Problem 94 - Prealgebra

Question

Simplify. $$36-9+20$$

Step-by-Step Solution

Answer

The simplified result is 47.

Step 1: Order of Operations

According to the order of operations (PEMDAS/BODMAS), we start by working from left to right when we only have addition and subtraction. Therefore, we will first calculate the subtraction: \(36 - 9\).

Step 2: Subtraction

Perform the subtraction from the previous step: \(36 - 9 = 27\). Now, we have \(27 + 20\) remaining.

Step 3: Addition

Proceed to add the remaining numbers: \(27 + 20 = 47\).

Key Concepts

Addition and Subtraction

In mathematics, addition and subtraction are fundamental arithmetic operations. These operations are often performed from left to right, especially when they appear consecutively in a calculation, provided no parentheses or other operations take precedence. This sequence is essential to obtaining correct results. For example, if you have the expression \(36 - 9 + 20\), you should first perform the subtraction before moving to addition.

• Subtract 9 from 36: \(36 - 9 = 27\)
• Then, add 20 to 27: \(27 + 20 = 47\)

Understanding this sequence is crucial because reversing the order could lead to incorrect results. Always move from left to right, ensuring you handle addition and subtraction in the order they appear unless other rules like parentheses direct your actions.

PEMDAS

PEMDAS is an acronym used to remember the order of operations in mathematics: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). It is a helpful guideline for solving expressions that involve multiple operations. When there are only addition and subtraction in an expression, like in our problem, you follow them as they appear from left to right.
In the expression \(36 - 9 + 20\):

• Without parentheses, begin with subtraction: \(36 - 9 = 27\).
• Then, proceed to addition: \(27 + 20 = 47\).

PEMDAS ensures that you carry out mathematical operations in the right order, preventing confusion and errors. Always remember, operations higher in the PEMDAS hierarchy are completed before moving to those lower in the order.

BODMAS

BODMAS is another mnemonic that outlines the order of operations similar to PEMDAS. It stands for Brackets, Order (meaning powers, roots), Division and Multiplication (from left to right), Addition and Subtraction (from left to right). This rule helps decide which calculation to perform first in an expression. Remember, for expression \(36 - 9 + 20\), even using BODMAS:

• Brackets and orders are absent, so move to the leftmost operation.
• Subtraction first: \(36 - 9 = 27\).
• Addition follows: \(27 + 20 = 47\).

Whether using PEMDAS or BODMAS, the goal remains to systematically and accurately solve expressions. Both acronyms ultimately guide you through simplifying expressions in the correct sequence.