6th Grade
Numbers &
Operations
2
*Factor
17
Factor Tree
3
Common Factor
18
Exponent
4
*Greatest Common Factor
19
Simplify
5
*Multiple
20
Integer
6
Common Multiples
7
*Least Common Multiples
8
Product
9
Quotient
10
Sum
11
Difference
12
Order of Operations
13
Estimate
14
*Prime Number
15
*Composite Number
16
*Prime Factorization
1
Factor
A number that is multiplied by another
number to find a product
Examples:
4 x 7 = 28
4
x7
28
The factors are 4 and 7.
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2
Common Factor
• A number that is a factor of two or more
numbers
Example:
factors of 6: 1, 2, 3, 6
• factors of 12: 1, 2, 3, 4, 6, 12
• The common factors of 6 and 12 are
1, 2, 3, and 6.
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3
greatest common factor
(GCF)
• The greatest factor that two or more numbers
have in common
Example:
18: 1, 2, 3, 6, 9, 18
30: 1, 2, 3, 5, 6, 10, 15, 30
6 is the GCF of 18 and 30.
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4
Multiple
• The product of a given whole number and
another whole number
Example:
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5
Common Multiple
• A number that is a multiple of two or more
numbers
Example:
multiples of 4:
4, 8, 12, 16, 24, 32, 36, 40, 44, 48 . . .
multiples of 6:
6, 12, 18, 24, 30, 36, 42, 48 . . .
• A common multiple of 4 and 6 is 24, 48, 36
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6
least common multiple
(LCM)
• The smallest number, other than zero, that is
a common multiple of two or more numbers
Example:
multiples of 6: 6, 12, 18, 24, 30, 36
multiples of 9: 9, 18, 27, 36, 45, 54
The LCM of 6 and 9 is 18.
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7
Product
• The answer to a multiplication problem
Example:
6 x 2 = 12
• The product is 12.
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8
Quotient
• The number, not
including the
remainder, that
results from dividing
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• Example:
quotient
9
sum
The answer to an
addition problem
Example:
12 + 7 = 19
The sum is 19.
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10
Difference
• The answer in a subtraction problem
Example:
8–5=3
• 3 is the difference.
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11
Order of Operations
• The rules for performing operations in expressions with
more than one operation;
1. first perform the operations in parentheses,
2. clear the exponents,
3. perform all multiplication and division, left to right
4. and then perform all addition and subtraction, left to right
Example:
10 ÷ 2 + 8 x 23 - 4 Clear exponent.
10 ÷ 2 + 8 x 8 - 4 Multiply and divide.
5 + 64 - 4 Add and subtract.
65
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10 ÷ (2 + 8) x 23 - 4
10 ÷ 10 x 23 - 4
10 ÷ 10 x 8 - 4
8-4
4
Add inside parentheses.
Clear exponent.
Multiply and divide.
Subtract.
12
Estimate
• To find a number that is close to an exact
amount
Example:
32x9 30x10= 300 estimate
32 x 9 is about 300.
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13
Prime Number
• A whole number greater than 1 whose
only factors are 1 and itself
Example:
Prime
Number Factors
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Not Prime
Number Factors
3
1, 3
6
1, 2, 3, 6
5
1, 5
9
1, 3, 9
2
1, 2
4
1, 2, 4
14
Composite Number
• A whole number that has more than two
factors
Examples:
Composite Numbers
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Not Composite Numbers
Number
Factors
Number
Factors
4
1, 2, 4
1
1
6
1, 2, 3, 6
2
1, 2
8
1, 2, 4, 8
3
1, 3
9
1, 3, 9
5
1, 5
15
Prime Factorization
• A number written as the product of all its
prime factors
Example:
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16
Factor Tree
• A diagram that shows the prime factors of
a number
Example:
The prime factors of 24 are 2 and 3.
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17
Exponent
• The number that tells how many times a
base is to be used as a factor
Example:
The exponent is 3, indicating that 8 is used as a factor 3
times.
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18
Simplify
• Simplifying (or reducing) fractions means to make the
fraction as simple as possible.
Example
Why say four-eighths (4/8) when you really mean half (1/2) ?
4/
2/
1/
•
==>
==>
8
4
2
(Four-Eighths)
(Two-Quarters)
(One-Half)
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19
Integers
• The set of whole numbers and their
opposites
Example:
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20