Dividing is the operation of splitting a number into equal parts or groups. When we divide one number by another, we are essentially finding out how many times the second number can fit into the first number.

When dividing, we use a few key terms:

- Dividend: The number being divided.
- Divisor: The number by which the dividend is being divided.
- Quotient: The result of the division.
- Remainder: The amount left over when the dividend cannot be evenly divided by the divisor.

For example, in the division problem 15 ÷ 3:

- The dividend is 15.
- The divisor is 3.
- The quotient is 5 (15 ÷ 3 = 5).
- There is no remainder in this case, as 15 is evenly divisible by 3.

Long division is a method used to divide larger numbers. The basic steps for long division are:

- Divide: Divide the leftmost digit of the dividend by the divisor. This is the first digit of the quotient.
- Multiply: Multiply the divisor by the first digit of the quotient, and write the result below the dividend.
- Subtract: Subtract the result from the previous step from the part of the dividend that has not been used yet.
- Bring down: Bring down the next digit of the dividend next to the result from the previous step.
- Repeat: Repeat steps 1-4 until there are no more digits to bring down.

There are a few key properties of division that are important to understand:

- Identity Property: The quotient of any number and 1 is the number itself. For example, 8 ÷ 1 = 8.
- Zero Property: The quotient of 0 divided by any non-zero number is 0. For example, 0 ÷ 5 = 0.
- Division by Zero: Division by zero is undefined in mathematics. It cannot be determined.

Now that we've covered the basics of division, it's time to practice some problems. Here are a few to get you started:

- What is the quotient of 27 ÷ 9?
- Perform long division for 144 ÷ 12.
- Is it possible to divide by zero? Why or why not?

After practicing these problems, you should have a solid understanding of the concept of dividing numbers. Good luck!

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Algebra (NCTM)

Represent and analyze mathematical situations and structures using algebraic symbols.

Develop an initial conceptual understanding of different uses of variables.

Use symbolic algebra to represent situations and to solve problems, especially those that involve linear relationships.

Recognize and generate equivalent forms for simple algebraic expressions and solve linear equations

Grade 7 Curriculum Focal Points (NCTM)

Number and Operations and Algebra: Developing an understanding of operations on all rational numbers and solving linear equations

Students extend understandings of addition, subtraction, multiplication, and division, together with their properties, to all rational numbers, including negative integers. By applying properties of arithmetic and considering negative numbers in everyday contexts (e.g., situations of owing money or measuring elevations above and below sea level), students explain why the rules for adding, subtracting, multiplying, and dividing with negative numbers make sense. They use the arithmetic of rational numbers as they formulate and solve linear equations in one variable and use these equations to solve problems. Students make strategic choices of procedures to solve linear equations in one variable and implement them efficiently, understanding that when they use the properties of equality to express an equation in a new way, solutions that they obtain for the new equation also solve the original equation.