Question

definitions
one of the reasons that good math students often don’t get the credit they deserve on the psat is that they’ve forgotten one or more of these definitions—or they read too fast and skip over these “little” words. be sure you know them cold and watch out for them!
match the words with their definitions, and then come up with some examples. answers can be found in part iv.

1. integers
2. positive numbers
3. negative numbers
4. even numbers
5. odd numbers
6. factors
7. multiples
8. prime numbers
9. distinct
10. digit

a. numbers that a certain number can be divided by, leaving no remainder
examples:

b. integers that cannot be divided evenly by 2
examples:

c. numbers that have no fractional or decimal parts
examples:

d. numbers that are greater than zero
examples:

e. having a different value
examples:

f. integers that can be divided by 2 evenly (with no remainder)
examples:

g. numbers that are less than zero
examples:

h. numbers that have exactly two distinct factors: themselves and 1
examples:

i. numbers that can be divided by a certain number with no remainder
examples:

j. a numerical symbol from 0 through 9 that fills a place in a number
examples:

Explanation:

1. Integers are whole - numbers without fractional or decimal parts. Examples: - 3, 0, 5.
2. Positive numbers are greater than zero. Examples: 1, 2.5 (but here we focus on whole positive numbers like 1, 2, 3).
3. Negative numbers are less than zero. Examples: - 1, - 2.
4. Even numbers are integers divisible evenly by 2. Examples: 2, 4, 6.
5. Odd numbers are integers not divisible evenly by 2. Examples: 1, 3, 5.
6. Factors are numbers that a certain number can be divided by, leaving no remainder. Examples: Factors of 6 are 1, 2, 3, 6.
7. Multiples are numbers that can be divided by a certain number with no remainder. Examples: Multiples of 3 are 3, 6, 9.
8. Prime numbers have exactly two distinct factors: themselves and 1. Examples: 2, 3, 5.
9. Distinct means having a different value. Examples: In the set {1, 2}, 1 and 2 are distinct.
10. A digit is a numerical symbol from 0 through 9 that fills a place in a number. Examples: In 123, 1, 2, and 3 are digits.

Answer:

1. c. Examples: - 3, 0, 5
2. d. Examples: 1, 2, 3
3. g. Examples: - 1, - 2
4. f. Examples: 2, 4, 6
5. b. Examples: 1, 3, 5
6. a. Examples: For 6, 1, 2, 3, 6
7. i. Examples: For 3, 3, 6, 9
8. h. Examples: 2, 3, 5
9. e. Examples: In {1, 2}, 1 and 2
10. j. Examples: In 123, 1, 2, 3