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Chapter 1: Problem 102

Write a numerical expression for each phrase and simplify. 9 less than \(-13\)

Short Answer

Expert verified
-22

Step by step solution

01

- Understand the Phrase

The phrase is '9 less than \(-13\). This means we need to subtract 9 from \(-13\).
02

- Write the Numerical Expression

Convert the phrase into a mathematical expression: \(-13 - 9\).
03

- Simplify the Expression

To subtract 9 from \-13, add the two values: \(-13) + ( -9 ) = -22\). Using the rule of adding two negative numbers, we combine their absolute values and keep the result negative.

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Key Concepts

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

Numerical Expressions
When we talk about numerical expressions, we refer to mathematical phrases that include numbers and operation signs. In this exercise, the phrase '9 less than \( -13 \)' is such an example. To convert this phrase into a numerical expression, we identify the operation (subtraction) and numbers involved (9 and -13). So, '9 less than \( -13 \)' becomes \( -13 - 9 \).
Understanding how to construct these expressions is the first step towards solving math problems.
Remember, breaking down the phrase into a mathematical form is crucial for the next steps, making it easier to simplify the expression later.
Negative Numbers
Negative numbers are numbers less than zero, and they are represented with a minus sign (-). In our exercise, both numbers involved, -13 and -9, are negative.
Working with negative numbers follows specific rules:
  • Adding two negative numbers: Add their absolute values (ignore the negative sign) and place a negative sign before the result.
  • Subtracting a negative from a positive: This becomes addition of the absolute values.
  • Subtracting a positive from a negative: Keep the negative sign and add the absolute values, as seen in '9 less than -13'.
These rules make dealing with negative numbers straightforward once understood. In our case, applying these rules shows why \( -13 - 9 = -22 \).
Simplification of Expressions
Simplification of numerical expressions involves reducing them to their simplest form. After we have the numerical expression \( -13 - 9 \), we apply the rules for negative numbers.
Let's see how to simplify:
  • Identify the operation: subtraction.
  • Recognize both numbers are negative: subtract 9 from -13.
  • Apply the rule: Instead of subtracting 9, we add its absolute value to 13 and keep the sign negative. This yields \( -22 \).

    • Through simplification, we ensure the final result is easy to understand and ready to use in further calculations.

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Most popular questions from this chapter

To find the average (mean) of a group of numbers, we add the numbers and then divide the sum by the number of terms added. For example, to find the average of \(14,8,3,9,\) and \(1,\) we add them and then divide by 5. $$ \frac{14+8+3+9+1}{5}=\frac{35}{5}=7 \leftarrow \text { Average } $$ Find the average of each group of numbers. \(23,18,13,-4,\) and \(-8\)

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