Section 1.5 Multiplication of Whole Numbers and Area 41 Multiplication Property of 0 The product of any number and 0 is 0. Examples: 5 0 0 5 0 0 0 12 0 The product can easily be understood by writing the product as repeated addition. 0 0 0 0 0 0 Add 0 five times. Multiplication Property of 1 The product of any number and 1 is that number. Examples: 1 4 4 3 1 3 The last property of multiplication involves both addition and multiplication. 214 32. First consider the expression By performing the operation within parentheses first, we have 214 32 2172 14 We get the same result by multiplying 2 times each addend within the parentheses: 214 32 12 42 12 32 8 6 14 This result illustrates the distributive property of multiplication over addition (sometimes we simply say distributive property for short). Distributive Property of Multiplication over Addition The product of a number and a sum can be found by multiplying the number by each addend. Example: 5(7 3) (5 7) (5 3) Applying the Distributive Property of Multiplication Over Addition Example 3 Apply the distributive property and simplify. a. b. Solution: a. 314 82 713 02 314 82 13 42 13 82 12 24 36 b. 713 02 17 32 17 02 21 0 21 Answers 6. 7. 15 02 15 82; 40 12 62 12 42; 20 ⎫⎪⎪⎪⎬⎪⎪⎪⎭ Skill Practice Apply the distributive property and simplify. 6. 216 42 7. 510 82 Two other important properties of multiplication involve factors of 0 and 1.
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