Problem 39 - Algebra A Combined Function

Question

Translate each phrase to an expression and simplify. Subtract 8 from 7 .

Step-by-Step Solution

Answer

7 - 8 = -1

Step 1: Identify the Operation

The phrase "subtract 8 from 7" involves subtraction. Here, the number 8 is being subtracted from the number 7.

Step 2: Translate the Phrase to an Expression

To translate the phrase into a mathematical expression, we write it as follows: 7 - 8.

Step 3: Perform the Subtraction

Subtract 8 from 7. This calculation is performed as follows: 7 - 8 = -1.

Step 4: Confirm the Simplification

Check if the expression can be simplified further. Since -1 is already in its simplest form, it remains as is.

Key Concepts

Understanding Subtraction

Subtraction is one of the four basic arithmetic operations, alongside addition, multiplication, and division. It involves removing a smaller number from a larger one to find the difference between them. In simple terms, it's like counting backwards. This operation is denoted by the minus sign (–). When you "subtract 8 from 7," it means you start with 7 and take away 8, moving left on the number line. This results in a negative number, as you can't take a larger number from a smaller one without venturing into negatives. The process reflects movement: moving from 7 steps back by 8 spaces, landing at -1. This understanding is foundational for working with negative numbers and understanding their role in arithmetic.

Expression Translation

Expression translation involves turning verbal phrases into mathematical expressions. This is crucial in bridging everyday language with mathematical operations.
When you read a phrase like "subtract 8 from 7," you're translating the words into a numerical expression, written as \( 7 - 8 \). The structure is essential: you start with the number 7 and subtract 8 from it.

• Identify keywords: "subtract" suggests the operation of subtraction.
• Order matters: "from" indicates which number is being reduced.

This systematic approach helps in ensuring everyone understands and writes arithmetic operations in a standard format. Translation skills are powerful tools in problem-solving, making it easier to handle increasingly complex mathematical expressions.

Arithmetic Simplification

Arithmetic simplification is about reducing an expression to its most concise and understandable form. It's the process of performing operations to reach the simplest possible version of a number or expression.
In the case of \( 7 - 8 \), the calculation leads you directly to \( -1 \). There's nothing more to simplify, as \(-1\) is already as straightforward as this expression can get. Simplification ensures clarity and is essential for solving advanced mathematical problems, where initial expressions may be long and cumbersome.

• Check each calculation step for accuracy.
• Ensure the result is presented in the simplest form possible.

Grasping simplification practices ensures calculations are efficient and results are clear and concise.