Problem 38 - Elementary Algebra

Question

For exercises 1-80, evaluate. $$ 5-0 \div 7 $$

Step-by-Step Solution

Answer

5

Step 1: Understand the Expression

The given expression is \(5 - 0 \div 7\). Here, subtraction and division operations are present. The order of operations must be followed: perform division before subtraction.

Step 2: Perform Division First

Identify the division part of the expression. Calculate \(0 \div 7\): \[ 0 \div 7 = 0 \] So, the expression simplifies to: \[ 5 - 0 \]

Step 3: Perform Subtraction

Now, subtract 0 from 5: \[ 5 - 0 = 5 \]

Step 4: Final Answer

The simplified value of the expression \(5 - 0 \div 7\) is 5.

Key Concepts

Division

In mathematics, division is one of the basic arithmetic operations. It can be thought of as the process of determining how many times one number is contained within another.
For example, in the expression given in the exercise, we have 0 divided by 7.
When any number is divided by another number, we are essentially splitting it into that many equal parts.
Now, when it comes to dividing zero by any number, the result is always zero.
This is because zero divided into any number of pieces is still zero.
To put it mathematically: \( 0 \div 7 = 0 \)
It doesn’t matter what number we are dividing by, if we start with zero, the result is always zero.

Subtraction

Subtraction is another basic arithmetic operation, which represents the process of taking one quantity away from another.
In the given exercise, after performing the division, the expression simplifies to 5 - 0.
Here, we need to subtract 0 from 5.
It's important to note that subtracting zero from any number leaves the number unchanged.
Mathematically, this is represented as: \[ 5 - 0 = 5 \]
So, subtracting zero does not alter the value of the original number.

Simplification

Simplification is the process of reducing a mathematical expression to its simplest form.
To simplify an expression, you follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right)).
First, you perform any division or multiplication operations, and then proceed to addition or subtraction.
In our exercise, we start with the expression \( 5 - 0 \div 7 \).
According to the order of operations, we first carry out the division: \[ 0 \div 7 = 0 \]
Then, substitute this back into the expression, so we have: \[ 5 - 0 = 5 \]
This is the simplest form of the expression, making our final answer: 5.