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Grade 6 Distributive Property & Combining Like Terms Worksheet with Answers

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distributive property combining like terms worksheet

Grade 6 Distributive Property & Combining Like Terms Worksheet with Answers

This type of exercise typically involves algebraic expressions where one must first distribute a factor across terms within parentheses and then simplify the resulting expression by grouping similar terms. For example, simplifying 3(2x + 5) + 4x requires distributing the 3 to both 2x and 5, yielding 6x + 15 + 4x. Then, combining the like terms 6x and 4x gives the simplified expression 10x + 15.

Mastering this combined skill is fundamental to algebra and its numerous applications across mathematics and related fields. It allows for the simplification of complex expressions, making them easier to solve and analyze. This simplification process underpins problem-solving in areas ranging from basic equation manipulation to advanced calculus and physics. Historically, the development of algebraic notation and techniques for manipulating expressions, including these core concepts, marked a significant advancement in mathematical thought, enabling more abstract and powerful reasoning.

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Grade 6: Distributive Property & Combining Like Terms Worksheet

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distributive property with combining like terms worksheet

Grade 6: Distributive Property & Combining Like Terms Worksheet

This fundamental algebraic concept involves multiplying a single term by a sum or difference of terms within parentheses. For example, 3(x + 2) simplifies to 3x + 6 by multiplying both x and 2 by 3. This process is frequently coupled with the simplification of expressions by combining similar terms. This might involve adding or subtracting terms with the same variable and exponent, such as simplifying 3x + 2x + 6 to 5x + 6. Practice problems on worksheets reinforce these skills through repetitive application in varied scenarios.

Mastery of these combined skills forms a cornerstone of algebra, laying the groundwork for solving equations, factoring, and working with more complex mathematical concepts. By breaking down complex expressions into simpler forms, these processes streamline calculations and provide a more manageable approach to problem-solving. Historically, the development of these algebraic techniques has been crucial for advancements in various fields, from physics and engineering to computer science and economics.

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6+ Distributive Property & Combining Like Terms Worksheets

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distributive property and combining like terms worksheet

6+ Distributive Property & Combining Like Terms Worksheets

A foundational skill in algebra involves simplifying expressions using two key concepts: expanding expressions using the principle of multiplication over addition and subtraction, and collecting similar variable terms and constant numerical values. For example, the expression 3(x + 2) + 2x – 5 can be simplified to 5x + 1 by distributing the 3 to both x and 2 (resulting in 3x + 6), then adding the like terms 3x and 2x, and finally combining the constants 6 and -5. Practice materials often take the form of structured exercises providing opportunities to apply these simplification techniques.

Mastering these techniques is crucial for progressing to more advanced algebraic manipulation, equation solving, and ultimately, a deeper understanding of mathematical relationships. This groundwork is essential for success in STEM fields and reinforces logical reasoning skills applicable in a wide range of disciplines. These core concepts have been integral to mathematical education for centuries, contributing to the development of more complex mathematical ideas and their applications in science and technology.

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