Problem 15 - Fundamentals of Mathematics

Question

Find the sums and differences. $$21+16+42+11$$

Step-by-Step Solution

Answer

The sum is 90.

Step 1: Add First Two Numbers

Start by adding the first two numbers together. Calculate \(21 + 16\). \(21 + 16 = 37\).

Step 2: Add Third Number

Now, add the result from Step 1 to the third number. Calculate \(37 + 42\). \(37 + 42 = 79\).

Step 3: Add Fourth Number

Finally, add the result from Step 2 to the fourth number. Calculate \(79 + 11\). \(79 + 11 = 90\).

Key Concepts

Step-by-Step Problem Solving

Step-by-step problem solving is a powerful approach to tackling any math problem.
It involves breaking down complex problems into smaller, more manageable parts.
This makes it easier to work through each part systematically and arrive at the solution.

• Each step should be clear and concise, focusing on a single task.
• Sequential steps help to maintain order and ensure nothing is overlooked.
• Completing each step in a logical order helps prevent errors and miscalculations.

Working through the problem in smaller pieces allows you to focus on specific aspects like addition, subtraction, or other operations. For example, with the problem of adding numbers like 21, 16, 42, and 11, first add the first two numbers. Once done, use that sum to continue adding the next numbers, one at a time. This minimizes the chance for mistakes and ensures that each part is correctly solved before moving to the next.

Arithmetic Operations

Arithmetic operations are the building blocks of mathematics.
They include basic processes like addition, subtraction, multiplication, and division.
Understanding these operations is essential for solving various math problems.

• Addition: Combines two or more numbers to get a total sum.
• Subtraction: Determines the difference between numbers by taking one away from another.
• Multiplication: Increases a number by adding it to itself a specified number of times.
• Division: Splits a number into equal parts or groups.

In the context of our exercise, addition is key. It involves adding numbers in a sequence to find the total sum. Start by adding the two numbers and then carry the resulting sum forward, adding each of the next numbers one by one. This systematic approach ensures that you efficiently reach the correct total sum of 90.

Number Sequences

Number sequences involve a set of numbers ordered in a logical structure.
Each number in the sequence is related to its predecessor in some manner. Number sequences are used frequently in mathematics to identify patterns or solve equations. In arithmetic, these can help simplify the step-by-step process. Knowing that you are working with an ordered set of numbers lets you apply familiar processes, like addition, effectively. In our exercise:

• The sequence starts with 21 and must add each subsequent number (16, 42, and 11).
• This highlights the importance of processing numbers in the order they appear to maintain clarity in computation.
• By understanding the sequence logic, you prepare for more complex math problems involving patterns or repeated operations.

In any ordered sequence, consistently applying operations like addition can help you find the desired result, as it did here, leading to a total sum of 90.