Problem 62 - Fundamentals of Mathematics

Question

Add and subtract as in dicated. Add the sum of \(19,161,201,166,127,\) and 44 to the difference of the sums of \(161,2,455,\) and \(85,\) and \(21,26,48,\) and 187 .

Step-by-Step Solution

Answer

The result is 1139.

Step 1: Adding the First Series of Numbers

First, calculate the sum of the series of numbers given: \(19, 161, 201, 166, 127,\) and \(44\). Start by computing:\[19 + 161 + 201 + 166 + 127 + 44 = 718\]So, the sum of the first series is \(718\).

Step 2: Adding the Second Series of Numbers

Next, calculate the sum of the second series of numbers given: \(161, 2, 455,\) and \(85\).Compute:\[161 + 2 + 455 + 85 = 703\]So, the sum of this series is \(703\).

Step 3: Adding the Third Series of Numbers

Now, find the sum of the third series of numbers: \(21, 26, 48,\) and \(187\).Compute:\[21 + 26 + 48 + 187 = 282\]So, the sum of the third series is \(282\).

Step 4: Finding the Difference Between the Second and Third Series

Now, find the difference between the sums obtained in Steps 2 and 3.Compute the difference:\[703 - 282 = 421\]So, the difference is \(421\).

Step 5: Adding First Sum to Difference

Finally, add the sum from Step 1 to the difference obtained in Step 4.Compute:\[718 + 421 = 1139\]Thus, the final result after adding the first sum to the difference is \(1139\).

Key Concepts

Sum of Numbers

When dealing with sums, the main goal is combining multiple numbers into one total figure. This is the core of addition in arithmetic, where you simply add numbers together to determine their aggregate value. It's important to line numbers up correctly, especially in columns by their units, tens, hundreds, etc., to ensure you do not make errors.

• Adding a series: To find the sum of a series, add each number step by step.
• Order of numbers: In addition, the order doesn't matter thanks to the commutative property (e.g., 2 + 3 is the same as 3 + 2).

In our problem, we needed to first find the sum of a series of numbers like \[19, 161, 201, 166, 127, \text{ and } 44\]. By adding these numbers together, we got a sum of \[718\]. This process involves focusing on each number, adding them sequentially to avoid mistakes.

Difference of Sums

Finding the difference involves subtracting one sum from another. This is useful when comparing two groups of numbers. The process requires carefully calculating each sum separately before moving on to subtraction. Ensure you arrange numbers properly according to their place value for accurate subtraction.

• Step one: Calculate each sum individually.
• Step two: Subtract the smaller sum from the larger sum.

In the exercise, we calculated the sum of \[161, 2, 455, \text{and } 85\] which resulted in \[703\], and the sum of \[21, 26, 48, \text{and } 187\] which gave us \[282\]. To find the difference, we subtracted:\[703 - 282 = 421\]. This difference is crucial for further operations.

Arithmetic Operations

Arithmetic is a broad term covering basic mathematical operations such as addition, subtraction, multiplication, and division. These operations are foundational to most mathematical calculations and problem-solving.

• Addition: Combining numbers to get their total.
• Subtraction: Finding out how much one number exceeds another.
• Order of operations: Remember that calculations are usually processed in a specific order. Here, first find sums, then differences, and finally combine results.

In the context of our problem, we utilized both addition and subtraction:
First, by adding numbers to find separate sums, and later, using subtraction to determine the difference between these sums.

Step by Step Solution

Step by step solutions guide the reader through the entire problem-solving process in an easy and logical way. It helps break down complex problems into manageable steps. The key is to tackle one part of the problem at a time.

• Understand each part of the problem.
• Follow a clear sequence of steps to solve it.
• Check your work for errors to ensure accuracy.

In the given problem, we started by summing all required numbers, then moved carefully through finding the needed difference before finally adding final calculated sums together. Each of these steps was crucial for arriving at the correct solution of \[1139\]. Approaching complex arithmetic problems systematically boosts understanding and minimizes errors.