quotient: the number resulting from dividing one number by another. inverse operation: two operations that undo each other. Addition and subtraction are inverse operations. Multiplication and division are inverse operations. Examples: 4 + 5 = 9; 9 5 = 4 6 x 5 = 30; 30 ÷ 5 = 6 – fact families: a collection of related addition and subtraction facts, or multiplication and division facts, made from the same numbers. For 7, 8, and 15, the addition/subtraction fact family consists of 7 + 8 = 15, 8 + 7 = 15, 15 8 = 7, and 15 7 = 8. For 5, 6, and 30, the – – multiplication/division fact family consists of 5 x 6 = 30, 6 x 5 = 30, 30 ÷ 5 = 6, and 30 ÷ 6 = 5. properties of operations: Here a, b and c stand for arbitrary numbers in a given number system. The properties of operations apply to the rational number system, the real number system, and the complex number system. Associative property of addition (a + b) + c = a + (b + c) Commutative property of addition (a + b) + c = a + (b + c) Additive identity property of 0 a + 0 = 0 + a = a Existence of additive inverses For every there exists so that + (–a) = (–a) + = 0 a a a –a Associative property of multiplication (a = a b) c (b c) Commutative property of multiplication a = b b a Multiplicative identity property of 1 a = 1 = a 1 a Existence of multiplicative inverses For a there exists 1/a so that a = 1/a = 1. 1/a a ≠ Distributive property of multiplication over addition a + c) = a + a (b b c decomposing: breaking a number into two or more parts to make it easier with which to work.
quotient: the number resulting from dividing one number by another. inverse operation: two operations that undo each other. Addition and subtraction are inverse operations. Multiplication and division are inverse operations. Examples: 4 + 5 = 9; 9 – 5 = 4 6 x 5 = 30; 30 ÷ 5 = 6 fact families: a collection of related addition and subtraction facts, or multiplication and division facts, made from the same numbers. For 7, 8, and 15, the addition/subtraction fact family consists of 7 + 8 = 15, 8 + 7 = 15, 15 – 8 = 7, and 15 – 7 = 8. For 5, 6, and 30, the multiplication/division fact family consists of 5 x 6 = 30, 6 x 5 = 30, 30 ÷ 5 = 6, and 30 ÷ 6 = 5. properties of operations: Here a, b and c stand for arbitrary numbers in a given number system. The properties of operations apply to the rational number system, the real number system, and the complex number system. Associative property of addition (a + b) + c = a + (b + c) Commutative property of addition (a + b) + c = a + (b + c) Additive identity property of 0 a + 0 = 0 + a = a Existence of additive inverses For every a there exists –a so that a + (–a) = (–a) + a = 0 Associative property of multiplication (a b) c = a (b c) Commutative property of multiplication a b = b a Multiplicative identity property of 1 a 1 = 1 a = a Existence of multiplicative inverses For a ≠ there exists 1/a so that a 1/a = 1/a a = 1. Distributive property of multiplication over addition a (b + c) = a b + a c decomposing: breaking a number into two or more parts to make it easier with which to work.
Unit_3_OA_C_7_Multiply_Divide_Within_100.docx