a mathematical phrase that contains numbers and operations Example: 5 x 4 - 9

a mathematical sentence that uses an equal sign to show that two quantities are the same as one another Example: y = 2x + 4

distributive property

a rule that states for any numbers a, b, and c, a(b + c) = ab + ac. Example: 4(2 + 15) = 4 x 2 + 4 x 15 = 8 + 60 = 68

a number that is a factor of two or more numbers Example: factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 factors of 24: 1, 2, 3, 4, 6, 8, 12, 24 common factors of 60 and 24: 1, 2, 3, 4, 6, and 12

includes two elements: the base and the exponent Example: 63

the factor that is multiplied repeatedly in the power Example: 2 = 2 x 2 x 2

the number of times the base is used as a factor Example: 2 = 2 x 2 x 2 exponent = 3

greatest common factor (GCF)

the largest factor two or more numbers have in common Example: factors of 16: 1, 2, 4, 8, 16 factors of 12: 1, 2, 3, 4, 6, 12 common factors: 1, 2, 4 greatest common factor: 4

commutative property of multiplication

rule that states that for any numbers a and b, the product a x b is equal to the product b x a Example: 29 x 3 = 87 = 3 x 29 = 87

least common multiple (LCM)

the smallest multiple (other than zero) that two or more numbers have in common Example: multiples of 60: 60, 120, 180, 240, 300, 360, 420, 480 . . multiples of 24: 24, 48, 72, 96, 120, 144, 168, 192, 216, 240 . . . LCM of 60 and 24: 120

multiplicative inverse of the number - flip a/b to b/a. The product of the fraction and its multiplicative inverse is 1. Example: The reciprocal of 3/7 is 7/3. 3/7 x 7/3 = 21/21 = 1

associative property of multiplication

states that when you are adding or multiplying numbers, the way they are grouped (i.e., which numbers are calculated first inside parentheses) does not change the final result Example: (a+b)+c = a + (b+c)

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Factors and Multiple

Module 1 - Topic 1

Question	Answer
numeric expression	a mathematical phrase that contains numbers and operations Example: 5 x 4 - 9
equation	a mathematical sentence that uses an equal sign to show that two quantities are the same as one another Example: y = 2x + 4
distributive property	a rule that states for any numbers a, b, and c, a(b + c) = ab + ac. Example: 4(2 + 15) = 4 x 2 + 4 x 15 = 8 + 60 = 68
common factor	a number that is a factor of two or more numbers Example: factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 factors of 24: 1, 2, 3, 4, 6, 8, 12, 24 common factors of 60 and 24: 1, 2, 3, 4, 6, and 12
power	includes two elements: the base and the exponent Example: 63
base	the factor that is multiplied repeatedly in the power Example: 2 = 2 x 2 x 2
exponent	the number of times the base is used as a factor Example: 2 = 2 x 2 x 2 exponent = 3
greatest common factor (GCF)	the largest factor two or more numbers have in common Example: factors of 16: 1, 2, 4, 8, 16 factors of 12: 1, 2, 3, 4, 6, 12 common factors: 1, 2, 4 greatest common factor: 4
commutative property of multiplication	rule that states that for any numbers a and b, the product a x b is equal to the product b x a Example: 29 x 3 = 87 = 3 x 29 = 87
least common multiple (LCM)	the smallest multiple (other than zero) that two or more numbers have in common Example: multiples of 60: 60, 120, 180, 240, 300, 360, 420, 480 . . multiples of 24: 24, 48, 72, 96, 120, 144, 168, 192, 216, 240 . . . LCM of 60 and 24: 120
reciprocal	multiplicative inverse of the number - flip a/b to b/a. The product of the fraction and its multiplicative inverse is 1. Example: The reciprocal of 3/7 is 7/3. 3/7 x 7/3 = 21/21 = 1
associative property of multiplication	states that when you are adding or multiplying numbers, the way they are grouped (i.e., which numbers are calculated first inside parentheses) does not change the final result Example: (a+b)+c = a + (b+c)

Created by: astalnaker

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