Question

State in words the inverse operation. Divide by 10 .

Short answer

Answer: The inverse operation of "Divide by 10" is "Multiply by 10."

Step-by-step solution

Identify the given operation

The given operation is "Divide by 10." When a number is divided by 10, it is reduced by a factor of 10.

Determine the inverse operation

The inverse operation should reverse the effect of dividing by 10. To undo division, we can use multiplication. As the given operation divides by 10, we need to multiply back by the same factor. So, the inverse operation is "Multiply by 10."

Key concepts

division

Division is an arithmetic operation where you take a number and split it into equal parts. Imagine having a pizza and sharing it with your friends. If you divide a pizza into 10 slices and you have 10 friends, each gets one slice. Mathematically, division is represented by the symbol "/". For example, if you have 20 apples and you divide them equally among 4 people, you perform the division operation: \[ 20 \div 4 = 5 \] Each person will receive 5 apples.

Division is essentially the process of determining how many times one number is contained within another. This understanding is fundamental in many areas of math, such as solving equations and finding averages.

multiplication

Multiplication is the arithmetic operation that represents combining equal groups of objects. It is essentially repeated addition. Suppose you have 4 bags with 3 marbles in each bag. To find the total number of marbles, multiply the number of bags by the number of marbles in each:\[ 4 \times 3 = 12 \] There are 12 marbles in total.

Multiplication also has interesting properties:

• Commutative Property: The order in which you multiply numbers doesn't matter, i.e., \( a \times b = b \times a \).
• Associative Property: The way numbers are grouped in multiplication doesn't affect the outcome, i.e., \((a \times b) \times c = a \times (b \times c)\).
• Distributive Property: A number that multiplies a sum can be distributed to multiply each addend separately, i.e., \( a \times (b + c) = a \times b + a \times c \).

Understanding multiplication is crucial for solving problems in mathematics and real-life situations.

arithmetic operations

Arithmetic operations are the basic building blocks of mathematics. They include addition, subtraction, multiplication, and division. Each operation has its significance and a unique role:

• Addition: Combining numbers to get a total, written as "+".
• Subtraction: Removing one number from another, represented by "-".
• Multiplication: Repeated addition or scaling a number, expressed with "\( \times \)".
• Division: Splitting a number into equal parts or determining how many times one number fits into another, shown with "\( \div \)".

These operations are interrelated by the concept of inverse operations. For example, multiplication is the inverse of division, and vice versa. This means performing one operation can "undo" the other. Understanding these basic operations helps in manipulating numbers and solving complex problems, forming the foundation for advanced mathematical concepts.