order of operations: The steps for simplifying expressions are: 1. compute inside grouping symbols, including parentheses ( ), brackets [ ], and braces { }, and above or below division bar —— 2. compute with exponents 3. multiply and divide in from left to right 4. add and subtract in order from left to right vertical number line: Part II Instructional Connections outside the Focus Cluster – factor: A factor is a term that divides a given quantity evenly (with a remainder of 0). As a verb, factor means to resolve (divide) a given quantity in 2 the form of its factors. For example, 6 is factored in the form of 2 x 3. The terms 2 and 3 are factors of the given quantity 6. 4x3 5x is – x 2 x 2 2. factored in the form of (4x 5). The terms and (4x 5) are the factors of 4x3 5x – – – expand linear expression: The form a quantity takes when written as a continued product, using the distributive property of multiplication over 2. addition. For example, the quantity x 2 (4x 5) in expanded form is 4x3 5x – – linear expression: A linear expression can be comprised of a variable, a number, or a combination of variables, numbers, and operation symbols , y such that the exponents for all variables in the expression are limited to 0 and 1. For example: (or ), 16, 47 + 19, 2x 3. – properties of operations: The properties of operations apply to the rational number system, the real number system, and the complex number system, when a, b and c stand for arbitrary numbers in a given number system. The properties include: associative property of addition (a + b) + c = a + (b + c) commutative property of addition a + b = b + a additive identity property of 0 a + 0 = 0 + a = a existence of additive inverses a + (–a) = (–a) + a = 0 associative property of multiplication (a x b) x c = a x (b x c) commutative property of multiplication a x b = b x a
order of operations: The steps for simplifying expressions are: 1. compute inside grouping symbols, including parentheses ( ), brackets [ ], and braces { }, and above or below division bar —— 2. compute with exponents 3. multiply and divide in from left to right 4. add and subtract in order from left to right vertical number line: Part II – Instructional Connections outside the Focus Cluster factor: A factor is a term that divides a given quantity evenly (with a remainder of 0). As a verb, factor means to resolve (divide) a given quantity in the form of its factors. For example, 6 is factored in the form of 2 x 3. The terms 2 and 3 are factors of the given quantity 6. 4x3 – 5x 2 is factored in the form of x 2 (4x – 5). The terms x 2 and (4x – 5) are the factors of 4x3 – 5x 2. expand linear expression: The form a quantity takes when written as a continued product, using the distributive property of multiplication over addition. For example, the quantity x 2 (4x – 5) in expanded form is 4x3 – 5x 2. linear expression: A linear expression can be comprised of a variable, a number, or a combination of variables, numbers, and operation symbols such that the exponents for all variables in the expression are limited to 0 and 1. For example: , y (or ), 16, 47 + 19, 2x – 3. properties of operations: The properties of operations apply to the rational number system, the real number system, and the complex number system, when a, b and c stand for arbitrary numbers in a given number system. The properties include: associative property of addition (a + b) + c = a + (b + c) commutative property of addition a + b = b + a additive identity property of 0 a + 0 = 0 + a = a existence of additive inverses a + (–a) = (–a) + a = 0 associative property of multiplication (a x b) x c = a x (b x c) commutative property of multiplication a x b = b x a
Unit_7_NS_A_1_3_Operations_with_Rational_Numbers_Final.docx