Problem 78 - Elementary Algebra

Question

Add or subtract and reduce to lowest terms. $$ 1115+915 $$

Step-by-Step Solution

Answer

2030

Step 1: Identify the Operation

The task requires you to add two numbers: 1115 and 915.

Step 2: Add the Numbers

Add the numbers 1115 and 915. Write down the operation: \[ 1115 + 915 = 2030 \]

Step 3: Reduce to Lowest Terms

Since 2030 is already a whole number, reducing a whole number to the lowest term simply means the number itself, as whole numbers cannot be further simplified.

Key Concepts

Addition

Addition is one of the basic arithmetic operations that involves combining two or more numbers to get a total sum. It is akin to bringing two groups of objects together. We apply addition in our original exercise to combine the numbers 1115 and 915.

• Take each digit of the numbers you're adding, align them by their place values (units, tens, hundreds).
• Start adding from the rightmost digit (units place) and move to the left, carrying over the sum when it exceeds 9.
• For the exercise 1115 + 915, add systematically and ensure each place value is processed correctly. For example, - Start at units: 5 + 5 = 10, write 0 and carry over 1. - Move to tens: 1 (carry-over) + 1 + 1 = 3. - Next, hundreds: 1 + 9 + 1 = 11, write 1 and carry over 1. - Finally, thousands: 1 (carry-over) + 1 = 2.

The sum should correctly total to 2030, demonstrating addition's power to find totals quickly and accurately.

Whole Numbers

Whole numbers form a fundamental part of mathematics. They are non-negative numbers that do not include fractions or decimals. Simply put, whole numbers range from zero onwards and go to infinity. Whole numbers include:

• Zero (0)
• Positive integers (like 1, 2, 3, ...)

In the math exercise, both 1115 and 915 are whole numbers, which simplifies the addition process. Since whole numbers are straightforward and lack fractional components, operations like addition and subtraction are clear-cut, with minimal room for error during calculations, making whole numbers optimal for operations in basic arithmetic. Understanding whole numbers: - They ensure integrity of quantity without fragments. - Used extensively in counting and ordering.

Reducing to Lowest Terms

The phrase "reduce to lowest terms" is often associated with fractions, where it involves simplifying a fraction to its smallest possible equivalent. However, when dealing with whole numbers, the term has a different implication. Considering the exercise's result 2030, here's what you should know:

• Whole numbers are inherently in their simplest form.
• For fractions, you'd divide both numerator and denominator by their greatest common divisor (GCD) to achieve the lowest terms.
• For integers like 2030, no further reduction is possible.

Thus, reducing to lowest terms when working with whole numbers simply means ensuring the number is expressed as an integer without unnecessary zeroes or decimals. Hence, in this case, 2030 is already in its reduced form.