Problem 3 - Fundamentals of Mathematics

Question

Complete the following statements. 17 ? 8 = _____ since _____ +8 = 17.

Step-by-Step Solution

Answer

17 - 8 = 9, since 9 + 8 = 17.

Step 1: Understand the Given Statement

The statement given is 17 ? 8 = _____, and we are told that _____ + 8 = 17. Our objective is to find out what the '?' symbol should be replaced with, and what the blank should be filled with.

Step 2: Translate Addition to Subtraction

Since the statement includes '+8', think about the reverse operation, subtraction. If a number plus 8 equals 17, then that number is 17 minus 8.

Step 3: Perform the Subtraction

Calculate 17 - 8 to find the missing number. This gives us 9, so the blank can be filled with 9.

Step 4: Fill in the Missing Symbols

Since 17 - 8 equals 9, replace the '?' with '-' because the operation being used is subtraction. The complete statement is: 17 - 8 = 9.

Key Concepts

Addition

Addition is one of the fundamental operations in arithmetic. It involves combining two or more numbers to calculate their total value. This operation is denoted by the plus sign "+". For example:

• In the expression 3 + 5, the numbers 3 and 5 are called addends.
• The result of this addition process is known as the sum, which in this case is 8.

Addition is applicable in various real-life situations, such as calculating the total number of apples if you start with three apples and add five more. It's also significant when making financial decisions, like figuring out your total expenses by adding individual costs.
The learnings from addition extend to understanding other arithmetical operations like subtraction, where it can be ingeniously reversed.

Subtraction

Subtraction is essentially the opposite operation of addition. In subtraction, you determine the difference between numbers by removing one from another. This operation is denoted by the minus sign "-". It allows us to find out what remains when quantities are taken away. For example:

• In the expression 10 - 4, the number 10 is the minuend and 4 is the subtrahend.
• The result, or difference, in this case, is 6.

Understanding subtraction is essential for everyday tasks. If you have 10 cookies and you eat 4, you subtract 4 from 10 to find out you have 6 cookies left.
Subtraction is handy for solving equations involving addition. As shown in the exercise, if 9 + 8 equals 17, then by subtracting 8 from 17, you arrive back at 9, confirming subtraction as a reverse mechanism of addition.

Problem Solving

Problem solving involves the ability to use logic and arithmetic operations to find solutions to problems. It often requires understanding the relationship between numbers and employing operations like addition or subtraction.
In the example given, starting with the equation 17 ? 8 = _____, a problem solver would assess the information given - namely that something plus 8 equals 17. This directs the solver towards the operation needed, subtraction in this case, to deduce that 17 minus 8 equals 9.
Effective problem solving involves:

• Identifying what is being asked
• Choosing the correct operation to use
• Carrying out calculations carefully
• Verifying the solution by plugging it back into the original problem

By following these steps, you ensure that your solution not only makes sense numerically but also fits contextually within the parameters of the problem posed. This skill is highly valuable for mathematics and beyond, as it nurtures critical thinking and analytical abilities.