Problem 321 - Prealgebra

Question

In the following exercises, translate and simplify. 366 less than 814

Step-by-Step Solution

Answer

The simplified form is 448.

Step 1: Translate the Problem Statement

The problem states '366 less than 814'. This means that 366 is subtracted from 814. In mathematical notation, this can be written as: 814 - 366

Step 2: Perform the Subtraction

Subtract 366 from 814: 814 - 366 = 448

Step 3: Verify the Calculation

Double-check the subtraction to ensure it is correct: 814 - 366 ------ 448

Key Concepts

subtraction

Subtraction is one of the four fundamental arithmetic operations. It represents taking away objects from a collection. Here's a closer look at the concept, with an example to make it simple.

Imagine you have 814 apples and you give away 366 apples. The process of removing these apples can be represented by subtraction.

• The number you start with is called the minuend (814 in this case).
• The number you are subtracting is called the subtrahend (366 here).
• The answer you get is called the difference (448).

The basic rule in subtraction is to subtract each digit of the subtrahend from the corresponding digit of the minuend, starting from the rightmost digit (units place).

When you subtract 366 from 814:

814 − 366
You subtract from right to left:
4 - 6 (borrow 1 from tens place), 1 becomes 11; 11 - 6 = 5
0 - 6 (borrow 1 from hundreds place), 0 becomes 10; 10 - 6 = 4
1 (hundreds place) - 1 (hundreds place) - 0 (borrow counted) = 4

So, the result is 448.

mathematical translation

Mathematical translation involves converting a word problem or statement into a mathematical expression. This step helps to clarify and simplify the problem, making it easier to solve.

In our example, '366 less than 814', needs to be translated into a mathematical equation. This phrase means we need to subtract 366 from 814.

To translate:

• Identify the key terms and numbers. In this case, '366' and '814'.
• 'Less than' indicates subtraction.

Hence, '366 less than 814' translates to the equation 814 - 366. Breaking down such phrases can demystify the problem and help you tackle it with confidence.

verification of calculation

Verification of calculation is the process of checking that your solution is correct. It's an essential step to ensure accuracy in your work.

In our problem, after performing the subtraction of 366 from 814, we got the result 448. Verification involves rechecking the calculation to confirm it's right.

Let's re-check:

• Align the numbers vertically.
• Subtract each column starting from the right.

This step-by-step rechecking ensures you didn't make any mistakes in borrowing or basic subtraction.

Another method is to add the difference back to the subtrahend:
448 + 366 should equal the minuend (814). If it matches, your subtraction was correct.

Always verifying your calculations helps in developing accuracy and confidence in solving math problems.