Arithmetic Laws PDF

Arithmetic Laws Lesson 1 SLIDESMANIA.C  You are selling cupcakes to help cover the cost of your new bicycle. Two of your friends show up at your cupcake sale to support you. Aiden buys 1 chocolate...

Arithmetic Laws Lesson 1 SLIDESMANIA.C  You are selling cupcakes to help cover the cost of your new bicycle. Two of your friends show up at your cupcake sale to support you. Aiden buys 1 chocolate cupcake and 2 vanilla cupcakes. Gabrielle buys 4 strawberry cupcakes. Write an equation representing the number of cupcakes bought. 1+2+4 SLIDESMANIA.C =7  What if Aiden dislikes chocolate cupcakes and decides to buy only 1 vanilla cupcake? What if Gabrielle as well chooses to change her order and buys the 2 chocolate cupcakes and 4 strawberry cupcakes? 1+2+4 SLIDESMANIA.C =7 What do you notice about  There are three main number properties/laws: * Commutative Property * Associative Property * Distributive Property. SLIDESMANIA.C  Commutative Property The commutative property states that the numbers on which we perform the operation can be moved or swapped from their position without making any difference to the answer. SLIDESMANIA.C  Commutative Property Addition - When two or more numbers are added, the sum is the same regardless of the order in which the numbers are added. 3 + 5 = 8 or 5 + 3 = 8 Multiplication - When two or more numbers are multiplied together, the product is the same regardless of the order in which the numbers are multiplied. 3 x 5 = 15 or 5 x 3 = 15 SLIDESMANIA.C  You Try! Apply the commutative law in the following mental calculations then solve: 1. 25 + 28 + 1525 = + 15 + 28 = 68 2. 16 + 8 + 4 =16 + 4 + 8 = 28 77 += 3. 123 + 66 + 77 123 + 66 = 266 SLIDESMANIA.C  You Try! Apply the commutative law in the following mental calculations then solve: 1. 4 × 9 × 5 = 4 × 5 × 9 = 180 2. 5 × 15 × 2 =5 × 2 × 15 = 150 3. 2 × 65 × 50 2=× 50 × 65 = 6500 SLIDESMANIA.C  1. Copy and correctly complete the following: a) (3 ×5) × 7 = 3 × (5 × _____) b) 5 × (____ × 8) = (____× 7) × 8 c) 9+ (3 + 5) = (____ + 3) + 5 d) (___ +1)+ 8 = 2+ (____+ 8) SLIDESMANIA.C  Associative Property The associative property gets its name from the word “Associate”, and it refers to the grouping of numbers. This property states that when three or more numbers are added (or multiplied), the sum (or product) is the same regardless of the grouping. SLIDESMANIA.C  Associative Property Addition - When three or more numbers are added, the sum is the same regardless of the way in which the numbers are grouped. (3 + 4) + 5 = 3 + (4 + 5). Multiplication - When three or more numbers are multiplied, the product is the same regardless of the way in which the numbers are grouped. 6 x (4 x 3) = 72 or (6 x 4) x 3 = 72 SLIDESMANIA.C  You Try! Apply the associative law in the following mental calculations then solve: 1. 9 + 17 + 39 =+ (17 + 3) = (9 + 17) + 3 = 29 2. 14 + 6 + (14 9= + 6) + 9 = 14 + (6 + 9) = 29 3. 31 + 9 + 6(31=+ 9) + 6 = 31 + (9 + 6) = 46 SLIDESMANIA.C  You Try! Apply the associative law in the following mental calculations then solve: 1. 2 × 3 × 4(2=× 3) × 4 = 2 × (3 × 4) = 24 2. 5 × 3 × 6( 5=× 3) × 6 = 5 × (3 × 6) = 90 3. 29 × 25 × (294= × 25) × 4 = 29 × (25 × 4) = 2900 SLIDESMANIA.C  Distributive Property Distributive property helps us to simplify the multiplication of a number by a sum or difference. As the name suggests, it distributes the expression. For example: a x (b + c) Using the distributive property, we can expand the expression as: SLIDESMANIA.C  Distributive Property Distributive property of Multiplication Addition SLIDESMANIA.C  Distributive Property Distributive property of Multiplication: Subtraction SLIDESMANIA.C  You Try! Apply the distributive law in the following mental calculations then solve: 1. 4 × (5 + 9) =4 × 5 + 4 × 9 = 56 2. 3 × (7 – 3) =3 × 7 – 3 × 3 = 12 3. 4 × (15 – 8) 4=× 15 – 4 × 8 = 28 SLIDESMANIA.C