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The Expressions with parentheses exercise appears under the (none). This exercise used to be on one of the missions under The World of Math, but it was removed due to reordering, renaming, or other changes. This exercise helps understand the use and importance of parentheses.

Types of Problems

There are four types of problems in this exercise:

  1. What is being done: This problem has a worked out arithmetic problem involving parentheses. The student is asked to select which of the situations is being modeled by the expression.
    Ewp1

    What is being done

  2. When parentheses matter: This problem has several arithmetic expressions written in a column on the left. The student is asked to select correctly whether the parentheses are important to the expression or if removing them would leave the value unchanged.
    Ewp2

    When parentheses matter

  3. Write numerical expression: This problem describes a situation. The student is asked to write a numerical expression that models the situation being described.
    Ewp3

    Write numerical expression

  4. Evaluate expression: This problem has a numerical expression which the student is asked to correctly evaluate.
    Ewp4

    Evaluate expression

Strategies

This exercise is easy to get accuracy as most of the problems are really just based on order of operations. The speed badges are also easy because the tolerances are set generously because of one somewhat lengthy problem.

  1. On When parentheses matter the left column is that the expression is changed (they do matter) and the right is that the value is unchanged (they don't matter).
  2. On When parentheses matter the answer is generally that when parentheses are around multiplication they don't matter and when they are around addition they do.
  3. On When parentheses matter the notable exception to two above is that in a\times b+(c+d) the parentheses don't matter.
  4. On Write numerical expression the problem evaluates whatever you write, so you can just write the actual numerical answer to the problem if you wish.

Real-life Applications

  1. Work problems often ask us to calculate how long it will take different people working at different speeds to finish a task. The algebraic models of such situations often involve rational equations derived from the work formula, W = rt. The amount of work done (W) is the product of the rate of work (r) and the time spent working (t). The work formula has 3 versions:
    W = rt
    t = \frac{W}{r}
    r = \frac{W}{t}

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