Tham khảo tài liệu 'awa practise 8', ngoại ngữ, anh ngữ phổ thông phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | --------------------------------------- ARITHMETIC ------------------------------------------- Multiplication Any number times one is itself. One is the multiplicative identity element. a X 1 a 5 X 1 5 Inverse Property This property is often used when you want a number to cancel out in an equation. Addition The additive inverse of any number is its opposite. a a 0 3 3 0 Multiplication The multiplicative inverse of any number is its reciprocal. a X 11 1 6 X 6 1 Distributive Property This property is used when two different operations appear multiplication and addition or multiplication and subtraction. It basically states that the number being multiplied must be multiplied or distributed to each term within the parentheses. a b c ab ac or a b - c ab - ac 5 a 2 5 X a 5 X 2 which simplifies to 5a 10 2 3x - 4 2 X 3x- 2 X 4 which simplifies to 6x - 8 Order of Operations The operations in a multistep expression must be completed in a specific order. This particular order can be remembered as PEMDAS. In any expression evaluate in this order P Parentheses grouping symbols first E then Exponents MD Multiplication Division in order from right to left AS Addition Subtraction in order from left to right Keep in mind that division may be done before multiplication and subtraction may be done before addition depending on which operation is first when working from left to right. 323 --------------------------------- ARITHMETIC Examples Evaluate the following using the order of operations 1. 2 X 3 4 - 2 2. 32- 16 - 5 - 1 3. 2 42- 9 3 -1 Answers 1. 2 X 3 4 - 2 6 4 - 2 Multiply first. 10 - 2 Add and subtract in order from left to right. 8 2. 32- 16 5 - 1 32- 16 4 Evaluate parentheses first. 9 - 16 4 Evaluate exponents. -7 4 Subtract and then add in order from left to right. -3 3. 2 42- 9 3 - 1 2 16 - 9 3 - 1 Begin with the innermost grouping symbols and follow PEMDAS. Here exponents are first within the parentheses. 2 7 3 - 1 Continue with the order of operations working from the .
