Problem 4 - Algebra 1: Concepts and Skills

Question

Evaluate the expression. $$ 16 \div 4-2 $$

Step-by-Step Solution

Answer

The evaluated result of the expression is 2.

Step 1: Perform Division

Start by performing the division in the expression: \( 16 \div 4 = 4 \). The revised expression now is \( 4 - 2 \).

Step 2: Perform Subtraction

Now, subtract 2 from 4: \( 4 - 2 = 2 \).

Key Concepts

Division

Division is one of the four basic operations in arithmetic. It is the process of finding out how many times a number is contained within another number. In the context of the expression given (\( 16 \div 4 \)),the number 16 is called the 'dividend,'while the number 4 is the 'divisor.' The result of the division is known as the 'quotient'.

• Dividend: The number you want to divide up.
• Divisor: The number you are dividing by.
• Quotient: The result or the number of times the divisor fits into the dividend.

Performing the division in this expression,you divide 16 by 4, which results in 4:\[ 16 \div 4 = 4 \].This is because 4 fits into 16 exactly 4 times.Understanding division in real-world settingslike sharing or distributing items equallyhelps solidify your grasp on this concept.

Subtraction

Subtraction is another fundamental arithmetic operation.It involves taking one number away from another.This operation finds the difference between two numbers.In the expression (\( 4 - 2 \)),4 is called the 'minuend,'and 2 is the 'subtrahend.'The result is known as the 'difference.'

• Minuend: The starting number from which another number is to be subtracted.
• Subtrahend: The number that is to be subtracted from the minuend.
• Difference: The result after the subtraction.

Subtraction tells us how far apart two numbers are.In our exercise, subtracting 2 from 4 leaves us with\( 4 - 2 = 2 \).This calculation shows that if we start with 4and remove 2, we are left with 2.

Arithmetic Expressions

Arithmetic expressions are mathematical phrases using numbers,operators like addition, subtraction, multiplication,and division, and sometimes parentheses.The key to solving these expressions is understandingthe 'Order of Operations.'This set of rules ensures that calculations are performedin a consistent and correct manner.A common acronym to remember this order is PEMDAS,which stands for:

• P: Parentheses first
• E: Exponents (i.e., powers and square roots, etc.)
• MD: Multiplication and Division (left to right)
• AS: Addition and Subtraction (left to right)

In our example, the expression\( 16 \div 4 - 2 \)is solved by first performing the division(\( 16 \div 4 = 4 \))and then the subtraction (\( 4 - 2 = 2 \)).Following the correct order of operations is crucialfor accurately solving arithmetic expressions.