Problem 211 - Prealgebra

Question

In the following exercises, translate and simplify. The difference of 100 and 76

Step-by-Step Solution

Answer

The difference of 100 and 76 is 24.

Step 1 - Understand the Problem

The problem asks to find the difference between two numbers: 100 and 76. The word 'difference' indicates that subtraction is needed.

Step 2 - Set Up the Equation

Translate the word problem into a mathematical equation. Here, it translates to: 100 - 76

Step 3 - Perform the Calculation

Subtract the smaller number from the larger number: 100 - 76 = 24

Step 4 - Write the Final Answer

The result of the subtraction is the difference. So, the difference of 100 and 76 is 24.

Key Concepts

difference

In mathematics, the term 'difference' refers to the result of subtracting one number from another. When we talk about finding the difference between two numbers, we're essentially looking for how much smaller one number is compared to the other.
For example, in the exercise given, we need to find the difference between 100 and 76. This can be visualized as taking away 76 from 100. When we do the subtraction, what remains is what we call the difference.
Using the concept of difference is crucial in solving many mathematical problems and helps understand how one value compares to another. It's a fundamental skill that will be used many times, so understanding it thoroughly is very beneficial.

equation

An equation is a mathematical statement that shows the equality between two expressions. It often includes variables, constants, numbers, and arithmetic operations such as addition, subtraction, multiplication, and division.
In the given exercise, the equation is derived from the phrase 'the difference of 100 and 76'. The equation for this problem is: \[100 - 76\text{.}\]By translating the word problem into an equation, we can see clearly what mathematical operation needs to be performed. Understanding how to set up an equation from a word problem is a critical skill in mathematics. It allows us to take verbal descriptions and turn them into solvable mathematical expressions.
Once the equation is set up, solving it is just a matter of performing the arithmetic operations indicated.

calculation

Calculation refers to the process of finding an answer using mathematical or logical operations. In the context of the given exercise, the calculation involves performing the subtraction of 76 from 100.
Here's how we do it step-by-step:

• First, write down the larger number (100).
• Then, write the smaller number below it (76).
• Align the digits by their place values (units, tens, etc.).
• Subtract each digit starting from the rightmost place value (units).
• If needed, borrow from the next left place value.

When we calculate 100 - 76, we get 24. This number is the result of our calculation, showing the difference between the original two numbers.
Mastering basic calculations like subtraction is essential for solving more complex mathematical problems and for everyday tasks such as budgeting or measuring quantities.