Problem 111 - Prealgebra

Question

In the following exercises, translate each phrase into math notation and then simplify. $$ 33 \quad \text {increase} \text { by } 49$$

Step-by-Step Solution

Answer

82

Step 1 - Translate the Phrase

Identify the key elements of the phrase '33 increase by 49' and translate them into mathematical notation. 'Increase by' typically means addition. Translate the phrase into the expression: a = 33 + 49

Step 2 - Perform the Addition

Now, compute the sum of 33 and 49. 33 + 49 = 82

Key Concepts

addition

Addition is one of the four basic arithmetic operations. It combines two or more numbers to get a sum. For example, in our exercise, we have the phrase '33 increase by 49.'

• The key indicating the addition operation here is 'increase by.'
• Addition is represented with the plus symbol (+).

When you add 33 and 49, you combine these quantities to find out how much they are together. In mathematical notation, this is written as: \(33 + 49 = 82\).
Learning how to identify and perform addition is fundamental in mathematics and daily life activities, like summing money, time, or objects.

mathematical notation

Mathematical notation is a system to express mathematical concepts and relationships through symbols and signs.

• In the phrase '33 increase by 49,' we recognize the words 'increase by' and translate them into a mathematical operation, addition.
• This gives us the mathematical expression: \(33 + 49\).

Notation makes it easier to perform calculations by providing a clear and unambiguous method to display numbers and operations. It’s the language of mathematics. Translating words into mathematical notation helps in solving problems more efficiently.

simplification

Simplification is the process of making an expression or equation easier to work with by combining or reducing its parts.

• In our exercise, after translating '33 increase by 49' to \(33 + 49\), we perform the actual calculation.
• The calculation of 33 plus 49 yields 82. Therefore, we have simplified the expression \(33 + 49\) to a single number, 82.

The simplification process reduces complexity, making it easier to understand and use the result in further calculations or real-world applications. It’s like cleaning up clutter to see things more clearly.

math exercises

Math exercises help build skills in problem-solving and understanding mathematical concepts through practice.

• Our example starts with translating a phrase into math notation, then performing addition to simplify the expression.
• These exercises reinforce core concepts such as identifying operations ('increase by' means add) and translating them into mathematical expressions.

Regular practice with math exercises enhances comprehension and speed in solving problems. They serve as a bridge between theoretical math and its practical application. By tackling varied exercises, students not only improve their mathematical knowledge but also their critical thinking and logical reasoning skills.