Exercises

1. Evaluate the following.
   1. \(3 \times 7 - 6 \div \dfrac{1}{3}\)
   2. \(\dfrac{1}{3} \times (2+4)+7\)
   3. \(16 \times \left(\dfrac{3}{4}+\dfrac{1}{8} \right)\div 0.4\)
   4. \(39 \div (0.9+0.4)-2\times(4+1)\)
2. Evaluate using the distributive property.
   1. \(5\times (8 - 3)\)
   2. \((6+4) \div 2\)
   3. \(4 \times (20+7)\)
3. Using the distributive property, Brian's solution to a problem is given below.\[\begin{align*} 998 \div 0.2 &= 998 \div \dfrac{2}{10} \\ &= (1000 - 2) \div \dfrac{2}{10} \\ &= 1000 \times \dfrac{2}{10} - 2 \times \dfrac{2}{10} \\ &= 200 - \dfrac{4}{10} \\ &= 200 - 0.4 \\ &= 199.6 \\ \end{align*}\] Is Brian's solution correct?  Show how you know.
4. Remove all unnecessary brackets.
   1. \((3\times 5)+\left(\dfrac{1}{2} + \dfrac{5}{2}\right)\times 2 = 21\)
   2. \(\Big((3+3\times3) \div 4\Big) - (27-24)=0\)
5. 1. Add brackets in different ways to get as many different answers as you can.
      1. \(15-7+3-1\)
      2. \(7 + 8 \times 3 - 4\)
   2. How many different answers did you get for each expression?
6. Turn the written instructions into mathematical expressions; then evaluate.
   1. Subtract \(\dfrac{3}{4}\) from \(\dfrac{7}{8}\).
      Then multiply the result by \(3\).
      Then add \(4\) to this result.
   2. Divide \(7\) by \(0.56\).
      Then add \(5\) to the result.
      Then multiply this result by \(16\).
   3. Divide \(7\) by \(0.25\) and then add \((-16)\).
      Subtract \((-5)\) from \((-3)\).
      Multiply the two results.
7. Use each of the digits \(1, ~2, ~3,~ 4\) (in any order) and each of the operations \(+,~ -,~ \times\) (in any order) exactly once to form an expression that meets each condition. You can use brackets if needed.
   1. An expression that equals \(-3\).
   2. An expression to make the largest number you can obtain.
   3. An expression to make the smallest number you can obtain.