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Chapter 1: Problem 32

Translate each sentence to a mathematical statement and then simplify. Subtract -10 from -20

Short Answer

Expert verified
The result is -10.

Step by step solution

01

Understand the Words

The sentence "Subtract -10 from -20" suggests taking away the number -10 from the number -20. In mathematical terms, this means you are performing the operation: \[-20 - (-10)\]
02

Set Up the Equation

Write down the mathematical equation for the subtraction problem described: \[-20 - (-10)\]
03

Simplify the Expression

When you subtract a negative number, it is equivalent to adding its positive counterpart. Thus, we can transform the expression: \[-20 - (-10) = -20 + 10\]
04

Perform the Calculation

Now perform the addition: Add 10 to -20. This gives:\[-20 + 10 = -10\]
05

Write the Simplified Answer

The simplified answer is:\[-10\]

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Key Concepts

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

Mathematical Statements
Translating a sentence into a mathematical statement involves converting words into mathematical symbols and expressions. This is a crucial skill in algebra because it allows you to solve problems by applying mathematical operations. Let's break it down:
  • Identify Key Terms: Look for words like "subtract," "add," "multiply," or "divide." These indicate the operations you need to perform.
  • Order Matters: Pay attention to the order of terms. In our example, "Subtract -10 from -20," it means you start with -20 and take away -10.
  • Use Symbols: Translate words into operations and numbers. The statement becomes: \[-20 - (-10)\]
This representation makes it possible to calculate the problem mathematically. It's like turning a sentence into a recipe to follow.
Subtraction of Negative Numbers
Handling negative numbers can be tricky, but understanding how to subtract them simplifies many algebraic problems. Here鈥檚 how:
  • Subtracting a Negative: When you subtract a negative number, you're actually adding its opposite. For example, \[-20 - (-10)\] turns into \[-20 + 10\].
  • Why Does This Happen? Think of subtraction as taking away. If you "take away a loss," you gain. Hence, subtracting a negative is like adding.
Another way to visualize this is with temperatures: If it鈥檚 -20 degrees and it warms up by the effect of subtracting a cold front of -10 degrees, it effectively becomes -10 degrees.
Simplification of Expressions
Simplification means making a mathematical expression as simple as possible. This is vital for solving equations efficiently. Let's explore:
  • Combining Like Terms: Group similar numbers or variables to reduce the expression. For example,\[-20 + 10\] simplifies directly to \[-10\].
  • Prioritize Operations: Follow the order of operations (PEMDAS/BODMAS) to ensure accuracy.
  • Final Form: The simplest form is often the most recognizable and easiest to work with. Here, the expression \[-20 + 10\] equals \[-10\], which is our final answer.
Simplifying expressions helps clarify the problem and makes further calculations more straightforward.

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