Problem 32 - Prealgebra

Question

Find each sum or product. Explain your reasoning. $$74+22+6$$

Step-by-Step Solution

Answer

The sum of 74, 22, and 6 is 102.

Step 1: Add the first two numbers

To begin, add the first two numbers in the expression, which are 74 and 22. \(74 + 22 = 96\). This simplifies our expression to 96 + 6.

Step 2: Add the result to the third number

Now, take the result from Step 1, which is 96, and add the third number, 6.\(96 + 6 = 102\). This calculation completes the operation needed to find the sum of all three numbers.

Key Concepts

Mental Math

Mental math involves doing calculations in your mind without the use of paper, pencil, or calculator. It is a valuable skill because it enhances your ability to compute faster and more efficiently.

When you approach a problem like \(74 + 22 + 6\), mental math can make the process quicker. You can start by breaking down each number into easy-to-handle components. For instance, think of 22 as 20 + 2.

Now you add 74 and 20, which gives you 94. Then add the remaining 2 to 94 to get 96.

Finally, bring in the last number, 6, and adding it to 96 gives you 102.

• Practice regularly to enhance your mental math skills.
• Use rounding and estimates to simplify complex problems.
• Always double-check your mental results with written calculations to verify accuracy.

With practice, mental math becomes a natural and intuitive skill that can greatly benefit daily arithmetic tasks.

Step-by-Step Calculation

A step-by-step calculation is a methodical approach to solving an arithmetic problem by breaking it down into smaller, manageable parts.

This approach is useful when dealing with more complex problems or ensuring accuracy. In the given problem \(74 + 22 + 6\), the solution was broken down into two primary steps for clarity.

Firstly, focus on adding the first two numbers, which are 74 and 22.

This sum yields 96.

Next, you take the result of 96 and add the remaining number 6 to complete the calculation, resulting in 102.

• Step-by-step methods help in avoiding careless errors.
• It builds a strong foundation in understanding arithmetic operations.
• Each step should be clearly understood before proceeding to the next.

This systematic method provides clarity and helps to build confidence when performing calculations.

Arithmetic Reasoning

Arithmetic reasoning involves understanding and applying the principles of arithmetic to solve problems logically and accurately. It is more than performing calculations; it requires thinking about numbers and their relationships.

In solving \(74 + 22 + 6\), arithmetic reasoning helps in planning the order of operations and choosing the best strategy.

You should recognize the convenience of pairing numbers that are easy to add together. This could mean starting with the smaller or more round numbers, to simplify the calculation process.

Using arithmetic reasoning, you understand why you start by adding 74 and 22 first, because they are the first two numbers and easier to group, which means it logically follows to add the result, 96, to the next available number, 6.

• Helps identify the most efficient way to solve a problem.
• Encourages looking for patterns and relationships in numbers.
• Develops a deeper understanding of the logic behind arithmetic operations.

This type of reasoning makes arithmetic not only a calculation task but a strategic one, as well.