Problem 59 - Fundamentals of Mathematics

Question

Add and subtract as in dicated. Add the differen ce of 997,468 and 292,513 to the difference of 22,140 and 8,617 .

Step-by-Step Solution

Answer

The result of the operation is 718,478.

Step 1: Find the First Difference

First, determine the difference between 997,468 and 292,513. Subtract 292,513 from 997,468: \(997,468 - 292,513 = 704,955\).

Step 2: Find the Second Difference

Now, calculate the difference between 22,140 and 8,617. Subtract 8,617 from 22,140: \(22,140 - 8,617 = 13,523\).

Step 3: Add the Two Differences

Add the results from Step 1 and Step 2 together. \(704,955 + 13,523 = 718,478\).

Key Concepts

Understanding Addition

Addition is one of the fundamental operations in arithmetic that involves combining two or more numbers to find their total. This operation is represented by the plus symbol "+". When we add numbers, we move to a higher value. For example, when we add 2 and 3, we get 5.

In our exercise, after finding the two differences, we performed an addition to combine them. This is similar to summing the outcomes of separate calculations to get a final result.

• Addition is associative, meaning you can group numbers differently without changing the sum. For instance, ((a + b) + c) = (a + (b + c)).
• This operation is also commutative, so the order doesn’t affect the result: a + b = b + a.

These properties make addition a flexible and fundamental operation in arithmetic.

Exploring Subtraction

Subtraction is another key arithmetic operation used to find the difference between numbers. The operation is shown by the minus sign "-". When we subtract, we are essentially looking for what remains when one number is taken away from another.

In the solution step-by-step, subtraction was used twice. The first subtraction found the difference between 997,468 and 292,513, and the second between 22,140 and 8,617. Subtraction helps in identifying how much more one value is than another.

• Unlike addition, subtraction is neither commutative nor associative. This means that changing the order of numbers affects the result: a - b is not the same as b - a.
• Subtraction can also be thought of as the inverse of addition. For example, if a + b = c, then c - b = a.

Understanding these concepts is crucial for solving arithmetic problems effectively.

Problem Solving with Arithmetic

Problem solving in arithmetic often involves a combination of operations such as addition and subtraction. The key is to break the problem into smaller steps, solve each step, and then combine the results.

In this particular exercise, the problem involved finding two differences through subtraction and then using addition to combine those results.

• First, identify what the problem is asking. Here, we needed to add the difference of two pairs of numbers.
• Then, perform each operation in sequence; first subtraction, then addition.

By understanding the order of operations and using strategic planning, you can simplify complex arithmetic problems, achieving accurate results every time. Problem solving like this is not only about numbers, but also about developing logical thinking and confidence in handling mathematical challenges.