Problem 95 - Fundamentals of Mathematics

Question

For the following problems, find the solutions. Subtract 42 from the sum of 16 and 56 .

Step-by-Step Solution

Answer

The solution is 30.

Step 1: Calculate the Sum

Start by adding the numbers 16 and 56 together. This will give you the total sum of these two numbers. \[ 16 + 56 = 72 \]

Step 2: Subtraction Operation

Now subtract 42 from the sum obtained in Step 1. This will give you the final result.\[ 72 - 42 = 30 \]

Key Concepts

Addition

Addition is one of the fundamental operations in basic arithmetic. It involves combining two or more numbers to get a total or sum. Understanding addition is crucial as it lays the groundwork for other arithmetic operations such as multiplication and division.
Additions can be visualized with objects or pictures which makes it easier for learners to grasp its concept.

• When you add numbers, you start by writing them one below the other if they are vertically added, aligning them by their place values.
• Units are added to units, tens to tens, and so on.

For example, when adding 16 and 56:

• Add the digits in the unit's place: 6 + 6 = 12. Write down 2 and carry over 1 to the next column.
• Add the digits in the ten's place: 1 (carry) + 1 + 5 = 7.
• The sum of 16 and 56 is 72.

This example shows addition working through the combination of smaller sums and is a simple yet powerful tool in problem solving.

Subtraction

Subtraction is an arithmetic operation that represents the process of taking away numbers or finding the difference between them. It is essentially the reverse of addition.
Understanding subtraction is pivotal, as it not only helps in solving direct problems but also plays a key role in reverse calculations like finding missing addends.

• In subtraction, the larger number (minuend) is written first followed by the smaller number (subtrahend).
• Subtraction can be visualized as removing objects from a collection, which makes it easier to understand for beginners.

For example, to subtract 42 from 72:

• Start by subtracting the units: 2 - 2 = 0.
• Then, subtract the tens: 7 - 4 = 3.
• The result of 72 - 42 is 30.

This example illustrates how subtraction helps in problem-solving by reducing stepwise differences to find the final answer.

Problem Solving Steps

Problem-solving in mathematics often involves a structured approach to break down a problem into manageable parts. Following a set of steps ensures that the problem is tackled efficiently. Involve critical thinking and sequential processing through these steps:
1. **Understand the Problem** - Carefully read the problem to know what is being asked.
2. **Plan** - Determine the operations required such as addition or subtraction. Decide the sequence in which to solve the steps.
3. **Execute** - Perform the operations, checking each step as you go to avoid errors.

• For problems involving multiple steps, it's often useful to first handle any bracketed numbers or sub-problems.
• Write down each step to keep track of the process.

In our original exercise, the steps were:

• Step 1: Find the sum of two numbers.
• Step 2: Use the sum in a subtraction problem.

Having a clear step-by-step method can demystify even complex problems, making them simpler and more approachable.