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Evaluating expressions

Algebraic expressions

Japanese school year: Junior high 1

What you learn

You will learn how to substitute specific numbers for variables to evaluate algebraic expressions. This skill is essential for calculating results from formulas in geometry and physics. Having a solid understanding of the four basic operations with positive and negative numbers is recommended before beginning.

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Key points

Before substituting numerical values into variables, simplify the algebraic expression as much as possible. This reduces steps and prevents calculation errors.

When substituting negative numbers or fractions into variables, enclose them in parentheses. This is essential to prevent mistakes with signs, especially in powers and subtractions.

This inequality shows that parentheses change the result. (−a)2(-a)^2 squares both the minus sign and aa to become positive, whereas −a2-a^2 squares only aa, keeping the minus sign.

(−a)2≠−a2(a≠0)(-a)^2 \neq -a^2 \quad (a \neq 0)

This formula explains that adjacent variables abab imply multiplication with the sign ×\times omitted. Restore the multiplication a×ba \times b when substituting numbers.

ab=a×bab = a \times b

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