Problem 108 - Prealgebra

Question

In the following exercises, translate each phrase into math notation and then simplify. $$\text { the sum of } 12 \text { and } 19$$

Step-by-Step Solution

Answer

31

Step 1: Translate the Phrase

Identify the key elements of the phrase: 'the sum of 12 and 19'. The key operation here is 'sum' which means addition.

Step 2: Convert to Math Notation

Translate the phrase into math notation. In this case, 'the sum of 12 and 19' translates to: 12 + 19

Step 3: Simplify the Expression

Perform the addition to simplify the expression: 12 + 19 = 31

Key Concepts

Addition

Addition is one of the most basic arithmetic operations. It involves calculating the total of two or more numbers or quantities. When you add numbers together, you are combining them to get a larger number.
For example, if you have 3 apples and you add 2 more apples, you now have 5 apples. The same logic applies to adding larger numbers as well.
In the problem we are working with, the phrase 'the sum of 12 and 19' means we need to find the result of adding 12 and 19 together.

Translation to Math Notation

Translating verbal phrases to math notation is a crucial skill in mathematics. This skill allows us to convert words into symbols and numbers, making it easier to understand and solve problems.
To translate 'the sum of 12 and 19' to math notation, we need to recognize that 'sum' indicates an addition operation. We then write the numbers and the addition symbol in math notation:
12 + 19
This simple step helps bridge the gap between word problems and mathematical expressions, making it easier to perform computations.

Simplification

Simplification is the process of reducing an expression to its simplest form. Once we have translated the phrase into a mathematical expression, we need to perform the actual operation to simplify it.
In our example:
12 + 19
To add these two numbers, we start with the ones place. Adding 2 and 9 gives us 11. We write down 1 and carry over 1 to the tens place.
Next, we add the tens place numbers along with the carried-over 1 (1 + 1 + 2), which gives us 3.
Combining our results, we get 31.
Therefore, the simplified form of 'the sum of 12 and 19' is 31. Simplification helps us to present the answer in its most straightforward and understandable form.