Problem 42 - Fundamentals of Mathematics

Question

Find the value of each of the following. Use a calculator to check each result. $$ 2+7-10+2 $$

Step-by-Step Solution

Answer

The value is 1.

Step 1: Simplify the Expression

Let's start by rewriting the expression in a simpler form. Begin by solving left to right: \(2 + 7\). This gives us \(9\).

Step 2: Continue with Subtraction

Subtract 10 from the value found in Step 1. \(9 - 10\) equals \(-1\).

Step 3: Add Remaining Value

Now add 2 to the result from Step 2. \(-1 + 2\) equals \(1\).

Step 4: Verify with a Calculator

Use a calculator to confirm the result. Enter the expression \(2 + 7 - 10 + 2\) and check if it equals 1.

Key Concepts

Addition

Addition is one of the fundamental arithmetic operations. It involves combining two or more numbers to find their total or sum. When you add numbers, you're counting them together. In the given exercise, addition is used twice.

Here’s how addition works in simple terms:

• You start with two numbers, say 2 and 7.
• You put them together to form a new number, which is 9 in this case (as 2 + 7 equals 9).

Addition is typically represented by the plus sign (+). It’s important to make sure you add numbers in the correct order listed, especially when you are solving an expression step by step. This is the first step in solving the exercise provided.

Subtraction

Subtraction is another basic arithmetic operation closely related to addition. It involves taking one number away from another. This operation helps in finding how many are left or the difference between two numbers. In our exercise, we use subtraction right after performing the addition.

Here’s the subtraction in action:

• You have 9, which was the result of your previous addition (2 + 7).
• Now, subtract 10 from 9. This operation can be thought of as removing 10 units from the group.
• The result is -1. Since 10 is bigger than 9, you end up with a negative number.

Subtraction uses the minus sign (-) to indicate the operation. Recognizing when and how to subtract properly helps in managing combined mathematical operations effectively.

Order of Operations

The order of operations is an essential concept in arithmetic that dictates the correct sequence to follow when performing multiple operations in a mathematical expression. It ensures that everyone arrives at the same answer. Usually, the rules are remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

In the given exercise:

• There are no parentheses or exponents.
• Since all the operations are either addition or subtraction, you solve them in the order they appear from left to right.

By following the order of operations correctly, we simplified the expression to find the right answer (in this case, the final result was 1). The order of operations helps clarify which calculations to complete first and ensures that the expression is solved accurately.