Problem 212 - Prealgebra

Question

In the following exercises, translate and simplify. The difference of 1,000 and 945

Step-by-Step Solution

Answer

The difference is 55.

Step 1: Understand the Problem

Identify the key components in the statement. The phrase 'the difference of 1,000 and 945' suggests a subtraction operation.

Step 2: Set Up the Mathematical Expression

Translate the verbal statement into a mathematical equation. The difference of 1,000 and 945 is written as: \( 1000 - 945 \)

Step 3: Perform the Subtraction

Subtract 945 from 1,000 to find the difference: \[ 1000 - 945 = 55 \]

Step 4: Simplify (if needed)

Check if the result can be simplified further. In this case, the difference is already in its simplest form as a single number: 55.

Key Concepts

Subtraction

Subtraction is one of the basic operations in arithmetic, and it helps us find the difference between two numbers. When you subtract one number from another, you are essentially figuring out how much one number is less than the other. For example, in the statement 'the difference of 1,000 and 945', we are asked to find out how much 1,000 is greater than 945. Let's break it down:

• Start with the larger number: 1,000.
• Subtract the smaller number: 945.

Using subtraction, you'll get: \( 1000 - 945 = 55 \). The result is 55. Subtraction helps us solve many everyday problems, like calculating change, comparing quantities, and determining intervals of time.

Mathematical Expression

A mathematical expression is a combination of numbers, operations, and sometimes variables. It represents a particular value or relationship. In our example, the phrase 'the difference of 1,000 and 945' needs to be translated into a mathematical expression. This is done as follows:

• The word 'difference' indicates subtraction.
• Write the numbers in the order they're given.

This gives us the expression: \( 1000 - 945 \). Expressions can be simple, like this one, or complex, involving multiple operations and variables.

Simplification

Simplification is the process of making a mathematical expression as simple as possible. In subtraction problems like the one we have here, simplification usually means performing the subtraction to find a single number. Let's look at our example again. After writing the mathematical expression \( 1000 - 945 \), we need to find the difference by performing the subtraction:\br>\[ 1000 - 945 = 55 \]. After performing the operation, the result is 55, which is already in its simplest form. In other words, there is nothing left to simplify further. Simplification helps in understanding problems quicker and often makes solving them easier.