Question

Evaluate the expression. $$237-188 \div 4$$

Short answer

The result of evaluating the expression \(237 - 188 \div 4\) is 190.

Step-by-step solution

Perform Division

First, execute the division operation. Thus, \(188 \div 4 = 47\). The expression now becomes \(237 - 47\).

Perform Subtraction

Following PEMDAS, after performing the division operation, proceed with the subtraction. Therefore, \(237 - 47 = 190\)

Key concepts

PEMDAS

Understanding how to correctly evaluate an arithmetic expression is crucial, and that's where PEMDAS comes in. PEMDAS stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). This acronym helps students remember the order in which operations should be performed when evaluating expressions.

For example, in the expression given in the exercise \(237-188 \div 4\), division comes before subtraction according to PEMDAS. Therefore, you execute the division \(188 \div 4 = 47\) first, before subtracting that result from 237. Ignoring this order could lead to incorrect results and confusion. Think of PEMDAS as a roadmap that guides you through the necessary steps to reach the correct destination - the solution to your problem.

Arithmetic Operations

Arithmetic operations form the foundation of mathematics and are essential to understand various mathematical concepts. The four basic arithmetic operations include addition, subtraction, multiplication, and division. In performing arithmetic operations, it is necessary to follow the rules and order of operations (PEMDAS) to ensure accuracy.

For instance, in our exercise, we deal with subtraction and division. It's important to note that multiplication and division have the same precedence and are performed from left to right. This means if an expression includes both multiplication and division, you start with the one that appears first from left to right before moving on to addition or subtraction. Mastering these operations and their correct execution allows for the proper evaluation of more complex problems.

Evaluating Expressions

Evaluating expressions involves finding the value of numerical or algebraic expressions by performing arithmetic operations in the correct order. The step-by-step process ensures that each part of the expression is simplified systematically.

Let's delve a bit deeper using our exercise \(237-188 \div 4\). While evaluating, we first locate any parentheses (there are none in this case), handle any exponents (again, none here), and then move on to the division. Performing the division \(188 \div 4\), we update the expression to \(237 - 47\). Finally, we perform the subtraction, simplifying the expression to \(190\). Breaking down the evaluation process step by step helps students understand where they're heading, what's coming up next, and ensures that every 'mathematical signpost' is respected along the way, which is paramount for achieving the right solution.