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Exercise Set 1.1: Numbers

State whether each of the fol lowing numbers is prime,
composite, or neither. If composite, then list all the
factors of the number .

Answer the following.

3. In (a)-(e), use long division to change the
following fractions to decimals .

Notice the pattern above and use it as a
shortcut in (f)-(m) to write the following
fractions as decimals without performing
long division.

4. Use the patterns from the problem above to
change each of the following decimals to either a
proper fraction or a mixed number.

State whether each of the following numbers is
rational
or irrational. If rational, then write the
number as a ratio of two integers . (If the number is
already written as a ratio of two integers, simply
rewrite the number.)


Circle all of the words that can be used to describe
each of the numbers below.

7. −9

Even Odd Positive Negative
Prime Composite Natural Whole
Integer Rational Irrational Real
Undefined      

8.

Even Odd Positive Negative
Prime Composite Natural Whole
Integer Rational Irrational Real
Undefined      

9.

Even Odd Positive Negative
Prime Composite Natural Whole
Integer Rational Irrational Real
Undefined      

10. -4/7

Even Odd Positive Negative
Prime Composite Natural Whole
Integer Rational Irrational Real
Undefined      

Answer the following.

11. Which elements of the set
  belong
to each category listed below?
(a) Even
(b) Odd
(c) Positive
(d) Negative
(e) Prime
(f) Composite
(g) Natural
(h) Whole
(i) Integer
(j) Real
(k) Rational
(l) Irrational
(m) Undefined

Exercise Set 1.1: Numbers

12. Which elements of the set
belong to each category listed below?
(a) Even
(b) Odd
(c) Positive
(d) Negative
(e) Prim
(f) Composite
(g) Natural
(h) Whole
(i) Integer
(j) Real
(k) Rational
(l) Irrational
(m) Undefined

Fill in each of the following tables. Use “Y” for yes if
the row name applies to the number or “N” for no if it
does not.

13.

  1 -55
Undefined          
Natural          
Whole          
Integer          
Rational          
Irrational          
Prime          
Composite          
Real          

14.

  2.36
Undefined          
Natural          
Whole          
Integer          
Rational          
Irrational          
Prime          
Composite          
Real          

Answer the following. If no such number exists, state
“Does not exist.”

15. Find a number that is both prime and even.
16. Find a rational number that is a composite
number.
17. Find a rational number that is not a whole
number.
18. Find a prime number that is negative.
19. Find a real number that is not a rational number.
20. Find a whole number that is not a natural
number.
21. Find a negative integer that is not a rational
number.
22. Find an integer that is not a whole number.
23. Find a prime number that is an irrational number.
24. Find a number that is both irrational and odd.

Answer True or False. If False, justify your answer.j
25. All natural numbers are integers.
26. No negative numbers are odd.
27. No irrational numbers are even.
28. Every even number is a composite number.
29. All whole numbers are natural numbers.
30. Zero is neither even nor odd.
31. All whole numbers are integers.
32. All integers are rational numbers.
33. All nonterminating decimals are irrational
numbers.
34. Every terminating decimal is a rational number.

Answer the following.
35. List the prime numbers less than 10.
36. List the prime numbers between 20 and 30.
37. List the composite numbers between 7 and 19.
38. List the composite numbers between 31 and 41.
39. List the even numbers between and .
40. List the odd numbers between and .

Fill in the appropriate symbol from the set { <, >, = } .

Answer the following.

57. Find the additive inverse of the following
numbers. If undefined, write “undefined.”

58. Find the multiplicative inverse of the following
numbers. If undefined, write “undefined.”

59. Find the multiplicative inverse of the following
numbers. If undefined, write “undefined.”

60. Find the additive inverse of the following
numbers. If undefined, write “undefined.”

61. Place the correct number in each of the following
blanks:
(a) The sum of a number and its additive
inverse is _____. (Fill in the correct
number.)
(b) The product of a number and its
multiplicative inverse is _____. (Fill in the
correct number.)

62. Another name for the multiplicative inverse is
the ____________________.

Order the numbers in each set from least to greatest
and plot them on a number line .
(Hint: Use the approximations and
.)

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