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Chapter 1: Problem 2

Define the key terms. a. Multiplication b. Factor c. Product d. Area e. Area of a rectangle

Short Answer

Expert verified
Multiplication: repeated addition of a number. Factor: divides another number exactly. Product: result of multiplication. Area: space inside a 2D shape. Area of a rectangle: length 脳 width.

Step by step solution

01

- Define Multiplication

Multiplication is an arithmetic operation where a number is added to itself a specified number of times. For instance, multiplying 3 by 4 (written as 3 脳 4) involves adding 3 to itself 4 times: 3 + 3 + 3 + 3 = 12.
02

- Define Factor

A factor is a number that divides another number exactly without leaving a remainder. For example, the factors of 12 include 1, 2, 3, 4, 6, and 12.
03

- Define Product

Product is the result obtained from multiplying two or more numbers. For example, the product of 3 and 4 is 12, as 3 脳 4 = 12.
04

- Define Area

Area is the amount of space inside the boundary of a two-dimensional shape, measured in square units. For example, the area of a square with sides of 1 meter each is 1 square meter.
05

- Define Area of a Rectangle

The area of a rectangle is calculated by multiplying its length by its width. For example, a rectangle with a length of 5 units and a width of 3 units has an area of 5 脳 3 = 15 square units.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Multiplication
Multiplication is an essential arithmetic operation in mathematics. It involves adding a number, called the *multiplicand*, to itself a specified number of times indicated by the *multiplier*. For instance, when we multiply 3 by 4, written as 3 脳 4, we add 3 to itself four times to get 12.

Here鈥檚 a simple illustration:
  • 3 脳 4 = 3 + 3 + 3 + 3 = 12
This operation is useful for various mathematical tasks, such as calculating totals, areas, and more.
Factor
A factor is a number that divides another number perfectly, without leaving any remainder. In other words, if you can divide a number by another number and the result is a whole number, the second number is a factor of the first.

For example:
  • The factors of 12 are 1, 2, 3, 4, 6, and 12, because 12 梅 1 = 12, 12 梅 2 = 6, 12 梅 3 = 4, 12 梅 4 = 3, 12 梅 6 = 2, and 12 梅 12 = 1.
Understanding factors is crucial for simplifying fractions, finding greatest common divisors, and solving various algebraic equations.
Product
The term *product* refers to the result obtained when two or more numbers are multiplied together. This is a key concept in various areas of mathematics including algebra, geometry, and arithmetic.

For example, when we multiply 3 and 4, the product is 12 because:
  • 3 脳 4 = 12
Recognizing the product helps in understanding the relationships between numbers and can simplify problem-solving in more complex mathematical contexts.
Area
The area is the measure of space inside the boundaries of a two-dimensional shape. It is always measured in square units, such as square meters, square centimeters, or square inches.

For a square with sides of length 1 meter, the area would be:
  • 1 meter 脳 1 meter = 1 square meter
Knowing how to calculate the area is essential in geometry, land measurement, and various real-world applications where space and surface coverage are considered.
Area of a Rectangle
The area of a rectangle is found by multiplying its length by its width. Length and width are the sides of the rectangle. Understanding this helps in calculating spaces for things like floors, walls, and more.

For example, if a rectangle has a length of 5 units and a width of 3 units, the area is:
  • 5 units 脳 3 units = 15 square units
This formula, Area = Length 脳 Width, is simple yet powerful in solving many geometric problems.

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Most popular questions from this chapter

On a number line, what number is 3 units to the left of \(7 ?\)

Write the number in words. $$108$$

Fill in the blank with the inequality symbol \(<\) or \(>\). $$14 \square 24$$

Convert the numbers to expanded form. $$58$$

For each English sentence, write a mathematical expression and simplify. Divide 877 by 14.
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