Mixed-Operator Expressions

A mixed-operator expression contains at least one addition or subtraction sign and at least one multiplication or division sign. To evaluate mixed-operator expressions, follow a couple of simple steps:

  1. Evaluate all multiplication and division from left to right.

    Begin evaluating a mixed-operator expression by underlining all the multiplication or division in the problem.

  2. Evaluate addition and subtraction from left to right.

Sample question

  1. What’s –15 x 3 / –5 – (–3) x –4?

    –3. Start by underlining all the multiplication and division in the problem; then evaluate all multiplication and division from left to right:

    15 x 3 / –5(–3) x –4

    = –45 / –5 – (–3) x –4

    = 9 – (–3) x –4

    = 9 – 12

    Finish up by evaluating the addition and subtraction from left to right:

    = –3

Practice questions

  1. Evaluate 8 – 3 x 4 / 6 + 1.

  2. Find 10 x 5 – (–3) x 8 / –2.

  3. –19 – 7 x 3 + –20 / 4 – 8 = ?

  4. What’s 60 / –10 – (–2) + 11 x 8 / 2?

Following are the answers to the practice questions:

  1. 8 – 3 x 4 / 6 / 1 = 7.

    Start by underlining and evaluating all multiplication and division from left to right:

    8 – 3 x 4 / 6 / 1

    = 8 – 12 / 6 + 1

    = 8 – 2 + 1

    Now evaluate all addition and subtraction from left to right:

    = 6 + 1 = 7

  2. 10 x 5 – (–3) x 8 / –2 = 38.

    Start by underlining and evaluating all multiplication and division from left to right:

    10 x 5(–3) x 8 / –2

    = 50 – (–3) x 8 / –2

    = 50 – (–24) / –2

    = 50 –12

    Now evaluate the subtraction:

    = 38

  3. –19 – 7 x 3 + –20 / 4 – 8 = 53.

    Start by underlining and evaluating all multiplication and division from left to right:

    –19 – 7 x 3 + –20 / 4 – 8

    = –19 – 21 + –20 / 4 – 8

    = –19 – 21 + –5 – 8

    Then evaluate all addition and subtraction from left to right:

    = –40 + –5 – 8 = –45 – 8 = –53

  4. 60 / –10 – (–2) + 11 x 8 / 2 = 40.

    Start by underlining and evaluating all multiplication and division from left to right:

    60 / –10 – (–2) + 11 x 8 / 2

    = –6 – (–2) + 11 x 8 / 2

    = –6 – (–2) + 88 / 2

    = –6 – (–2) + 44

    Now evaluate all addition and subtraction from left to right:

    = –4 + 44 = 40

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