Problem 45 - Fundamentals of Mathematics

Question

Combine the numbers as indicated. $$874+845+295-900$$

Step-by-Step Solution

Answer

The result is 1114.

Step 1: Combine like terms

First, combine the positive numbers together: \(874 + 845 + 295\). To do this, first add \(874 + 845 = 1719\).

Step 2: Continue addition

Now, add the result from Step 1 to the remaining positive term: \(1719 + 295 = 2014\). This is the sum of all the positive numbers.

Step 3: Perform the subtraction

Subtract the negative number from the result of Step 2: \(2014 - 900 = 1114\). This gives the final result.

Key Concepts

Addition

In arithmetic, addition is used to calculate the sum of two or more numbers. It's one of the four basic operations, and it's as simple as counting up. In this exercise, the goal was to add three numbers together: 874, 845, and 295.
Let's break down how this works:

• Start with 874 and 845.
• Add them together to get 1719.

After the first step is completed and you have a sum, you proceed to add the remaining number, 295.
Here's how:

• Take the sum of 874 and 845, which is 1719, and add 295.
• This results in a new sum: 2014.

So, addition is simply collecting all positive numbers and finding out how much they add up to. It's like stacking blocks to see how tall the tower gets. Add carefully to avoid errors.

Subtraction

Subtraction is the operation of finding the difference between two numbers. It helps us determine how much one quantity is less than another. In problems like the one at hand, it's often used to remove something from the figure attained through addition.
Once we conducted all our additions and calculated their sum to be 2014, the exercise asked us to subtract 900 from this total:

• Start with the total sum of positive numbers, which is 2014.
• Subtract 900 from this total.

This subtraction looks like this: 2014 minus 900 results in 1114.
Think of subtraction as taking away or decreasing, just like when you eat a cookie—the total is one less. Pay attention to lining up numbers correctly and subtracting each column properly to avoid mistakes.

Combining Like Terms

In arithmetic calculations, the concept of combining like terms often appears alongside addition and subtraction. This concept involves grouping numbers or expressions that are similar, and it greatly simplifies solving problems. Let's connect this to our exercise:
When we say 'combine like terms,' we're essentially talking about gathering all terms that can easily be added or subtracted together.
In the exercise, our terms included:

• Two groups: positive numbers (874, 845, 295) and a single negative number (-900).

By first focusing our attention on the group of positive numbers, we effectively simplify the problem:

• First, add all positive numbers together. This gives one sum.
• Second, subtract the negative number from that sum.

Combining like terms allows you to perform calculations in a structured and clear way. It ensures you don't mix different types of operations or lose track of your calculations, leading to a more accurate and faster solution.