Problem 109 - Prealgebra

Question

In the following exercises, translate each phrase into math notation and then simplify. $$\text { the sum of } 90 \text { and } 65$$

Step-by-Step Solution

Answer

90 + 65 = 155

Step 1: Identify Key Components

Recognize the components of the phrase: 90 and 65.

Step 2: Translate to Mathematical Notation

The phrase 'the sum of 90 and 65' translates to the expression: \[90 + 65\]

Step 3: Perform the Addition

Add the two numbers together: 90 + 65. This gives: \[90 + 65 = 155\]

Key Concepts

Arithmetics

Arithmetics is a fundamental branch of mathematics. It involves basic calculations, including addition, subtraction, multiplication, and division. These operations form the building blocks for more advanced math topics.
When solving problems, understanding the basic rules and properties is essential.
For instance, addition in arithmetics follows the commutative property, which means the order of numbers does not change the result:

• For example, 90 + 65 is the same as 65 + 90.

Learning arithmetics strengthens problem-solving skills and helps in everyday life.

Addition

Addition is the process of finding the total or sum by combining two or more numbers. It's one of the first operations learned in math.
The symbol for addition is '+'.
When adding numbers, you start from the rightmost digit and move to the left, carrying over any extra value.
Here's a step-by-step example of adding 90 and 65:

• Start with the rightmost digits: 0 (from 90) + 5 (from 65) = 5.
• Move to the next digits to the left: 9 (from 90) + 6 (from 65) = 15.
• The final sum is 155.

Understanding addition makes it easier to handle more complex problems involving multiple steps or larger numbers.

Math Notation

Math notation is a system of symbols used to represent numbers and operations. It provides a clear and concise way to communicate mathematical ideas.
In this exercise, 'the sum of 90 and 65' translates to the math notation 90 + 65.
Mathematical notation helps in expressing complex concepts simply and systematically.
For example:

• The '+' symbol indicates addition.
• Numbers are placed on either side of the '+'.

When you understand math notation, you can easily translate word problems into mathematical expressions, making it simpler to perform calculations and find solutions.