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Chapter 15: Problem 45

Simplify. $$ 25-8 \cdot 3+1 $$

Short Answer

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Step by step solution

01

Follow the order of operations

When simplifying expressions, always remember to follow the order of operations: Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
02

Perform the multiplication

Identify and perform the multiplication in the expression first. Simplify \[ 25 - 8 \cdot 3 + 1 = 25 - 24 + 1 \].
03

Perform the subtraction

After the multiplication, perform the subtraction next. Simplify \[ 25 - 24 + 1 = 1 + 1 \].
04

Perform the addition

After completing the subtraction, perform the addition. Simplify \[ 1 + 1 = 2 \].

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Key Concepts

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

Simplifying expressions
Simplifying expressions involves breaking down complex mathematical statements into simpler forms. This makes them easier to understand and solve.

When you simplify expressions, always follow specific rules and steps called the order of operations. The acronym PEMDAS can help you remember this process:

鈥� **P**arentheses
鈥� **E**xponents
鈥� **M**ultiplication
鈥� **D**ivision
鈥� **A**ddition
鈥� **S**ubtraction

These rules ensure that everyone interprets and solves expressions the same way.

For example, in the expression \[ 25 - 8 \times 3 + 1 \], start by identifying and performing any multiplications first before moving on to additions or subtractions.
Multiplication
Multiplication is a core mathematical operation that involves combining equal groups. It is essential to perform multiplication before addition and subtraction in expressions.

In the expression \[ 25 - 8 \times 3 + 1 \], follow these steps:

  • First, identify the multiplication: \[ 8 \times 3 \]
  • Perform the multiplication: \[ 8 \times 3 = 24 \]

After performing the multiplication, the expression simplifies to \[ 25 - 24 + 1 \].

By handling multiplication first, you ensure correct and consistent results.
Addition and Subtraction
Addition and subtraction are fundamental arithmetic operations used to combine or separate values. In expressions, these operations should be carried out after handling parentheses, exponents, multiplication, and division.

Using the simplified expression \[ 25 - 24 + 1 \]:
  • First, perform the subtraction: \[ 25 - 24 = 1 \]
  • Next, perform the addition: \[ 1 + 1 = 2 \]

This order of operations guarantees accuracy. By performing subtraction and addition last, you respect the hierarchy set by PEMDAS, ensuring your answers are correct.

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