Division is a fundamental operation in mathematics that involves the distribution of a quantity into equal parts. It is the opposite of multiplication and is used to find out how many times one number (the divisor) is contained within another number (the dividend).

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

**Long Division:**A method of dividing one number by another using repeated subtraction and bringing down digits.**Short Division:**A quicker method of division, often used for simpler problems or with smaller numbers.**Division with Decimals:**Division involving numbers with decimal points.

**Identity Property:**The quotient of any number divided by 1 is the number itself.**Zero Property:**The quotient of 0 divided by any number is 0.**Division by Zero:**Division by zero is undefined in mathematics.

Here are some sample division problems to practice:

- To divide by a power of 10, simply move the decimal point to the left the same number of places as the number of zeros in the power of 10.
- To check your division, multiply the quotient by the divisor and add the remainder, if any. The result should be equal to the dividend.

By understanding the principles and practicing division problems, you can become proficient in this fundamental mathematical operation.

Study GuideSimilarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer keyUsing Similar Polygons Worksheet/Answer keySimilar Polygons Worksheet/Answer keyUsing Similar Polygons Worksheet/Answer keySimilar Polygons

Number and Operations (NCTM)

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

Understand and use ratios and proportions to represent quantitative relationships.

Compute fluently and make reasonable estimates.

Develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios.

Geometry (NCTM)

Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

Understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects.

Create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship.

Apply transformations and use symmetry to analyze mathematical situations.

Describe sizes, positions, and orientations of shapes under informal transformations such as flips, turns, slides, and scaling.

Measurement (NCTM)

Apply appropriate techniques, tools, and formulas to determine measurements.

Solve problems involving scale factors, using ratio and proportion.

Grade 8 Curriculum Focal Points (NCTM)

Geometry and Measurement: Analyzing two- and three-dimensional space and figures by using distance and angle

Students use fundamental facts about distance and angles to describe and analyze figures and situations in two- and three-dimensional space and to solve problems, including those with multiple steps. They prove that particular configurations of lines give rise to similar triangles because of the congruent angles created when a transversal cuts parallel lines. Students apply this reasoning about similar triangles to solve a variety of problems, including those that ask them to find heights and distances. They use facts about the angles that are created when a transversal cuts parallel lines to explain why the sum of the measures of the angles in a triangle is 180 degrees, and they apply this fact about triangles to find unknown measures of angles. Students explain why the Pythagorean Theorem is valid by using a variety of methods - for example, by decomposing a square in two different ways. They apply the Pythagorean Theorem to find distances between points in the Cartesian coordinate plane to measure lengths and analyze polygons and polyhedra.