Answers and Solutions


  1.  \(16\) 
    \(-25\)
    \(4\frac{1}{3}\)
    \(-3\frac{3}{8}\)
     \(0\) 
    1. True.
    2. False.  Only some integers are whole numbers.  For example, \(4\) is an integer and a whole number, but \(-5\) is only an integer.
    3. False. Since negative numbers include rational numbers, it is possible to have a negative number that is not an integer.  For example, \(-\dfrac{3}{4}\) is a negative number but it is not an integer.
  3. \(5^\circ\)C describes a temperature  \(5^\circ\)C above \(0^\circ\)C.
  4. A Venn diagram showing the Whole number inside the Integers and both of those are inside the Rational numbers.Each new number system contains the previous type within it. Integers are the whole numbers with negatives now included.  Rational numbers are all the integers in addition to their divisions (i.e., fractions).  The diagram shows number systems positioned inside to illustrate that each new system of numbers builds upon the previous one.
  5. Answers may vary. Possible solutions include
    • measurements in cooking and baking (e.g., \(\frac{1}{4}\) cup or \(\frac{1}{2}\) L), and
    • measuring distances (e.g., walking \(\frac{3}{4}\) km to your friend's house).
    • We can start by considering all of the pizzas together as one order of pizza.  If \(7\) friends share the order of pizza, each friend gets \(\dfrac{1}{7}\) of the whole order.
    • We could also consider each pizza to be the whole.  In this case, if \(7\) friends share \(5\) pizzas, then each friend gets \(\dfrac{5}{7}\) of a pizza.
    • Finally, there are  \(40\) slices of pizza total since
      \(5\) pizzas \(\times~ 8\) slices each \(=~40\) total slices
      In this case, if \(7\) friends share \(40\) slices of pizza, then each friend gets \(\dfrac{40}{7}\) slices of pizza.
    • \(+2500\), or \(2500\), represents \(2500\) m above sea level.
    • \(-394\) represents \(394\) m below sea level.