Simplify and understand (22q²)/9 — step-by-step algebra explanation

Step-by-step explanation of the algebraic expression (22q²)/9: how to simplify it, why it's already in lowest terms, alternative forms (mixed number, decimal), and worked examples.

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We are given the expression (22q²)/9. Let's examine and simplify it step by step.

  1. Rewrite the expression as a coefficient times q².

    (22q²)/9 = (22/9)·q². This shows the coefficient of q² is 22/9.

  2. Check if the fraction 22/9 can be reduced.

    Factor the numerator and denominator: 22 = 2·11, 9 = 3·3. They share no common prime factors, so gcd(22,9) = 1. Therefore 22/9 is already in lowest terms.

  3. Alternative equivalent forms.
    • Fractional coefficient: (22/9)·q² (the simplest exact form).
    • Mixed number: 22/9 = 2 4/9, so the expression = (2 4/9)·q².
    • Decimal (approx.): 22/9 ≈ 2.444... so ≈ 2.444…·q².
    • Factored constant form: you can write 22q²/9 = (2·11/9)·q² = (2/9)·(11q²), but this doesn't simplify further.
  4. Worked numerical examples.
    • If q = 3: (22·3²)/9 = (22·9)/9 = 22.
    • If q = 1: (22·1²)/9 = 22/9.
    • If q = 1/3: q² = 1/9, so (22·(1/9))/9 = 22/81.
    • If q = 0: the expression = 0.
  5. Conclusion.

    The expression is already simplified: (22q²)/9 = (22/9)·q². There is no further algebraic simplification possible unless you substitute a specific value for q.

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