Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Properties of Real Numbers Objective: Identify and use properties of real numbers. The Commutative Property • You can add and multiply real numbers in any order. • Examples: 2+7=7+2 3●9=9●3 • Algebraically: a+b=b+a ab = ba The Commutative Property • Commute: to move to and from Think of commuting to and from school. Just like you moving from one place to the other, numbers can too! State whether each situation below is commutative or not commutative. 1) Waking up in the morning and going to school. not commutative 2) Brushing your teeth and combing your hair. commutative 3) Putting on your socks and putting on your shoes. not commutative 4) Eating cereal and drinking orange juice. commutative The Associative Property • You can regroup real numbers when you add and multiply. • Examples: (6 + 8) + 2 = 6 + (8 + 2) (7 ● 4) ● 5 = 7 ● (4 ● 5) • Algebraically: (a + b) + c = a + (b + c) (ab)c = a(bc) The Associative Property • Associate: to keep company, as a friend Think of associating with your friends: you hang out with them and stick together. Numbers in parentheses are grouped, or friends! Commutative vs. Associative Identify each property shown below. 1) 7 + 4 = 4 + 7 Comm. Prop. Of Add. 2) 6 (2 8) (6 2) 8 Assoc. Prop. Of Mult. 3) 5 9 9 5 Comm. Prop. Of Mult. 4) (4 + 2) + 3 = (2 + 4) + 3 Comm. Prop. Of Add. Identity Property of Addition • The sum of 0 and any number is the number • Example with numbers: 4 + 0 = 4 • Algebraic example: a+0=a Identity Property of Multiplication The product of 1 and any number is the number Example with numbers: 8x1=8 Algebraic example: ax1=a The Distributive Property • Multiply the outside value with the quantity in the parentheses. • Examples: 3(4 + 8) = 3(4) + 3(8) 3(12)= 12 + 24 36 = 36 • Algebraically: a(b + c) = ab + ac a(b – c ) = ab – ac The Distributive Property • Distribute: to spread out, to share Think of mail. The postal worker must distribute all letters to the houses. One person, many houses: One number to all numbers in the parentheses! The Distributive Property • Use the Distribute Property to rewrite and/or solve. 1) 9(52) 2) 12(98) 3) 7(34) Simplify using the distributive property. 1) 5(x 3) 4) 4(3 y) 5 x 5 3 43 4 y 12 4y 5x 15 2) 6(y 7) 6 y 6 7 6y 42 5) 10(x 7) 3) 3(m 8) 3 m 3 8 6) 4(k 2) 4 k 4 2 3m 24 10 x 10 7 10x 70 4k 8 Simplify using the distributive property. 1) 4(x 7) 4) 7(8 x) 4 x 4 7 78 7 x 4x 28 2) y(y 3) y y y3 y 3y 2 3) x(2x 9) x 2x x 9 2x 9x 2 56 7x 5) x(a b c) xa xb xc ax bx cx 6) 4(3 m k) 43 4 m 4 k 12 4m 4k Which Property is Represented? • • • • • • 1 + (6 + 7) = (1 + 6) + 7 1 x 10 = 10 3x5=5x3 6+0=6 4 x (4 x 2) = (4 x 4) x 2 x+y=y+x