Problem 87 - Algebra 1

Question

Evaluate the expression. $$ 17+100 \div 25-5 $$

Step-by-Step Solution

Answer

The evaluated expression is 16.

Step 1: Division

We start by performing the division operation in the expression: 100 ÷ 25 equals 4. So, the expression simplifies to: 17 + 4 - 5.

Step 2: Addition

Next, perform the addition operation: 17 + 4 equals 21. So, it simplifies to: 21 - 5.

Step 3: Subtraction

Finally, perform the subtraction operation: 21 - 5 equals 16.

Key Concepts

Arithmetic Operations

Arithmetic operations are the basic building blocks of mathematics. They include addition, subtraction, multiplication, and division.
Arithmetic operations follow specific rules known as the order of operations, which ensure that everyone solves a mathematical expression in the same way. These rules are often remembered by the acronym PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). Using these guidelines helps avoid confusion and ensures calculations are accurate.
In the exercise, understanding this order helped us prioritize division before moving on to addition and subtraction, leading to correct results.

Division

Division is splitting a number into equal parts or groups. It is one of the four basic operations of arithmetic and can be thought of in terms of how many times one number is contained within another.
In the expression provided, 100 is divided by 25. This division is performed first according to the order of operations, resulting in 4, because 25 fits into 100 exactly 4 times. This simplifies the problem and sets the stage for subsequent calculations.
Remember, division is performed before addition and subtraction unless parentheses or exponents are involved, emphasizing the critical role of following operation order.

Addition

Addition is the process of combining two or more quantities to find their total. In this exercise, once the division was solved, the next arithmetic operation was addition.
We had 17 + 4, aiming to combine these numbers into a single sum. The addition of 17 and 4 results in 21, moving us one step closer to solving the expression.

• Addition is easy to learn and performs as combining values.
• All numbers in an addition are known as addends.
• The result is called a sum.

Combining smaller calculations leads to easier handling of the overall expression.

Subtraction

Subtraction is essentially the opposite of addition. It involves removing a certain quantity from another to find the difference. In the final step of solving the provided expression, subtraction was used to arrive at the result.
With the expression simplified to 21 - 5, we take 5 away from 21. This process gives us 16, which is the final answer.
Subtraction, like addition, follows division if no parentheses intervene, confirming the final number.

• Subtraction tells how much is left after removing items.
• It helps to compare numbers by finding the difference.
• Enhances understanding of loss vs. gain concepts in everyday contexts.

Thus, subtraction completes this mathematical journey, revealing the expression's value.