Problem 97 - Prealgebra

Question

Simplify. $$9 \cdot 6+5$$

Step-by-Step Solution

Answer

The simplified value is 59.

Step 1: Identify the operations and their order

First, identify the operations in the given expression. The expression is \(9 \cdot 6 + 5\). According to the order of operations (PEMDAS/BODMAS), multiplication comes before addition.

Step 2: Perform the multiplication

Perform the multiplication operation first. Calculate \(9 \cdot 6\). Multiply 9 by 6 to get 54.

Step 3: Perform the addition

Now that we have calculated the multiplication, the expression is \(54 + 5\). Add 54 and 5 to get 59.

Key Concepts

PEMDAS

The order of operations is an essential concept in mathematics for evaluating expressions correctly. A popular acronym for remembering this order in the United States is **PEMDAS**. This stands for:

• **P**arentheses
• **E**xponents (or indices)
• **M**ultiplication
• **D**ivision
• **A**ddition
• **S**ubtraction

It is crucial to follow **PEMDAS** precisely to avoid mistakes when simplifying expressions.
When expressions contain multiple types of operations, begin with items enclosed in parentheses. Then, move on to exponents, followed by any multiplication or division from left to right. Finally, handle addition and subtraction, also from left to right.
Let's consider our given expression: \(9 \cdot 6 + 5\). According to **PEMDAS**, multiplication is performed before addition. Therefore,we first calculate \(9 \cdot 6 = 54\) before proceeding to add 5.

BODMAS

In several countries, particularly those following British educational traditions, a different acronym, **BODMAS**, is used to describe the order of operations.

• **B**rackets
• **O**rders (another term for exponents or powers)
• **D**ivision
• **M**ultiplication
• **A**ddition
• **S**ubtraction

While **BODMAS** serves the same function as **PEMDAS**, the order remains essentially unchanged.
Brackets (similar to parentheses) are prioritized, followed by orders.
Multiplication and division are treated equally and performed from left to right, according to their appearance. Addition and subtraction are handled last, with the same left-to-right rule.
In our expression \(9 \cdot 6 + 5\), **BODMAS** instructs us to perform multiplication prior to addition. The calculation proceeds as \(9 \cdot 6 = 54\), followed by adding 5 to yield 59.

Simplifying Expressions

Simplifying expressions involves reducing an expression to its most basic form without changing its value. By applying the order of operations (whether **PEMDAS** or **BODMAS**), we ensure that we simplify correctly.
To simplify an expression, always follow the established sequence of operations to avoid errors and achieve the correct result.
For example, in the expression \(9 \cdot 6 + 5\), we first handle the multiplication: \(9 \cdot 6 = 54\). Afterward, the remaining operations are straightforward to carry out, such as the addition to obtain \(54 + 5 = 59\).
Using such strategies will help in achieving consistent and correct results, reducing complex expressions easily and efficiently.