Problem 32 - Elementary Algebra

Question

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

Step-by-Step Solution

Answer

The result is -10.

Step 1: 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: \[-20 - (-10)\]

Step 2: Set Up the Equation

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

Step 3: Simplify the Expression

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

Step 4: Perform the Calculation

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

Step 5: Write the Simplified Answer

The simplified answer is:\[-10\]

Key Concepts

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’s 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’s -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.