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𝐴∗𝐵 =𝐵∗𝐴 Math Properties Commutative, Associative, Distributive, Identity, and Zero Properties What are properties? Math Properties are rules in math. Properties are always true for every number. **Once you go beyond the set of Real numbers the properties may no longer hold. Commute • To commute means to travel from one place to another. • For example, you commute to school in the morning. Commutative Property • Just like you commute from home to school, a number may commute from one spot to another. • A + B = B + A (The numbers change places.) • This is called the commutative property of addition. • Ex) 2 + 3 = 3 + 2 • Both 2 + 3 and 3 + 2 equal 5. The commutative property may be used with addition as seen previously and also with multiplication. • A*B=B*A • Ex) 3 * 5 = 5 * 3 • Both 3 * 5 and 5 * 3 equal 15. • This is called the commutative property of multiplication. Associate • An associate is a friend or someone you work with. • For example, the head cheerleader is an associate of the school mascot. Now imagine the football team played a late game and the cheerleader and mascot forgot to study for the math test. Suddenly the cheerleader associates with someone else. Associative Property The associative property is when a number associates with a different number. A + (B + C) A + B+ C (A + B) + C Associative Property • (A + B) + C = A + (B + C) is called the associative property of addition. • Ex) (2 + 3) + 4 = 2 + (3 + 4) • The order in which you add does not change your answer. • A * (B * C) = (A * B) * C is called the associative property of multiplication. Identity • Your identity is who you are. • Changing your clothes or getting a new haircut does not change your identity. • Your identity remains the same. Identity Property of Addition • A number also has an identity • The identity of a number is the value of the number • The additive identity is the number that when added to another number does not change the identity of the original number • 3 + __ 0 = 3 (What goes in the blank?) Zero • The additive identity is zero. • We can add zero to any number and the answer is the original number. Identity Property of Multiplication • We also have a multiplicative identity 1 = 3 (What goes in this blank?) • 3 * __ • We can multiply any number by one and the answer will be the original number. Identity Properties Identity Property of Addition A+0=A Identity Property of Multiplication A*1=A Zero Property • The zero property sounds just like what it is, a property about zero. • A*0=0 • The zero property tells us that any number multiplied by zero equals zero. Summary Property Name Rule Commutative Property of Addition A+B=B+A Commutative Property of Multiplication A*B=B*A Associative Property of Addition A + (B + C) = (A + B) + C Associative Property of Multiplication A * (B * C) = (A * B) * C Identity Property of Addition A+0=A Identity Property of Multiplication A*1=A Zero Property A*0=0 Distribute • Distribute means to deliver or pass out • If we distribute food to three boxes, we put food in each of the three boxes Distributive Property • • • • A(B + C) = A*B + A*C The A is the food and the boxes are B and C. We pass out A to each of B and C. In this case that means that we multiply A by both B and C separately and then add the resulting products. Ex) 4(X + 3) =4X + 12 4 X 4X 3 12 Now you try these examples. 1) 5(X + 3) = 5X + 15 2) 7(X + 4) = 7X + 28 3) 2(Z -3) = 2Z - 6 Summary Property Name Rule Commutative Property of Addition A+B=B+A Commutative Property of Multiplication A*B=B*A Associative Property of Addition A + (B + C) = (A + B) + C Associative Property of Multiplication A * (B * C) = (A * B) * C Identity Property of Addition A+0=A Identity Property of Multiplication A*1=A Zero Property A*0=0 Distributive Property A(B + C) = A*B + A*C Solve these in your notebook 1 ) Which equation shows the Commutative Property of Multiplication ? A. 6 x 8 - 4 x 8 = (6 - 4) x 2 B. 5 x 1 = 5 C. 2 x 3 = 2 + 2 + 2 D. 7 x 3 = 3 x 7 2 ) Which property is used in the following ? 8 x (7 + 5) = 8 x 7 + 8 x 5 A. Commutative Property B. None of the above C. Distributive Property D. Associative Property 3 ) Which is an example of Associative Property of Addition ? A. 6 + (-6) = 0 C. ( 4 + 9) + 5 = 4 + (9 + 5) B. 2 + 0 = 2 D. 3 + 4 = 4 + 3 4) Which of the following does not show the Commutative Property ? A. x + y = y + x B. 4 + y = y + 4 C. yx = xy D. xy - 3 = xy 5 ) Which equation shows the Identity Property of Multiplication ? A. a(b + c) = ab + ac B. a x 1 C. (a + b) + 5 = a + (5 + b) D. a + a + a = 3 x a 6 ) Which Property of Multiplication is shown ? (5 + 9) x 7 = 5 x 7 + 9 x 7 A. Commutative Property B. Associative Property C. Distributive Property D. Identity Property 7 ) Which of the following does not show the Commutative Property of Addition ? A. a + b = b + a B. 3x + 4y = 4y + 3x C. b = ba D. 4 + x = x + 4 8 ) Which Property of Addition does 7 + 0 = 7 illustrate ? A. Zero Property C. Distributive Property B. Commutative Property D. Identity Property