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Chapter 2: Problem 440

In the following exercises, simplify, using the order of operations. $$ 4+3 \cdot 5 $$

Short Answer

Expert verified
The simplified result is 19.

Step by step solution

01

Identify the Order of Operations

Remember the order of operations using BEDMAS/BODMAS (Brackets, Exponents/Orders, Division and Multiplication (from left to right), Addition and Subtraction (from left to right)).
02

Perform Multiplication First

According to the order of operations, multiplication comes before addition. So, start by calculating the multiplication: $$3 \times 5 = 15$$
03

Perform Addition

Now, add the result of the multiplication to the number 4: $$4 + 15 = 19$$

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Key Concepts

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

BEDMAS
The acronym **BEDMAS** stands for **Brackets, Exponents, Division/Multiplication, Addition/Subtraction**. This helps us remember the order in which we should perform operations when simplifying mathematical expressions.

Here's a brief summary of each step:
  • **Brackets (B)**: Solve expressions inside brackets first.
  • **Exponents (E)**: Evaluate powers or roots next.
  • **Division/Multiplication (DM)**: Perform these from left to right.
  • **Addition/Subtraction (AS)**: Finally, do these from left to right.

For instance, in the given problem, we have to consider these rules to solve the expression: \(4 + 3 \cdot 5\).
Notice there are no brackets or exponents involved, so we move to division/multiplication.
BODMAS
In some countries, the order of operations is referred to as **BODMAS**. This mnemonic stands for **Brackets, Orders, Division/Multiplication, Addition/Subtraction**. 'Orders' here is just another term for exponents and roots.

  • **Brackets (B)**: Solve what's inside parentheses first.
  • **Orders (O)**: Handle powers or roots next.
  • **Division/Multiplication (DM)**: Do these operations from left to right, as they appear.
  • **Addition/Subtraction (AS)**: Lastly, perform these from left to right.

Both BODMAS and BEDMAS follow the same logic, only the wording differs slightly.
Applying BODMAS to the problem \(4 + 3 \cdot 5\): we again skip brackets and exponents and move to multiplication first.
Simplifying Expressions
Simplifying expressions means reducing them to their simplest form. This often involves following the order of operations to combine like terms and perform arithmetic.

For the provided problem:

  • Start with the given expression: \(4 + 3 \cdot 5\)
  • Follow BEDMAS/BODMAS rules, prioritizing multiplication: \(3 \cdot 5 = 15\)
  • Substitute and perform the remaining addition: \(4 + 15 = 19\)

This results in our simplified expression being \(19\).
Always remember, the primary goal is clarity and simplicity, ensuring that every step logically follows from the previous one.

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