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Properties: Homework Guide When you write your properties I want you to explain how you knew the answer. Here are examples of how I would describe some properties and at the end there is an explanation about the term reciprocal. 1) x + 2 = 2 + x You write: This is the commutative property of addition because we are changing the order that we add the terms x and 2 in. We are allowed to do this because the result will be the same either way. 2) 3y=y×3 You write: This is the commutative property of multiplication because we are changing the order that we multiply the factors 3 and y in. We are allowed to do this because the result will be the same either way. 3) 3 + (d + 8) = (3 + d) + 8 You write: This is the associative property of addition because the order of the terms we are adding stays the same but the grouping symbols move. We are allowed to do this because the result will be the same either way. 4) (u×5)×r=u(5×r) You write: This is the associative property of multiplication because the order of the factors stays the same but the grouping symbols move. We are allowed to do this because the result will be the same either way. 5) 7(3 + 6) = 21 + 42 You write: This is the distributive property because seven is being distributed (multiplied) over 3 + 6 resulting in 21 + 42. 6) w + (5 – 5) = w You write: w + 0 = w Because 5 – 5 = 0, we know that this is the identity property of addition. If we add zero to any number the result is the same number. c 7) 8( )=8 c You write: 8(1) = 8 c Because ( ) equals 1, we know that this is the identity property of c multiplication. Any number times one equals the same number. 8) 8 + (-8) = 0 You write: This is the inverse property of addition because we are adding opposite numbers and the result is zero. 1 =1 6 You write: This is the inverse property of multiplication because we are multiplying 1 a number(6) and its reciprocal( ) and the result is one. 6 9) 6 × Reciprocal: The reciprocal of a whole number is always one over that number. For 1 example the reciprocalof 12 is . 12 The reciprocal of a fraction has the numerator and the denominator m 4 switched. For example the reciprocal of is . 4 m These are both examples of reciprocals because when you multiply them they both result in one. 1 12 1 12 1 12 1 12 × = 12 1 12 1 12 12 m 4 m4 m4 m 4 11 1 and × = 4 m 4m m4 m 4 Multiplying reciprocals with a result of one is the inverse property of multiplication. Try to write sentences about these properties! 1) x + (-x) = 0 2) c + (2– 2) = c 3) (e × 3) × 2=e(3 × 2) 1 4) 7 × = 1 7 5) 3 + 2 = 2 + 3 6) 1 + (2 + 3) = (1 + 2) + 3 7) 4 × 5 = 5 × 4 x 8) 9( )=9 x 9) 4(3 + w) = 12 + 4w