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7 Math Vocabulary # 11 (Number Properties and Factoring).notebook
7th Grade Math Vocabulary
Number Properties and Factoring
Ahrens
Distributive Property
Multiplying a sum by a number is the same as multiplying each addend in the sum by the same number and then adding the products.
also applies to subtraction
5
3
4
3
(3 + 2)
3x5=3(3+2)
Number Properties and Factoring Glossary
2
a(b­c)=ab­ac
a(b+c)=ab+ac
2(3+4)=
(2x3)+(2x4)
Distributive Property
Factoring
Prime Number
Using the Distributive Property in reverse, by dividing the addends by a common factor, to write rewrite a sum of two terms as a product
A positive integer that is greater than 1 and has exactly two factors, one and itself.
9 + 6
14 ­ 8
3
2
6 + 8
GCF
GCF
2
9 +6 = 3 ( 3 + 2 )
14 ­ 8=2(7­4)
GCF
6 + 8 =2 ( 3 +4 )
Prime #s to 30
2, 3, 5, 7, 11, 13, 17, 19, 23, 29
Factoring
A whole number that can A whole number that multiplies with divide into another another number to number with no remainder.
make a third number.
12
13
1 x 12
1 x 13
3 x 4
Any number with factors other than one and itself is composite.
6 factors
Composite Number
One is not a prime number, because it has only one factor.
Factor
A number that has more than two factors.
3 x 5 = 15
Two is the only even prime number.
1
Prime Number
Composite Number
2 x 6
2
Only 2 factors.
15 3 =5
3 x 5 = 15
3 is a factor of 15
3 and 5 are factors of 15
R
5 1
3 16
3 is not a factor of 16
Factor
1
7 Math Vocabulary # 11 (Number Properties and Factoring).notebook
Ahrens
Proper Factor
Prime Factorization
All of the factors of a number other than one and itself.
A number written as the product of all its prime factors.
7: 1, 7
6: 1, 2, 3, 6
Proper Factors: 2 and 3
9: 1, 3, 9
The number 7 does not have any proper factors.
18 = 2 x 3 x 3
or
2
18 = 2 x 3
Proper Factor: 3
Proper Factor
18 = 1 x 2 x 3 x 3
There is only one for any number.
Only prime numbers are included in prime factorizations.
Prime Factorization
Greatest Common Factor (GCF)
Relatively Prime
The largest number that will divide two or more numbers without a remainder.
Two numbers who only have 1 as a common factor.
12: 1, 2, 3, 4, 6, 12
16: 1, 2, 4, 8, 16 Common Factors are 1, 2, 4
GCF is 4
Using Prime Factorization
12 = 2 x 2 x 3
16 = 2 x 2 x 2 x 2
GCF = 2 x 2 1 and 2 are common factors, but not the greatest common factor.
8: 1, 2, 4, 8
15: 1, 3, 5
Only Common Factor is 1
GCF is 4
Greatest Common Factor
All prime numbers are relatively prime to every other number.
9: 1, 3, 9
15: 1, 3, 5, 15
Common Factors:
Relatively Prime
Least Common Multiple (LCM)
Multiple
The product of two whole numbers is a multiple of each of those numbers.
The smallest number that two or more numbers share as a multiple.
9: 9, 18, 27, 36, 45
3 x 5 = 15
15 is a multiple of 3. 4 x 5 = 20
2 x 6 = 12
5 and 4 are factors of 20, not multiples.
Factors Product / Multiple
Multiple
1 and 3
Using Prime Factorization
15: 15, 30, 45
LCM is 45
2
9 = 3 15 = 3 x 5
2: 2, 4, 6, 8
4: 4, 8
4 is the LCM, not 8
LCM = 3 x 3 x 5 LCM is 45
Least Common Multiple
2
7 Math Vocabulary # 11 (Number Properties and Factoring).notebook
Ahrens
Simplify
When the GCF of the numerator and denominator of a fraction is one.
4 12
4 1
=
4 3
To remove brackets, unnecessary terms and numbers by performing all possible operations.
2(3+2) = 2(5)
3y+4+2y
=5y+4
Simplify
3