Division is an operation that splits a number into equal parts or groups. The number being divided is called the dividend, the number by which it is being divided is called the divisor, and the result is called the quotient.

To perform basic division, use the following steps:

- Place the dividend inside the division bracket, and the divisor outside the bracket.
- Start by dividing the leftmost digit of the dividend by the divisor.
- If the divisor is greater than the first digit of the dividend, continue to the next digit until the divisor is less than the dividend.
- Write the quotient above the division bracket and multiply the divisor by the quotient.
- Subtract the product from the part of the dividend you have not yet divided.
- Bring down the next digit of the dividend and repeat the process until there are no digits left to bring down.
- The final result is the quotient.

Let's divide 456 by 6:

7 6 | 456 - 42 --- 36 36 --- 0

In this example, the quotient is 76, and there is no remainder. The result is a whole number.

Sometimes, when you divide, the division does not result in a whole number. In this case, you will have a remainder. The remainder is the amount left over after dividing as much as possible. You can express the remainder as a fraction or a decimal.

Here are some important concepts to remember when studying division:

- Understand the relationship between the dividend, divisor, and quotient.
- Practice basic division with single-digit divisors to build a strong foundation.
- Learn how to express remainders as fractions or decimals.
- Explore real-world problems that can be solved using division.
- Master long division for dividing larger numbers.

Remember, division is the opposite of multiplication. Understanding division will help you strengthen your overall math skills.

.Study GuideSimilarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer key

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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.