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Arithmetic · Arithmetic

Evaluate (18-20)^2/20 + (22-20)^2/20 + (20-20)^2/20

\frac{\left(20 - 20\right)^{2}}{20} + \frac{\left(18 - 20\right)^{2}}{20} + \frac{\left(22 - 20\right)^{2}}{20}

Step by step

  1. \left(-20 + 20\right)^{2} \cdot \frac{1}{20} + \left(-20 + 18\right)^{2} \cdot \frac{1}{20} + \left(-20 + 22\right)^{2} \cdot \frac{1}{20} = \left(-20 + 20\right)^{2} \cdot \frac{1}{20} + \left(-2\right)^{2} \cdot \frac{1}{20} + \left(-20 + 22\right)^{2} \cdot \frac{1}{20}

    Add: -20 + 18 = -2.

  2. \left(-20 + 20\right)^{2} \cdot \frac{1}{20} + \left(-2\right)^{2} \cdot \frac{1}{20} + \left(-20 + 22\right)^{2} \cdot \frac{1}{20} = \left(-20 + 20\right)^{2} \cdot \frac{1}{20} + 4 \cdot \frac{1}{20} + \left(-20 + 22\right)^{2} \cdot \frac{1}{20}

    Power: (-2)^2 = 4.

  3. \left(-20 + 20\right)^{2} \cdot \frac{1}{20} + 4 \cdot \frac{1}{20} + \left(-20 + 22\right)^{2} \cdot \frac{1}{20} = \left(-20 + 20\right)^{2} \cdot \frac{1}{20} + \frac{1}{5} + \left(-20 + 22\right)^{2} \cdot \frac{1}{20}

    Multiply: 4(1/20) = 1/5.

  4. \left(-20 + 20\right)^{2} \cdot \frac{1}{20} + \frac{1}{5} + \left(-20 + 22\right)^{2} \cdot \frac{1}{20} = \left(-20 + 20\right)^{2} \cdot \frac{1}{20} + \frac{1}{5} + 2^{2} \cdot \frac{1}{20}

    Add: -20 + 22 = 2.

  5. \left(-20 + 20\right)^{2} \cdot \frac{1}{20} + \frac{1}{5} + 2^{2} \cdot \frac{1}{20} = \left(-20 + 20\right)^{2} \cdot \frac{1}{20} + \frac{1}{5} + 4 \cdot \frac{1}{20}

    Power: 2^2 = 4.

  6. \left(-20 + 20\right)^{2} \cdot \frac{1}{20} + \frac{1}{5} + 4 \cdot \frac{1}{20} = \left(-20 + 20\right)^{2} \cdot \frac{1}{20} + \frac{1}{5} + \frac{1}{5}

    Multiply: 4(1/20) = 1/5.

  7. \left(-20 + 20\right)^{2} \cdot \frac{1}{20} + \frac{1}{5} + \frac{1}{5} = 0^{2} \cdot \frac{1}{20} + \frac{1}{5} + \frac{1}{5}

    Add: -20 + 20 = 0.

  8. 0^{2} \cdot \frac{1}{20} + \frac{1}{5} + \frac{1}{5} = 0 \cdot \frac{1}{20} + \frac{1}{5} + \frac{1}{5}

    Power: 0^2 = 0.

  9. 0 \cdot \frac{1}{20} + \frac{1}{5} + \frac{1}{5} = 0 + \frac{1}{5} + \frac{1}{5}

    Multiply: 0(1/20) = 0.

  10. 0 + \frac{1}{5} + \frac{1}{5} = \frac{0}{5} + 1 \cdot \frac{1}{5} + 1 \cdot \frac{1}{5}

    Rewrite every fraction over the common denominator 5.

  11. \frac{0}{5} + 1 \cdot \frac{1}{5} + 1 \cdot \frac{1}{5} = \frac{2}{5}

    Add: 0/5 + 1/5 + 1/5 = 2/5.

Reveal the answer
\frac{2}{5}