Problem 193 - Prealgebra

Question

In the following exercises, translate and simplify. 92 decreased by 67

Step-by-Step Solution

Answer

25

Step 1: Understanding the Problem

Identify the mathematical operation needed. 'Decreased by' indicates subtraction.

Step 2: Translate to a Mathematical Expression

Translate the phrase '92 decreased by 67' into a mathematical expression: a = 92 b = 67 a - b

Step 3: Perform the Subtraction

Subtract 67 from 92: 92 - 67 = 25

Key Concepts

understanding subtraction

Let's first get to understand what subtraction means. Subtraction is one of the basic arithmetic operations. It involves taking one number away from another.

For example, if you have 5 apples and you give 2 away, you subtract 2 from 5, leaving you with 3 apples.

In more technical terms, subtraction answers the question, 'How much less is one number compared to another?'

The result you get is called the difference.

In subtraction, the number from which you subtract is called the minuend, and the number you are subtracting is called the subtrahend. In our exercise, 92 is the minuend, and 67 is the subtrahend.

mathematical expression translation

Now that we understand subtraction, let's move on to translating words into a mathematical expression. In our problem, we have to translate the phrase '92 decreased by 67' into a mathematical expression.

Start by identifying the key terms:

• '92' and '67' are numbers.
• 'Decreased by' is a phrase indicating subtraction.

Translating the phrase into a mathematical expression involves writing it in a form that mathematicians use.

Here's how:
1. Write the first number: 92.
2. Replace 'decreased by' with a minus sign (-).
3. Write the second number: 67.

So, '92 decreased by 67' becomes: \( 92 - 67 \).

step-by-step subtraction

Finally, it's time to subtract the numbers. Here's how you do step-by-step subtraction:

1. Write the numbers in a vertical layout, aligning the digits by place value:

• 92
• - 67

2. Subtract the digits in the rightmost column (units) first:
2 (units) minus 7 (units). Since you can't subtract 7 from 2 without getting a negative number, you'll need to borrow from the next column. Borrowing 1 from the 9 tens makes it 8 tens, and adds 10 (ten) to 2 (units), making it 12 (units).

3. Now subtract: 12 units minus 7 units equals 5 units.

4. Move to the next left column (tens). Subtract 6 tens from 8 tens:
8 tens minus 6 tens equals 2 tens.

So, \( 92 - 67 = 25 \). The result, 25, is the difference between 92 and 67.

Understanding these steps lays a foundational block for more complex mathematical concepts and operations.