Problem 96 - Fundamentals of Mathematics

Question

For the following problems, find the solutions. Subtract 105 from the sum of 92 and 89 .

Step-by-Step Solution

Answer

76

Step 1: Calculate the Sum of 92 and 89

First, we need to find the sum of the two numbers given. Add 92 and 89 together.\( 92 + 89 = 181 \)

Step 2: Subtract 105 from the Sum

Now that we have the sum, 181, subtract 105 from it to find the solution.\( 181 - 105 = 76 \)

Key Concepts

Understanding Addition

Addition is one of the most basic operations in arithmetic, often considered the foundation for learning other mathematical concepts. When we talk about addition, we mean combining two or more numbers to form a larger number. In this context, addition is the process that helps us aggregate quantities to see the overall total.

Here's how you can think about addition in simple terms:

• Imagine having 92 apples in one basket and 89 apples in another. If you combine both baskets, you perform the operation called addition.
• In mathematical terms, you would say you are calculating the expression 92 + 89.
• Upon solving, you find that the total number of apples is 181.

A great way to make sense of addition is to use practical examples, like grouping objects or using a number line. Remember, the order in which you add numbers doesn't affect the sum, known as the commutative property of addition.

Practicing with different numbers can help improve your skills and understanding of how addition works.

Exploring Subtraction

Subtraction is another essential operation in basic arithmetic, which involves taking away a certain amount from a larger number. Think of subtraction as undoing addition, and it’s often referred to as finding the difference between numbers.

Consider subtraction as follows:

• If you have 181 apples and give away 105, you perform the operation of subtraction to find out how many apples are left.
• In a mathematical sense, you would compute the expression 181 - 105.
• Solving this gives you a result of 76, which indicates the remaining number of apples.

Subtraction can be visualized effectively using number lines, where you start at 181 and move backwards 105 steps. This operation isn't commutative, meaning that changing the order will give you different results (unlike addition). Subtraction is a practical tool for understanding how to manage quantities that decrease over time.

By regularly practicing subtraction, you can develop a deeper understanding of the concept and improve problem-solving skills.

Problem Solving Steps in Arithmetic

In mathematics, solving problems often requires steps that need to be carefully followed to find the correct solution. Problem-solving steps in arithmetic involve understanding the given problem, executing calculations, and verifying results.

Breaking down a problem-solving process can be helpful:

• Start by identifying the operation required: addition, subtraction, or a combination.
• Organize your approach by solving one step at a time. For our exercise, begin by adding 92 and 89 to find an intermediate sum.
• Next, continue to the subtraction phase, where you take away 105 from the sum obtained.
• Evaluate your final result – in our case, it's important to cross-check your calculations to ensure that the solution, 76, is accurate and makes sense.

Taking these problem-solving steps systematically can make even the most complex calculations manageable. It’s like having a roadmap that guides you through the math problem, eliminating confusion along the way. Regularly practicing this organized approach can lead to improved arithmetic proficiency and increased confidence in tackling various mathematical problems.