Problem 83 - Prealgebra

Question

Perform the indicated operations. $$80 \div 10 \div 2$$

Step-by-Step Solution

Answer

The result of the operation is 4.

Step 1: Understand the Order of Operations

In mathematical expressions, operations should be performed from left to right unless there are parentheses or exponents that dictate otherwise. In this case, there are only division operations.

Step 2: Perform the First Division

Start with the leftmost division operation. Divide 80 by 10: \[ 80 \div 10 = 8 \]

Step 3: Perform the Second Division

Take the result from the first division and perform the next division operation with 2: \[ 8 \div 2 = 4 \]

Key Concepts

Division

Division is one of the four fundamental arithmetic operations, along with addition, subtraction, and multiplication. It is essentially the operation of sharing or distributing a number (the dividend) into equal parts. One key element of division is the divisor, which is the number you divide by.
In the expression \(80 \div 10 \div 2\), division is used to break down 80 step-by-step into smaller parts. Starting with 80, we first divide by 10 and then take that result to divide by 2. This method ensures that the division is carried out accurately and in a sequence that respects the left-to-right order of operations.

• The dividend in our example starts as 80.
• The first divisor is 10.
• The second divisor, after the initial division, is 2.

Understanding how to perform these calculations helps you simplify complex numerical expressions and solve problems effectively in everyday situations.

Mathematical Expressions

Mathematical expressions are combinations of numbers and operations that evaluate to a number. They can be as simple as a single number or more complex with multiple operations and brackets. In the expression \(80 \div 10 \div 2\), the operations consisted only of division.
To solve mathematical expressions, one follows specific rules, commonly known as the order of operations. Here, since there are no parentheses or other higher-priority operations like multiplication or addition mixed in, we solve from left to right.

• This expression does not require parentheses, but parentheses can drastically change results if they were included.
• The consistent use of the left-to-right sequence in operations ensures results are reliable.
  

Grasping these basic principles helps in tackling more challenging expressions and learning how to manage more complicated mathematical calculations effectively.

Step-by-Step Solutions

Step-by-step solutions are a technique used to simplify complex expressions by breaking them down into manageable parts. For students, this approach is particularly beneficial as it clarifies each individual operation and how it contributes to the entire solution. Tackling one piece at a time reduces errors and builds confidence.
Let's illustrate with our problem \(80 \div 10 \div 2\):

• Step 1: Start by dividing 80 by 10, which equals 8.
• Step 2: Take the result of the first division, 8, and divide by 2, which gives the final answer of 4.
  

This method not only gives the correct answer but also reinforces understanding of doing division in sequences as per arithmetic rules. Practicing this approach is invaluable for enhancing mathematical proficiency and problem-solving skills.