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Chapter 2: Problem 67

Translate to a mathematical expression. Then simplify the expression. The sum of \(-23\) and 49

Short Answer

Expert verified
-23 + 49 = 26

Step by step solution

01

Identify the Numbers

The two numbers provided in the exercise are -23 and 49.
02

Translate to a Mathematical Expression

Translate the problem statement into a mathematical expression: -23 + 49.
03

Simplify the Expression

Perform the addition of the two numbers: -23 + 49 = 26.

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Key Concepts

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

Addition
Addition is the process of combining two or more numbers to get a total or sum. It鈥檚 one of the four basic operations in arithmetic and is often the first operation we learn as children. To add two numbers:
  • Write down the numbers one below the other.
  • Align them by their rightmost digits.
  • Start adding from the right and move towards the left.

For example, if we translate the phrase 'The sum of -23 and 49' into a mathematical expression, we get -23 + 49. This expression tells us to add -23 and 49 together. Here, -23 is being added to 49, resulting in the operation -23 + 49. After performing the addition, we get 26.
Negative Numbers
Negative numbers are numbers less than zero and are usually represented with a minus sign (-). They are used to denote values below a defined point, such as temperatures below zero or losses in finance.
When working with negative numbers, it鈥檚 important to remember:
  • Adding a negative number is the same as subtracting its absolute value.
  • Subtracting a negative number is the same as adding its absolute value.
  • Two negative numbers added together make a more negative number.

In the expression -23 + 49, -23 is a negative number. Subtracting 23 from 49 is the same as doing 49 - 23, which simplifies to 26.
Simplification
Simplification involves reducing a mathematical expression to its simplest form. This can make it easier to understand and solve.
For addition, simplification means performing the actual addition to get a single number.
In the exercise provided:
  • First, we have the expression -23 + 49.
  • Next, we perform the addition of -23 and 49.

This means subtracting 23 from 49, which results in 26. So, the simplified form of the expression -23 + 49 is 26. This shows that understanding how to simplify expressions can make complex problems more manageable and solving them more straightforward.

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Most popular questions from this chapter

Assume \(a>0\) (this means that \(a\) is positive) and \(b<0\) (this means that \(b\) is negative). Find the sign of each expression. $$b \div a$$

Rank the numbers from least to greatest. If \(d\) represents a negative number, then what is the sign of \(-(-d) ?\)

Assume \(a>0\) (this means that \(a\) is positive) and \(b<0\) (this means that \(b\) is negative). Find the sign of each expression. $$a-b$$

Rank the numbers from least to greatest. $$-15,-(-18),-|20|, 4^{2},|-3|^{2}$$

Translate each English phrase to a mathematical expression. Then simplify. 320 decreased by \(-20\)
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