Problem 228 Simplify. $$ \text { (a) } 4... [FREE SOLUTION]

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Chapter 1: Problem 228

Simplify. $$ \text { (a) } 46-(-37) \text { (b) } 46+37 $$

Short Answer

Expert verified

(a) 83 (b) 83

Step by step solution

Understand the Expression

You need to simplify two separate expressions. Let's start with part (a): 46 - (-37)

Simplify Part (a)

When you subtract a negative number, it is equivalent to adding the number. Thus: 46 - (-37) = 46 + 37

Calculate the Result of Part (a)

Now, perform the addition: 46 + 37 = 83

Understand Part (b)

Now simplify the second expression: 46 + 37

Calculate the Result of Part (b)

Perform the addition: 46 + 37 = 83

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Subtraction of Negative Numbers

When you subtract a negative number, it's like performing an addition. Think of it as taking away a debt, which actually increases your total.
In mathematical terms, subtracting a negative number is the same as adding the absolute value of that number. For instance, when you see 46 - (-37), you change the double negative into a positive. So, it becomes 46 + 37.
It's a fundamental concept in math that can simplify many problems. Just remember, a minus a negative equals a plus.

Addition

Addition is one of the primary operations in math. Here, you combine numbers to get a sum.
In our example, we have two parts where we need to add the numbers. Once we change 46 - (-37) into 46 + 37, it's straightforward. Simply line up the numbers:
46 + 37.
Then, add them together step by step:

6 + 7 = 13 (write down 3 and carry over 1)
4 + 3 = 7 (add the carried 1, so 7 + 1 = 8)

This results in 83. Adding is about combining amounts to get a larger number.

Integer Operations

Integers include all whole numbers and their negatives. Understanding how to perform operations with integers is key in math.
When dealing with integer operations, such as addition and subtraction, it's crucial to know the rules. A few important points are:

Adding two positive integers always gives a positive integer
Adding two negative integers results in a negative integer
Subtracting a positive integer from another positive integer depends on their sizes (can be positive or negative)
Subtracting a negative integer is the same as adding its positive counterpart
Adding a positive integer to a negative integer relies on their absolute values

These rules help solve expressions like 46 - (-37), transforming it into 46 + 37, and simplifying your calculations.

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91影视

Simplify. $$ \text { (a) } 46-(-37) \text { (b) } 46+37 $$

Short Answer

Step by step solution

Understand the Expression

Simplify Part (a)

Calculate the Result of Part (a)

Understand Part (b)

Calculate the Result of Part (b)

Key Concepts

Subtraction of Negative Numbers

Addition

Integer Operations

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