Problem 14 - Algebra 1

Question

State the inverse operation. Divide by 6.

Step-by-Step Solution

Answer

The inverse operation of division by 6 is multiplication by 6.

Step 1: Identify the Operation

Firstly, identify the provided operation in the exercise. In this case, the operation given is a division by 6.

Step 2: Find the Inverse Operation

To find the inverse operation of division by 6, you should perform the opposite operation. As division and multiplication are opposite operations, the inverse operation to division by 6 would be multiplication by 6.

Key Concepts

Division

When we talk about division, we are discussing an operation where we split a number into equal parts. Imagine you have 12 apples and you want to divide them among 3 friends. By performing the division, you would give each friend 4 apples.
Mathematically, this is expressed as:
\[ 12 \div 3 = 4 \]
Division asks how many times one number is contained within another. It's a core arithmetic operation used in everyday problem-solving, like splitting up bills or distributing tasks evenly.

• Dividend: the number being divided (e.g., 12).
• Divisor: the number we are dividing by (e.g., 3).
• Quotient: the result (e.g., 4).

Understanding division is crucial because it sets the stage for learning more complex mathematical concepts, such as inverse operations and fractions.

Multiplication

Multiplication is another fundamental operation in math. It combines equal groups into a larger total or helps you scale numbers by a factor. Consider you have 4 baskets, each containing 3 apples. Using multiplication, we find that the total number of apples is:
\[ 4 \times 3 = 12 \]
Multiplication can be thought of as repeated addition. In our apples example, it is like adding the number three four times.

• Factors: the numbers being multiplied (e.g., 4 and 3).
• Product: the result of a multiplication operation (e.g., 12).

Multiplication is the inverse of division. If you multiply something and then divide by the same number, you get back to where you started. For instance, if you multiply by 6 and then divide by 6, you return to the original value. This relationship is an essential aspect of understanding inverse operations.

Basic Arithmetic Operations

Basic arithmetic operations include addition, subtraction, multiplication, and division. These operations form the foundation of mathematics and are essential for solving everyday problems.
Addition is about combining numbers, while subtraction focuses on taking numbers away. Together, they lay the groundwork for understanding how numbers interrelate.
Multiplication and division, on the other hand, deal with scaling numbers up and down as discussed previously.
The beauty of these operations is in their interaction. For instance:

• Addition and subtraction are inverse operations. If you add a number and then subtract the same number, you return to your original number.
• Multiplication and division are also inverse operations. You multiply and then divide by the same number to revert to the initial value.

Mastering these operations is pivotal in advancing to more complex mathematical concepts and operations.