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Arithmetic · Arithmetic

Evaluate (45-50)^2/50 + (55-50)^2/50

\frac{\left(45 - 50\right)^{2}}{50} + \frac{\left(55 - 50\right)^{2}}{50}

Step by step

  1. \left(-50 + 45\right)^{2} \cdot \frac{1}{50} + \left(-50 + 55\right)^{2} \cdot \frac{1}{50} = \left(-5\right)^{2} \cdot \frac{1}{50} + \left(-50 + 55\right)^{2} \cdot \frac{1}{50}

    Add: -50 + 45 = -5.

  2. \left(-5\right)^{2} \cdot \frac{1}{50} + \left(-50 + 55\right)^{2} \cdot \frac{1}{50} = 25 \cdot \frac{1}{50} + \left(-50 + 55\right)^{2} \cdot \frac{1}{50}

    Power: (-5)^2 = 25.

  3. 25 \cdot \frac{1}{50} + \left(-50 + 55\right)^{2} \cdot \frac{1}{50} = \frac{1}{2} + \left(-50 + 55\right)^{2} \cdot \frac{1}{50}

    Multiply: 25(1/50) = 1/2.

  4. \frac{1}{2} + \left(-50 + 55\right)^{2} \cdot \frac{1}{50} = \frac{1}{2} + 5^{2} \cdot \frac{1}{50}

    Add: -50 + 55 = 5.

  5. \frac{1}{2} + 5^{2} \cdot \frac{1}{50} = \frac{1}{2} + 25 \cdot \frac{1}{50}

    Power: 5^2 = 25.

  6. \frac{1}{2} + 25 \cdot \frac{1}{50} = \frac{1}{2} + \frac{1}{2}

    Multiply: 25(1/50) = 1/2.

  7. \frac{1}{2} + \frac{1}{2} = 1

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

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