Problem 194 - Prealgebra

Question

In the following exercises, translate and simplify. 75 decreased by 49

Step-by-Step Solution

Answer

26

Step 1: Identify the operation

The phrase 'decreased by' indicates a subtraction operation.

Step 2: Translate the words into a mathematical expression

'75 decreased by 49' can be translated into the expression: 75 - 49

Step 3: Perform the subtraction

Subtract 49 from 75: 75 - 49 = 26

Key Concepts

Translation of phrases

Understanding how to translate phrases into mathematical expressions is essential in prealgebra. In this example, the phrase '75 decreased by 49' needs to be translated into an equation. Here, 'decreased by' signals a subtraction operation. We transform the phrase into a mathematical expression by identifying the numbers and operation involved. For '75 decreased by 49', we write it as 75 - 49. Noticing keywords like 'decreased by' can help you decide which mathematical operation to use.

Simplifying expressions

After translating the phrase into an expression, the next step is simplification. Simplifying an expression means performing the operations to reduce it to its simplest form. In this example, we start with the expression 75 - 49. Simplifying this expression means we need to perform the subtraction. This process involves basic arithmetic skills that will be used often in more advanced math concepts. Once the subtraction is completed, we have the simplified result: 26. Simplifying helps us understand the value of expressions and solve equations accurately.

Subtraction operation

The subtraction operation is a key concept in prealgebra. It indicates taking one quantity away from another. In our example, we see '75 decreased by 49'. When we perform this operation, we are subtracting 49 from 75. The subtraction process involves:

• Aligning the numbers vertically by place value
• Subtracting the digits starting from the right
• Borrowing if necessary from higher place values

This gives us the result of 26 when subtracting 49 from 75. Mastering subtraction is foundational for handling more complex math problems efficiently.