Problem 60 - Fundamentals of Mathematics

Question

For the following problems, perform the additions and round to the nearest hundred. $$ \begin{array}{r} 21 \\ 16 \\ \hline \end{array} $$

Step-by-Step Solution

Answer

The answer is 0.

Step 1: Perform the Addition

To find the total sum of 21 and 16, add these two numbers: 21 + 16. Calculate: 21 + 16 = 37.

Step 2: Round the Result to the Nearest Hundred

The sum calculated is 37. To round 37 to the nearest hundred, identify the nearest hundreds - 0 and 100. Since 37 is closer to 0 than to 100, we round 37 down to 0.

Key Concepts

Addition

Addition is one of the four basic operations in arithmetic. It's the process of finding the total or sum by combining two or more numbers. When performing addition, it's important to align the numbers by their place values, which means aligning them column by column, starting from the rightmost digit—the units column.
To add two numbers like 21 and 16:

• Start by writing them so that the units (rightmost digits) and tens align vertically.
• Beginning with the rightmost column (units), add the digits together. In this case, 1 (from 21) + 6 (from 16) = 7.
• Move to the next column (tens). Here, you add 2 (from 21) + 1 (from 16) = 3.

Thus, the total sum is 37.
The sum is the number that results from adding two or more addends, which in this example are the numbers 21 and 16. Understanding basic addition is crucial for rounding, as it's typically the first step before you decide if the sum needs to be rounded to a certain place value.

Whole Numbers

Whole numbers are a set of numbers that include all the positive integers along with zero and do not have fractions or decimals. They are the numbers we use for counting and ordering, such as 0, 1, 2, 3, and so on.
In the context of our problem:

• The numbers 21 and 16, as well as the resulting total, 37, are all whole numbers.
• Whole numbers can be easily added and are pivotal in establishing a baseline for more complex mathematical operations.

Because whole numbers do not include negative numbers, they are useful for quantifying quantities that can't be divided into parts, such as people, objects, or simple counts. This makes them crucial for various real-life applications, including rounding up or down to the nearest whole number or other significant place value.

Place Value

Place value refers to the position of a digit in a number, which determines its value. Each position in a number has a value that is a power of ten, such as units, tens, hundreds, thousands, and so on.
Understanding place value is essential when adding numbers or performing rounding tasks:

• In the number 37, the 7 is in the units place, and its value is 7.


• The 3 is in the tens place, and its value is 30 because it represents 3 tens.

Rounding requires mastery of place value because it helps in determining the proximity of a number to a certain place value. For example, to round 37 to the nearest hundred, we look at the tens and units to determine that 37 is closer to 0 than to 100.
When rounding, consider the digit in the place value you are rounding to and the digit immediately to the right. This tells you whether to round up or round down, ensuring accuracy in estimates and larger calculations.