Problem 100 - Fundamentals of Mathematics

Question

For the following problems, find the solutions. Add the difference between 63 and 47 to the difference between 55 and 11 .

Step-by-Step Solution

Answer

The solution is 60.

Step 1: Calculate the First Difference

First, we need to calculate the difference between 63 and 47. To do this, subtract 47 from 63: \[ 63 - 47 = 16 \]

Step 2: Calculate the Second Difference

Next, calculate the difference between 55 and 11. Subtract 11 from 55: \[ 55 - 11 = 44 \]

Step 3: Add Both Differences

Now that we have both differences, add them together. Add the result from Step 1 to the result from Step 2: \[ 16 + 44 = 60 \]

Key Concepts

Subtraction

Subtraction is a fundamental arithmetic operation that allows us to find the difference between two numbers. In simple terms, it involves taking away a certain quantity from another. For instance, when you have 63 units and you take away 47, you're left with 16 units. This is expressed mathematically as:
\[63 - 47 = 16\]Think of subtraction as a method to find out "how many more" or "how many less" one value is compared to another. This concept is particularly useful in everyday scenarios, such as calculating age differences, determining remaining distances, or finding out how much change you should get when buying something.

• Remember the basic rule: the larger number comes first when you subtract.
• Double-check your result by adding the difference back to the smaller number. It should equal the larger number you started with.

Addition

Addition is another key arithmetic operation that combines two or more numbers into a single sum. In our problem, once the differences were found from the subtraction step, the next task was to add them together. This is shown as:
\[16 + 44 = 60\]Addition is like gathering quantities together. It is the opposite of subtraction. In real life, addition is used when calculating the total of items in your shopping cart or figuring out the combined run score in a sports game.

• When adding, it’s often helpful to group numbers in tens for easier calculation.
• Try rearranging numbers when adding, as addition is commutative, meaning the order doesn’t affect the sum.

Arithmetic Calculation

Arithmetic calculation combines all basic operations: addition, subtraction, multiplication, and division. In the exercise, arithmetic calculation is showcased through both subtraction and addition to arrive at a final solution. Understanding arithmetic processes forms the foundation for more complex math topics like algebra and calculus.
These are core skills that can be built on:

• Subtraction: Removing a part from the whole, often used when dealing with expenditures, losses, or differences.
• Addition: Accumulating values, useful in tallying scores or summing totals.
• Exercises combining operations, like the one tackled here, enhance problem-solving skills.

By mastering these operations, you build a solid mathematical foundation enabling you to handle complex calculations with confidence.