The Elements of Number Sets
How to Apply the Table of Joy to Ratio Questions
Parentheses and the Associative Property

How to Evaluate Expressions with Multiplication and Division

Unless you’ve been using your free time to practice your Persian, Arabic, or Hebrew reading skills, you’re probably used to reading from left to right. Luckily, that’s the direction of choice for multiplication and division problems, too. When an expression has only multiplication and division, in any combination, you should have no trouble evaluating it: Just start with the first two numbers and continue from left to right.

Sample questions

  1. What is 15 / 5 x 8 / 6?

    4. Start at the left with the first two numbers, 15 / 5 = 3:

    15 / 5 x 8 / 6 = 3 x 8 / 6

    Continue with the next two numbers, 3 x 8 = 24:

    3 x 8 / 6 = 24 / 6

    Finish up with the last two numbers:

    24 / 6 = 4

  2. Evaluate –10 x 2 x –3 / –4.

    –15. The same procedure applies when you have negative numbers (just make sure you use the correct rule for multiplying or dividing by negative numbers). Start at the left with the first two numbers, –10 x 2 = –20:

    –10 x 2 x –3 / –4 = –20 x –3 / –4

    Continue with the next two numbers, –20 x –3 = 60:

    –20 x –3 / –4 = 60 / –4

    Finish up with the last two numbers:

    60 / –4 = –15

Practice questions

  1. Find 18 / 6 x 10 / 6.

  2. Evaluate 20 / 4 x 8 / 5 / –2.

  3. 12 / –3 x –9 / 6 x –7 = ?

  4. Solve –90 / 9 x –8 / –10 / 4 x 15.

Following are the answers to the practice questions:

  1. 18 / 6 x 10 / 6 = 5.

    Divide and multiply from left to right:

    18 / 6 x 10 / 6

    = 3 x 10 / 6

    = 30 / 6 = 5

  2. 20 / 4 x 8 / 5 / –2 = 4.

    20 / 4 x 8 / 5 / –2

    = 5 x 8 / 5 / –2

    = 40 / 5 / –2

    = 8 / –2 = –4

  3. 12 / –3 x –9 / 6 x –7 = 42.

    12 / –3 x –9 / 6 x –7

    = –4 x –9 / 6 x –7

    = 36 / 6 x –7

    = 6 x –7 = –42

  4. –90 / 9 x –8 / –10 / 4 x –15 = 30.

    –90 / 9 x –8 / –10 / 4 x –15

    = –10 x –8 / –10 / 4 x –15

    = 80 / –10 / 4 x –15

    = –8 / 4 x –15

    = –2 x –15

    = 30

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