Which set of numbers includes only integers?

Question

Left-brace negative 3, 0, StartFraction 5 Over 6 EndFraction, 5, 45 Right-brace
Left-brace negative 9, negative 3, 0, 5.7, 7.8 Right-brace
Left-brace negative 3, negative 2 and StartFraction 4 Over 5 EndFraction, 5, 7, 53 Right-brace
Left-brace negative 10, negative 7, 0, 98, 145 Right-brace

Answer 1

To determine which set of numbers includes only integers, we need to check each set for any non-integer values.

1. Set 1: { -3, 0, \(\frac{5}{6}\), 5, 45 }

   • Contains: -3 (integer), 0 (integer), \(\frac{5}{6}\) (not an integer), 5 (integer), 45 (integer)
   • Conclusion: Contains non-integer (\(\frac{5}{6}\)).

2. Set 2: { -9, -3, 0, 5.7, 7.8 }

   • Contains: -9 (integer), -3 (integer), 0 (integer), 5.7 (not an integer), 7.8 (not an integer)
   • Conclusion: Contains non-integers (5.7 and 7.8).

3. Set 3: { -3, -2 \(\frac{4}{5}\), 5, 7, 53 }

   • Contains: -3 (integer), -2 (integer), \(\frac{4}{5}\) (not an integer), 5 (integer), 7 (integer), 53 (integer)
   • Conclusion: Contains non-integer (\(\frac{4}{5}\)).

4. Set 4: { -10, -7, 0, 98, 145 }

   • All values are: -10 (integer), -7 (integer), 0 (integer), 98 (integer), 145 (integer)
   • Conclusion: All are integers.

The only set that includes only integers is:

{ -10, -7, 0, 98, 145 }