Division is the process of splitting a number into equal parts. It is the opposite of multiplication. In division, we have a dividend, a divisor, and a quotient. The dividend is the number being divided, the divisor is the number by which we divide, and the quotient is the result of the division.

For example, when we divide 12 by 3:

12 | : | 3 | = | 4 |

Here, 12 is the dividend, 3 is the divisor, and 4 is the quotient.

When learning about division, it's important to understand the following terms:

**Dividend:**The number being divided.**Divisor:**The number by which we divide.**Quotient:**The result of the division.**Remainder:**The amount left over when the dividend is not completely divisible by the divisor.**Divisibility:**The ability of a number to be divided by another number without leaving a remainder.

There are different methods for performing division:

**Long Division:**This is a method for dividing larger numbers. It involves writing out the dividend, divisor, and quotient, and then performing the division step by step.**Short Division:**This method is used for dividing by single-digit divisors. It's a quicker method than long division.**Repeated Subtraction:**In this method, we subtract the divisor from the dividend repeatedly until we reach zero or a remainder.

When working with division, it's important to remember the following rules:

**Division by zero:**Division by zero is undefined. It is not possible to divide a number by zero.**Divisibility rules:**These rules help determine if a number is divisible by another number without actually performing the division. For example, a number is divisible by 2 if its last digit is even.**Order of operations:**Division is performed after parentheses, exponents, and multiplication in the order of operations.

It's important to practice division problems to master the concept. Here are some sample problems to try:

- Divide 56 by 7.
- Find the quotient when 81 is divided by 9.
- If a number is divisible by 4 and 6, is it also divisible by 12?
- Perform long division to divide 325 by 5.

By practicing division problems and understanding the terminology and rules, you can become proficient in this important mathematical operation.

Good luck with your division studies!

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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.