Problem 103 - Fundamentals of Mathematics

Question

For the following problems, find the solutions. Subtract the difference between 18 and 7 from the sum of the differences between 42 and 13 , and 81 and 16 .

Step-by-Step Solution

Answer

The solution is 83.

Step 1: Calculate the difference between 18 and 7

To find the difference between two numbers, subtract the second number from the first. In this case, subtract 7 from 18: \[ 18 - 7 = 11 \]

Step 2: Calculate the difference between 42 and 13

Subtract 13 from 42 to find the difference: \[ 42 - 13 = 29 \]

Step 3: Calculate the difference between 81 and 16

Subtract 16 from 81 to find the difference: \[ 81 - 16 = 65 \]

Step 4: Find the sum of the two differences

Add the differences from Step 2 and Step 3: \[ 29 + 65 = 94 \]

Step 5: Subtract the first difference from the sum of the other two

Subtract the result from Step 1 from the result in Step 4: \[ 94 - 11 = 83 \]

Key Concepts

Subtraction

Subtraction is one of the fundamental arithmetic operations, which is taught very early in school. It involves taking one number away from another.
To perform subtraction, you subtract the second number from the first. This operation is straightforward but very important for solving more complex mathematics problems.

• For example, when subtracting 7 from 18, we calculate the difference: \[ 18 - 7 = 11 \]
• This tells us that when 7 is taken away from 18, 11 remains.

Understanding subtraction helps in breaking down bigger problems into smaller parts. In our original problem, we needed to subtract results from different parts to find the final answer.
Mastering subtraction will aid in solving basic and advanced math problems, from homework to daily life calculations.

Addition

Addition is another basic arithmetic operation, which is essentially combining two numbers to obtain a total.
It’s like gathering chocolates from two packs into a single group. The concept is simple but powerful, as it forms the basis of understanding higher-level math concepts.

• The addition process can be seen when we have the differences \[29 \] and \[65 \], and we combine them to get \[94 \]: \[ 29 + 65 = 94 \]
• Each number in the addition process is called an addend, and the result is called the sum.

Being comfortable with addition is important not just in solving math problems, but also in real-world scenarios such as calculating sums while shopping or tallying scores.

Problem Solving

Problem-solving in mathematics is the process of devising a strategy to find the unknown. It involves understanding the problem, devising a plan, carrying out the plan, and reviewing the solution.
In the original exercise, problem-solving is evident as it combines both subtraction and addition.

• Firstly, we needed to find differences between pairs of numbers: 18 and 7, 42 and 13, and 81 and 16.
• Then, we added those differences and adjusted the operations based on the problem's requirement.
• Finally, subtracting the first difference from the total sum achieved gave us the required solution.

Understanding how to solve word problems like these is key for students to progress in learning math, as it involves critical thinking and the application of basic operations like addition and subtraction. With practice, problem-solving becomes a fun challenge rather than a task.