Problem 31 - Elementary Algebra

Question

Translate each sentence to a mathematical statement and then simplify. Subtract 12 from 10

Step-by-Step Solution

Answer

-2

Step 1: Translation to Mathematical Expression

Translate the given sentence "Subtract 12 from 10" into a mathematical expression. When you subtract a number, it appears after the subtraction sign (-). Therefore, the expression is: \[ 10 - 12 \].

Step 2: Simplification of the Expression

Now, simplify the expression \( 10 - 12 \) by subtracting 12 from 10. This results in the expression \(-2\).

Key Concepts

Mathematical Expression

A mathematical expression is a combination of numbers, operations, and sometimes variables that together represent a mathematical concept or a quantity. In our exercise, we were given a simple sentence that needed to be translated into a mathematical expression: "Subtract 12 from 10." To do this, it's crucial to understand the structure of sentences in mathematics.

When the instruction uses the word "subtract," it signifies that you need to use the minus sign, "-". In the phrase "from 10," the number 10 is the starting value, so it comes first in the expression. The number being subtracted, in this case 12, follows the minus sign. This gives us the expression:

\[ 10 - 12 \]

By learning how to translate words into expressions, you'll better understand problems in math and find the solutions more easily.

Subtraction

Subtraction is one of the four fundamental arithmetic operations, allowing us to find the difference between two numbers. Represented by the minus sign, "-", it tells us how much remains when we take one quantity away from another. When the numbers involved are whole numbers, the outcome could be positive, negative, or zero.

Consider our example: "Subtract 12 from 10."
Here, subtraction is employed as follows:

• The starting number is 10.
• You subtract 12 from this number.

Since 12 is greater than 10, instead of getting a positive number, you end up with a negative number, which is \(-2\). This is an important concept to grasp, as it applies not just in math classes but in everyday situations, like when balancing a budget or determining how much time is left for an activity.

Simplification

Simplification in mathematics involves reducing an expression to its most basic form without changing its value. In our exercise, to simplify the expression \(10 - 12\), we performed the subtraction to find the simplest form of the number resulting from this calculation.

Here are the steps involved in simplification:

• Identify the operation, which is subtraction: \(10 - 12\).
• Perform the subtraction to find the result, \(-2\).

Simplifying expressions is a crucial skill in elementary algebra because it enables you to easily compare, compute, and understand the values and relationships between different expressions. Mastering simplification helps increase accuracy and efficiency in math problem-solving.