Aljabar | Matematika Kelas 7 Kurikulum Merdeka - Lengkap

Summary

In this educational video, Missinta introduces 7th-grade algebra concepts based on the Merdeka curriculum. She explains algebraic components like terms, coefficients, variables, and constants, and provides examples of like and unlike terms. The video covers fundamental operations such as addition, subtraction, multiplication, and division of algebraic expressions, using simple, relatable examples. Missinta walks through solving problems, including combining like terms, and demonstrates methods for multiplying binomials and simplifying algebraic fractions. The lesson is aimed at helping students understand and apply basic algebraic principles, providing both conceptual explanations and practical problem-solving strategies.

Takeaways

• 😀 Algebra involves mathematical expressions that use variables to represent unknown values.
• 😀 An expression can contain multiple terms, which are separated by addition or subtraction signs, such as in '2x + 9'.
• 😀 Like terms (terms with the same variable and exponent) can be combined, while unlike terms cannot be added together.
• 😀 A coefficient is the number in front of a variable (e.g., in '4x', '4' is the coefficient).
• 😀 Constants are numbers that do not have variables (e.g., '7' in '4x + 7').
• 😀 In addition or subtraction, only the coefficients of like terms are combined, not the variables themselves.
• 😀 For example, '2a + 4a' simplifies to '6a', as the variables are the same and only the coefficients are added.
• 😀 In multiplication, constants multiply with the terms inside parentheses. For example, '2(3a + 6)' becomes '6a + 12'.
• 😀 When multiplying binomials, distribute each term of one binomial with every term of the other. For example, '(x + 2)(x + 5)' becomes 'x² + 7x + 10'.
• 😀 Division of algebraic expressions can be simplified by factoring or dividing like terms, for example, 'x² + 3x + 2' divided by 'x + 1' results in 'x + 2'.

Q & A

What is algebra and why is it important?

Algebra is a branch of mathematics that deals with variables and the manipulation of symbols to represent unknown numbers. It is important because it helps in problem-solving, understanding patterns, and is foundational for advanced mathematical concepts.

What are the key components of an algebraic expression?

The key components of an algebraic expression include terms, coefficients, variables, and constants. Terms are parts of the expression separated by addition or subtraction, coefficients are numbers multiplying the variables, variables represent unknowns, and constants are numbers without variables.

How can you identify like and unlike terms in algebra?

Like terms in algebra have the same variables and exponents, such as 2x and 4x. Unlike terms have different variables or exponents, like 2x and 5xy or 3x² and 4x.

What is a coefficient in an algebraic expression?

A coefficient is the number that is multiplied by the variable in an algebraic term. For example, in 4x, 4 is the coefficient.

What is the difference between a constant and a variable?

A constant is a fixed number that does not change and is not multiplied by a variable, while a variable is a symbol (usually a letter) that represents an unknown value and can change.

What is the rule for adding or subtracting algebraic expressions?

You can only add or subtract terms that have the same variable and exponent. For example, 3x and 4x can be added together to form 7x, but 3x and 4y cannot be added because their variables are different.

How do you add or subtract terms with different variables?

You cannot directly add or subtract terms with different variables. You must group terms with the same variable and exponent together, while leaving others as they are.

What is the correct procedure for multiplying algebraic expressions?

When multiplying algebraic expressions, you apply the distributive property by multiplying each term in one expression by each term in the other expression. For example, multiplying (x + 2) by (x + 5) results in x² + 7x + 10.

How do you handle dividing algebraic expressions?

When dividing algebraic expressions, you simplify the terms by subtracting exponents for terms with the same base and dividing the coefficients. If the expressions involve multiple terms, factorization or polynomial division may be used.

What is the method of dividing polynomials using long division?

Long division of polynomials involves dividing the first term of the numerator by the first term of the denominator, then multiplying and subtracting the result from the original polynomial. This process is repeated with the remaining terms until you obtain the final result.