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Chapter 3: Problem 405

In the following exercises, simplify each expression. $$ 14+82 $$

Short Answer

Expert verified
96

Step by step solution

01

Identify the Operation

Notice that the expression involves addition. We are adding two numbers: 14 and 82.
02

Add the Numbers

Perform the addition operation by adding 14 and 82 together: \[ 14 + 82 = 96 \]
03

Simplified Expression

The simplified expression is obtained by adding the two numbers together. So, the final expression is 96.

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Key Concepts

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

basic arithmetic
Basic arithmetic forms the foundation of mathematics. It involves fundamental operations like addition, subtraction, multiplication, and division. Let's focus on addition, which combines two or more numbers to yield a total sum. For instance, when you add 14 and 82, you are performing an arithmetic operation.
Understanding basic arithmetic is crucial for solving more complex mathematical problems. It's the first step toward building a strong math foundation.
As you get comfortable with basic arithmetic, you will find it easier to handle larger numbers and more complex operations.
addition operation
Addition is one of the primary operations in mathematics. The process involves combining two or more numbers to find their total. In the given example, you need to add 14 and 82.

Here are the steps to perform the addition operation:
  • Identify the numbers to be added. In this case, they are 14 and 82.
  • Align the numbers by their place values (units, tens, hundreds, etc.).
  • Add the numbers starting from the rightmost digits (units).
  • Carry over any extra value to the next column if the sum exceeds 9.
Let's apply these steps:
1. Add the units place: 4 (from 14) + 2 (from 82) = 6.
2. Add the tens place: 1 (from 14) + 8 (from 82) = 9.
The result is 96, so \[14 + 82 = 96\].
mental math
Mental math is the ability to perform arithmetic calculations in your head. It's a useful skill that can save time and improve your number sense. When performing addition mentally, you can break down numbers to make the process easier.
In the example of adding 14 and 82, you can:
  • Round numbers to the nearest ten to simplify the operation.
  • Add the rounded numbers mentally and then adjust for the rounding.
Here's how you can do it:
  • Round 14 up to 20 (an adjustment of 6).
  • Add 82 and 20 to get 102.
  • Since we added an extra 6 to 14, subtract 6 from 102 to correct the total.
  • The result is 96.
This method helps you visualize numbers and perform quick calculations, enhancing both speed and accuracy.

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