Problem 102 - Prealgebra

Question

$$20+16 \div 2-5$$

Step-by-Step Solution

Answer

The result of the expression is 23.

Step 1: Identify the Order of Operations

The order of operations is essential when solving mathematical expressions. Remember the acronym PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

Step 2: Perform Division First

According to the order of operations, we first perform the division operation in the expression. Calculate \(16 \div 2\), which equals 8. The expression now becomes \(20 + 8 - 5\).

Step 3: Perform Addition

Next, carry out the addition part of the expression. Add \(20 + 8\), which equals 28. The expression simplifies to \(28 - 5\).

Step 4: Perform Subtraction

Finally, perform the subtraction operation. Subtract \(5\) from \(28\), which equals 23. So the result of the expression \(20 + 16 \div 2 - 5\) is 23.

Key Concepts

Understanding PEMDAS

When faced with a mathematical expression, it's important to know the order in which to perform each operation. This is where PEMDAS comes into play, which stands for:

• Parentheses
• Exponents
• Multiplication and Division (from left to right)
• Addition and Subtraction (from left to right)

PEMDAS helps ensure consistency when solving problems. Always start with any calculations inside parentheses. Next, take care of exponents. Then, handle any multiplication and division in the same step, working from left to right. Finally, perform addition and subtraction from left to right as well.
For example, in the expression given, you first handle the division step before moving on to addition and subtraction. This systematic approach helps avoid mistakes.

Executing Division in Expressions

Division in mathematical expressions requires careful attention because it can dramatically alter the outcome of an expression when not performed correctly.
When applying PEMDAS, division can be processed at the same time as multiplication, but only after any operations in parentheses or exponents are dealt with. It should always be performed from left to right.
For the expression given, after accounting for any parentheses or exponents (of which there were none), you perform the division with:

• Calculate: \(16 \div 2\)
• Result: 8

This simplifies part of the expression, making it easier to handle the remaining operations. Once the division is complete, you can proceed to the subsequent addition and subtraction steps.

Navigating Addition and Subtraction

Once you've finished any multiplication or division elements in an expression, you turn your attention to addition and subtraction. PEMDAS instructs us to handle these operations in the sequence they appear (from left to right), after addressing any earlier-stage operations.
In the original exercise, the expression simplified to \(20 + 8 - 5\) after division. You then perform the addition:

• Calculate: \(20 + 8 = 28\)

Next, go on to the subtraction:

• Calculate: \(28 - 5 = 23\)

Following this order lets you systematically solve expressions without losing track of steps. Ensuring you respect this sequence is key to reaching the correct answer.