Problem 35 - Algebra 1: Concepts and Skills

Question

Find the sum. $$-62+27$$

Step-by-Step Solution

Answer

-35

Step 1: Positioning the Numbers

First, list the numbers to be added. The numbers given are -62 and 27.

Step 2: Execute the Addition Operation

Next, we add -62 and 27. The sum is effectively -62 + 27, which equals -35 based on integer operations.

Key Concepts

Adding Negative Numbers

Adding negative numbers can initially be tricky, but it's quite simple if you remember how to interpret negative signs. When you add a negative number to another number, it's the same as subtracting the positive version of that number. For example:

• Add -5 to 10: This is equivalent to 10 - 5.
• Add -3 to -7: Think of it as combining two losses, which results in -10.

In the original exercise, when -62 is added to 27, think about it as 27 minus 62. This results in a negative number because 62 is greater than 27. Therefore, you'll end up with -35. This is how adding negative numbers impacts the operation.

Basic Arithmetic

Basic arithmetic involves just the foundational operations: addition, subtraction, multiplication, and division. Addition and subtraction can be particularly interesting, especially when negative numbers are involved.
In the specific problem, you are dealing with a straightforward addition:

• The formula looks like: -62 + 27.
• You start from -62, which is a negative level, and you aim to add something positive (27), which slightly nearby the zero on the number line.

Always keep the principles of arithmetic in mind:

• Adding a smaller number to a larger negative number will keep the result negative.
• If the positive number was greater, the result would shift to positive.

This vitality in numbers, especially in addition, forms the core of arithmetical operations.

Integer Operations

Integer operations are part of what makes math exciting and sometimes challenging! Integers include all whole numbers, both positive and negative, along with zero. When working with integer operations, such as addition, understanding how positive and negative signs interact is crucial.
In the exercise, the integer addition of -62 and 27 is key:

• Begin by recognizing the signs: -62 is negative and 27 is positive.
• Subtract the smaller absolute value from the larger absolute value, from larger - 62 to smaller - 27 in this case.
• The bigger magnitude dictates the sign of the answer. Here, the answer is negative because 62 is greater than 27 in magnitude.

This understanding assists in approaching problems correctly. Integer operations do more than follow set rules; they represent the reality of shifts along the number line and help in everyday calculations.