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Chapter 1: Problem 43

Simplify the given expression. $$ 15-2+5 $$

Short Answer

Expert verified
The simplified expression is 18.

Step by step solution

01

Identify the operations in the expression

The given expression is 15 - 2 + 5. It involves two operations: subtraction and addition.
02

Perform the subtraction first

Follow the order of operations (from left to right, since addition and subtraction have the same priority). First, subtract 2 from 15: \[15 - 2 = 13\].
03

Perform the addition

Now add 5 to the result from Step 2: \[13 + 5 = 18\].

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Addition
Addition is one of the fundamental operations in mathematics that involves combining two numbers to get a sum. In the context of the expression we're dealing with, addition helps us find the total or increase a value.
  • To perform addition, align the numbers' decimal points (if any) and add from right to left.
  • Carry over any values if the sum of a column exceeds 9.
In our example, after simplifying the subtraction, we encountered adding 5 to 13. This is a straightforward example where you simply bring two values together: \[13 + 5 = 18\]Always ensure to follow the sequence provided by the expression when dealing with multiple operations. But within any given step, addition is a relatively simple process of combining numbers.
Subtraction
Subtraction is the process of taking away one number from another, and it helps in determining the difference between values. In our exercise, subtraction is performed before addition due to the order of operations.
  • Line up the numbers by their place values.
  • If needed, borrow from the next higher place value to perform the subtraction.
In the expression, the subtraction step is: \[15 - 2 = 13\]Here, 2 is taken away from 15, leaving us with the difference of 13.
Simplification
Simplification aims to reduce expressions to their simplest form, making them easier to work with or understand. This often involves performing operations step by step to achieve a neat and concise result.
  • Identify all operations involved.
  • Follow the order of operations: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
In our example, the expression is simplified by first handling subtraction and then addition:1. Perform subtraction: \[15 - 2 = 13\]2. Followed by addition:\[13 + 5 = 18\]The final simplified result is 18, which is much easier to interpret or further use in calculations. Simplification makes expressions neat and avoids confusion, a key in mathematics.

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