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!

Study GuideIntroduction to Percent Worksheet/Answer key

Introduction to Percent Worksheet/Answer key

Introduction to Percent Worksheet/Answer key

Introduction to Percent Worksheet/Answer keyIntroduction to Percent

Number and Operations (NCTM)

Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

Work flexibly with fractions, decimals, and percents to solve problems.

Develop meaning for percents greater than 100 and less than 1.

Grade 7 Curriculum Focal Points (NCTM)

Number and Operations and Algebra and Geometry: Developing an understanding of and applying proportionality, including similarity

Students extend their work with ratios to develop an understanding of proportionality that they apply to solve single and multi-step problems in numerous contexts. They use ratio and proportionality to solve a wide variety of percent problems, including problems involving discounts, interest, taxes, tips, and percent increase or decrease. They also solve problems about similar objects (including figures) by using scale factors that relate corresponding lengths of the objects or by using the fact that relationships of lengths within an object are preserved in similar objects. Students graph proportional relationships and identify the unit rate as the slope of the related line. They distinguish proportional relationships (y/x = k, or y = kx) from other relationships, including inverse proportionality (xy = k, or y = k/x).

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.

Connections to the Grade 7 Focal Points (NCTM)

Number and Operations: In grade 4, students used equivalent fractions to determine the decimal representations of fractions that they could represent with terminating decimals. Students now use division to express any fraction as a decimal, including fractions that they must represent with infinite decimals. They find this method useful when working with proportions, especially those involving percents. Students connect their work with dividing fractions to solving equations of the form ax = b, where a and b are fractions. Students continue to develop their understanding of multiplication and division and the structure of numbers by determining if a counting number greater than 1 is a prime, and if it is not, by factoring it into a product of primes.