.

Always pay attention to the order in which you perform subtraction since \(a - b\) is not the same as \(b - a\). In our case, \(32 - 7\) gives \(25\), but \(7 - 32\) would yield a negative number. Thus, following the problem order is important to avoid mistakes.