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Chapter 2: Problem 54

Translate each English phrase to a mathematical expression. Then simplify. 150 decreased by 75

Short Answer

Expert verified
75

Step by step solution

01

Identify Key Phrases

The phrase to translate is '150 decreased by 75'. The key phrase here is 'decreased by', which indicates subtraction.
02

Translate to a Mathematical Expression

Using the key phrase 'decreased by', translate the English phrase to a mathematical expression: 150 decreased by 75 translates to 150 - 75.
03

Simplify the Expression

Perform the subtraction operation to simplify the expression:150 - 75 = 75.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Subtraction
Subtraction is a basic mathematical operation that signifies taking away one quantity from another. In simpler terms, if you have a number and you subtract another number from it, you are essentially removing parts of the original number.

For example, if you have 10 apples and you give away 3, you subtract 3 from 10. This operation is denoted as 10 - 3, which equals 7. This basic idea is crucial when dealing with more complex mathematical problems.

In our given exercise, the phrase '150 decreased by 75' uses the key term 'decreased by,' which indicates we should use subtraction. Thus, we write the mathematical expression as 150 - 75.
Simplifying Expressions
Simplifying expressions involves performing the operations within the expression to reduce it to a simpler form. This means carrying out any addition, subtraction, multiplication, or division operations.

Let's look at our exercise example again. The initial mathematical expression we got was 150 - 75. To simplify, we perform the subtraction: \[150 - 75 = 75\]

Now, our expression is simplified. Simplifying makes the result easier to understand and work with, and it often serves as a step toward solving larger problems.
Translating Phrases to Math
Translating phrases to math is an essential skill in algebra. It helps you convert real-world situations into mathematical expressions that can be worked on further.

The phrase '150 decreased by 75' tells us to use subtraction. Here are some key phrases to remember:

- 'Increased by' indicates addition.
- 'Decreased by' indicates subtraction.
- 'Product of' indicates multiplication.
- 'Quotient of' indicates division.

By learning these key phrases, you can translate almost any English phrase into a mathematical expression. This ability is very useful for solving word problems and understanding the relationship between numbers.

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Most popular questions from this chapter

Divide the real numbers, if possible. $$\frac{0}{-6}$$

Assume \(a>0\) (this means that \(a\) is positive) and \(b<0\) (this means that \(b\) is negative). Find the sign of each expression. $$-(a)$$

Translate each English phrase to a mathematical expression. Then simplify. 320 decreased by \(-20\)

Perform the indicated operation. $$(-7)^{2}$$

Perform the indicated operation. $$\frac{0}{-2}$$
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