Problem 5 - Intermediate Algebra

Question

Phrases such as increased by and more than are used to indicate the operation of ________ Phrases such as decreased by and less than are used to indicate the operation of

Step-by-Step Solution

Answer

Addition; Subtraction.

Step 1: Understanding the Terms

First, we will identify the key terms in the phrases provided. The terms "increased by" and "more than" suggest that we are making something larger or adding to a quantity. Conversely, "decreased by" and "less than" imply making something smaller or subtracting from a quantity.

Step 2: Determine the Mathematical Operations

Next, associate the terms with their respective mathematical operations. "Increased by" and "more than" correspond to the operation of addition, while "decreased by" and "less than" correspond to the operation of subtraction.

Key Concepts

Addition and Subtraction

In mathematics, addition and subtraction are two of the most fundamental arithmetic operations. They allow us to manipulate numbers by either combining them to get a larger total or reducing from a total to get a smaller number.

• Addition involves taking one number and increasing it by another. For example, if you have 5 apples, and you get 3 more apples, you now have 5 + 3 = 8 apples in total.
• Subtraction, on the other hand, is about taking away from a quantity. If you have 8 apples and you give away 3, you are left with 8 - 3 = 5 apples.

These operations are used to solve a wide range of problems in day-to-day activities, like budgeting, cooking, shopping, and splitting up resources among groups of people. Understanding how to effectively perform addition and subtraction enables us to make accurate calculations and solve practical problems.

Mathematical Terminology

Grasping mathematical terminology is crucial for understanding and solving problems effectively. Specific phrases often indicate particular operations, allowing us to translate real-world situations into mathematical expressions.

Phrases like "increased by" and "more than" suggest an operation where something is being added, leading to an increase in value. Conversely, phrases such as "decreased by" and "less than" signify subtraction, which involves reducing a quantity.

Recognizing and understanding these terminologies helps in decoding math problems, making it easier to determine which operations to apply when solving an equation or a word problem.

Understanding Mathematical Phrases

Understanding mathematical phrases is key to solving word problems. These phrases act as guides to which arithmetic operation needs to be performed.

For instance, when you see a phrase like "increased by 10," it indicates that you need to add 10 to a certain number. This is crucial because it aligns written verbal problems with algebraic expressions, such as transforming "a number increased by 10" to "x + 10".

• Increased by/More than - Signifies addition.
• Decreased by/Less than - Signifies subtraction.

Effective problem-solving in mathematics involves comprehending these phrases and translating them into actionable steps. This skill improves both your understanding and efficiency in solving mathematical tasks.