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Applying the Order of Operations

The order of operations works similarly how they work in mathematics. The order of operation is as follows:

  • parenthesis (( ))
  • mutliplication, division, and modulus working from left to right (*, /, %)
  • addition and subtraction working from left to right (+ and -)

Your Turn

Example 1

  • Predict the result of the following expression.
  • Check to see if you are correct by running it in the Java Playground.

Explanation:

  • The first operation is multiplication 5 * 7, which is 35. Leaving us with 3 + 35 % 4.
  • The second operation is modulus division 35 % 4, which is 3. Leaving us with 3 + 3.
  • The last operation is addition 3 + 3, which is 6.
  • So, 3 + 5 * 7 % 4 evaluates to 6.

Example 2

  • Predict the result of the following expression.
  • Explain how the addition of parenthesis influences the result.
  • Check to see if you are correct by running it in the Java Playground.

Explanation:

  • The parenthesis override the order of operations causing the first operation to be modulus division 7 % 4, which is 3. Leaving us with 3 + 5 * 3.
  • The next operation is multiplication 5 * 3, which is 15. Leavning us with 3 + 15.
  • The last operation is addition 3 + 15, which is 18.
  • So, 3 + 5 * (7 % 4) evaluates to 18.

Example 3

  • Predict the result of the following expression.
  • Explain how the addition of parenthesis influences the result.
  • Check to see if you are correct by running it in the Java Playground.

Explanation:

  • The parenthesis override the order of operations causing the first operation to be additiona, 3 + 5, which is 8. Leaving us with 8 * 7 % 4.
  • The next operation is multiplication 8 * 7, which is 56. Leaving us with 56 % 4.
  • The last operation is modulus 56 % 4. Since 56 is divisible by 4, there is no remainder and the result is 0.
  • So, (3 + 5) * 7 % 4 evaluates to 0.

Example 4

  • Predict the result of the following expression.
  • Explain how the addition of parenthesis influences the result.
  • Check to see if you are correct by running it in the Java Playground.

Explanation:

  • The parenthesis override the order of operations. Working left to right, the first operation that is evaluated is 3 + 5, which is 8. Leaving us with 8 * (7 % 4).
  • The next operation in parenthesis is then evaluated 7 % 4, which is 3. Leaving us with 8 * 3.
  • The last operation is multiplication 8 * 3, which is 24.
  • So, (3 + 5) * (7 % 4) evaluates to 24.

Resources

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Learn: Expressions and the Assignment Operator