Problem 14 - Fundamentals of Mathematics

Question

Determine the value of each of the following. \((34+18-2 \cdot 3)+11\)

Step-by-Step Solution

Answer

The value is 57.

Step 1: Solve the Multiplication

Identify the multiplication within the expression to simplify: \(2 \cdot 3\). Calculate \(2 \cdot 3 = 6\). Now replace \(2 \cdot 3\) with 6 in the expression. The expression becomes \(34 + 18 - 6 + 11\).

Step 2: Perform Addition and Subtraction

Start by performing addition and subtraction from left to right as per the order of operations. Begin with \(34 + 18\) which equals \(52\). Then subtract 6 from the result: \(52 - 6 = 46\). Finally, add 11 to \(46\): \(46 + 11 = 57\).

Key Concepts

Understanding Addition

Addition is one of the basic arithmetic operations and is used to find the total or sum of numbers. It's a way of combining values. When you perform addition, you start with two or more numbers and combine them into a single number, known as the sum.
For the expression we worked on, the addition operation was demonstrated when we calculated:

• The sum of two numbers, such as adding 34 and 18. It teaches us that adding increases the total, mathematically expressed as: \[34 + 18 = 52\]
• Then, we continued with adding 11 to a previous result, which finalized the addition process: \[46 + 11 = 57\]

Understanding the concept of addition lays a foundational skill in mathematics, helping in everyday calculations and more complex problem-solving scenarios.

The Role of Subtraction

Subtraction is the process of taking one number away from another. It is used to determine how much is left when a part is removed from a whole. In our example, subtraction happened after an addition within the expression:

• When we took the product of 2 and 3, yielding 6, which was then subtracted from the existing sum (after addition of 34 and 18): \[52 - 6 = 46\]

The order of operations stresses that subtraction follows any operation of multiplication or division in the sequence unless laid out differently with parentheses.
Understanding subtraction enriches problem-solving abilities by giving clarity on how changes in quantities affect overall totals.

Multiplication in Order of Operations

Multiplication is all about scaling numbers. In the case of this exercise, multiplication was prioritized as per the rules of the order of operations, also known as PEMDAS/BODMAS (Parentheses, Exponents, Multiplication, and Division, Addition and Subtraction).

• In the expression, multiplication was solved first, calculating \(2 \cdot 3 = 6\). This simplification was crucial before moving on to addition or subtraction, as per the rule that multiplication should be handled prior to addition and subtraction in a calculation sequence.

Knowing when and how to perform multiplication is vital in math tasks, as it sets up the correct order for further calculations. Proper understanding helps in applying the multiplication process correctly, ensuring all calculations lead to accurate results.