Problem 17 - Fundamentals of Mathematics

Question

For the following problems, perform the additions. If you can, check each sum with a calculator. $$83+16$$

Step-by-Step Solution

Answer

The sum of 83 and 16 is 99.

Step 1: Add the Ones Column

Let's start by adding the digits in the ones column: 3 (from 83) and 6 (from 16). Calculate: \[ 3 + 6 = 9 \] Since 3 + 6 is less than 10, we write 9 below the ones column without carrying over.

Step 2: Add the Tens Column

Next, add the digits in the tens column: 8 (from 83) and 1 (from 16). Since there was no carry from the ones column, we just add:\[ 8 + 1 = 9 \] Write 9 below the tens column.

Step 3: Write the Answer

Now combine the results from both columns. The number from the tens column (9) and the ones column (9) gives us:\[ 83 + 16 = 99 \] So the sum is 99.

Key Concepts

Addition Steps

When performing addition, breaking it down into steps can simplify what might initially seem complex. Always start by identifying the columns to add, commonly the ones, tens, hundreds, and so on.
- **Add the Ones Column**: This is the first step where you focus on adding up the smallest place values first. In our example of 83 + 16, add 3 and 6 to yield 9. Since the sum is less than 10, there's no need to carry over. - **Add the Tens Column**: Next, move to the next higher place, which is the tens column here. Add the digits 8 and 1, which results in 9. Again, there's no carryover needed because the total is under 10.
Writing down these results immediately helps in maintaining an organized record of your calculations. Finally, put the numbers from each column together to get the sum. In this case, the answer is 99.

Arithmetic Operations

Arithmetic operations form the basic foundation of mathematics which includes addition, subtraction, multiplication, and division. Each serves a unique function and helps in solving various types of problems.
Addition is used to find the total or sum when combining different quantities. It is commutative, meaning it gives the same result no matter the order of the numbers. For example, 3 + 6 and 6 + 3 will both result in 9.
By understanding these principles, you can approach more complicated mathematic problems with confidence. Arithmetic operations are applied not just in academic settings but also in real-world situations like budgeting and shopping.

Use of Calculator in Checking Math Problems

Using a calculator to verify your hand-written calculations can be very beneficial. It serves as a double-check ensuring accuracy, especially when managing larger numbers or more complex equations.
Benefits of using a calculator include: - **Speed**: Calculators help perform computations swiftly which can save time. - **Precision**: They reduce the risk of human error that can occur with manual calculations. - **Confidence**: Knowing you can verify your work reinforces your understanding and trust in the result.
However, it's important to first attempt solving the problems manually to strengthen math skills before using a calculator for confirmation. This practice encourages learning and applying mental math strategies effectively.