Problem 59 - Elementary Algebra

Question

Simplify. $$ 34+23-112 $$

Step-by-Step Solution

Answer

-55

Step 1: Perform Addition

Start by adding the first two numbers together: 34 + 23. Add these numbers to get 57 since 34 + 23 is equal to 57.

Step 2: Perform Subtraction

Now, take the result from Step 1 (which is 57) and subtract 112 from it: 57 - 112. To do this, calculate the difference between the numbers. Since 57 is less than 112, the result will be a negative number. The difference is -55.

Step 3: Final Result

The value you have after performing the subtraction is the simplified result. Therefore, the final answer is -55.

Key Concepts

Addition

Adding numbers is a fundamental task in mathematics. In this exercise, we start by adding the numbers 34 and 23. When adding, it's as though you are combining two groups of items into one larger group.

• Add the digits in the units place first: 4 + 3 = 7.
• Next, add the digits in the tens place: 3 + 2 = 5.

This gives us 57 as the total when you put the tens and the units together. Always make sure you add corresponds digits neatly under each other which helps in preventing errors. Once you've performed all possible additions, you've completed the task.

Subtraction

Subtraction is the reverse of addition. It involves taking away a certain number from another number. In this step, we take the sum from our addition (57) and subtract 112 from it.

• Compare the two numbers: it's clear 57 is less than 112.
• Subtract the smaller (57) from the larger (112) to find how much below zero you go.

Since 57 - 112 involves more removal than you have, it results in a negative number. Visualize this as going 55 steps below zero on the number line, reaching the answer -55. Understanding subtraction can help manage real-life scenarios like budgets or temperature drops.

Negative Numbers

Negative numbers can be puzzling because they represent values less than zero. We find them frequently in temperatures (like below freezing), owing money (debt), and more.

In our exercise, after subtraction, we have -55. This figure tells us that the subtraction took us 55 units below zero:

• Think of zero as sea level. Numbers below are underwater, just as -55 is.
• Negative values can be seen as deficits or shortages.

Remember, negative numbers are an essential part of mathematics. They allow us to describe the world accurately. Once grasped, you'll see they are much like a mirror image of positive numbers on the number line.