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Variables Tutorial 3c Variables A variable is any symbol that can be replaced with a number to solve a math problem. An open sentence has at least one variable. – – An algebraic equation is an open sentence. An open sentence can be proven neither true nor false until the variable is replaced with a number. Variables Letters are used to represent numbers, and these letters are referred to as variables. For example, in the equation 3 + x = 5, x is the letter that represents the numeral 2. However, in 3 + x = , the x is a variable that could represent many different numerals depending on the number placed in the blank. For example: 3 + x = 7 The variable x represents the numeral 4. 3 + x = 9 The variable x represents the numeral 6. 3 + x = 50 The variable x represents the numeral 47. Variables 3 + x = 7 The variable x represents the numeral 4. 3 + x = 9 The variable x represents the numeral 6. 3 + x = 50 The variable x represents the numeral 47. In each equation above, the variable is x , and the number 3 is called a constant because 3 represents the same value in each equation. The answer following the equal sign depends on the number assigned to the variable (x). Variables Algebraic equations have at least one variable. An algebraic equation can be proven neither true nor false until the variable is replaced with a number. Example: 6+2=x x must be 8 for this open sentence to be true 2 x 6 Examples 6+2=x x must be 8 for this equation to be true y = 12 - 6 y must be 6 Find the value of the variable that makes each equation true. 1. A = 6 + 2 A= 4 8 2. 23 - 6 = x x= 8 13 17 3. G = 12 + 7 G = 4. 21 - 7 = d 10 5 19 31 d = 14 17 28 Addition Properties Commutative Property of Addition : The order in which the numbers are added does not change their sum. Example : 15 + 3 Is the same as 3 + 15 15 + y Is the same as y + 15 Addition Properties Associative Property of Addition: The way that 3 or more numbers are grouped does not change their sum. Parentheses () may be used to show which numbers are added first. Example : (8 + 7) + 6 Is the same as 8 + (7 + 6) (8 + x) + 6 Is the same as (8 + 6) + x Addition Properties Additive Identity of Addition: The sum of any number and zero will always result in the original number. Example : 8+0=8 51 + 0 = 51 Choose the correct property. 1. 9 + 0 = 9 Associative Commutative Identity 2. 7 + 8 = 8 + 7 Associative Commutative Identity 3. (2 + 4) + 3 = 3 + (2 + 4) Associative Commutative Identity 4. W + v = v + W Associative Commutative Identity Addition & Subtraction In mathematics, subtraction is an operation that undoes addition. Subtraction is called the inverse(opposite) operation of addition. An addition equation can be rewritten as a subtraction equation: Example : 5 + 12 = 17 or 12 = 17 - 5 or 5 = 17 - 12 a + b = c or a = c - b or b=c-a 1. Which equation to the right is is equivalent to 5 + 15 = 20 ? 15 = 5 - 20 5 = 20 - 15 20 = 15 - 5 2. Which equation to the right is is equivalent to 8 + 9 = 17 ? 8 - 17 = 9 8 - 9 = 17 17 - 8 = 9 3. Which equation to the right is is equivalent to 24 = 17 + 7 ? 17 - 7 = 24 24 - 7 = 17 17 - 24 = 7 4. Which equation to the right is is equivalent to 55 = 26 + 29 ? 55 - 26 = 29 26 - 29 = 55 26 - 55 = 29 Review In mathematics, symbols are often used to represent ideas. For example, (=) means “is equal to”, the symbol(>) means “is greater than”, and (<) means “is less than”. The symbols , +, - and X or (•) are the operation symbols that you have used many times. Review cont . . . Letters are used to represent numbers, and these letters are referred to as variables. For example, in the equation 3 + x = 5, x is the letter that represents the numeral 2. However, in 3 + x = , the x is a variable that could represent many different numerals depending on the number placed in the blank. For example: 3 + x = 7 The variable x represents the numeral 4. 3 + x = 9 The variable x represents the numeral 6. 3 + x = 50 The variable x represents the numeral 47. Review cont . . . 3+x=7 3+x=9 3 + x = 50 The variable x represents the numeral 4. The variable x represents the numeral 6. The variable x represents the numeral 47. In each equation above, the variable is x , and the number 3 is called a constant because 3 represents the same value in each equation. The answer following the equal sign depends on the number assigned to the variable (x). Variables & Multiplication In multiplication problems, the symbols (X) or (•) are used to indicate multiplication. When variables are used, the signs for multiplication are left out. For example, “3” multiplied by the variable b will usually be written as 3b rather than 3 X b or 3•b. In the expression 3b, the number “3” is the constant (also known as the coefficient) and the letter b is the variable. Variables & Multiplication The letter a is a variable that could stand for any number. Lets work out a multiplication problem involving a variable. 5a = 30 a=6 Think to yourself: “5 multiplied by what number is equal to 30? 5 multiplied by 6 equals 30. Therefore the variable a equals 6. Variables & Division When variables are used in division problems, you will see the problem “8 divided by m as” 8 m or 8/m. Lets work out a Division problem involving a variable. 8m=4 m=2 Think to yourself: “8 divided by what number is equal to 4? 8 divided by 2 equals 4 - - since 4 times 2 equals 8. Therefore the variable m equals 2 Variable Expressions Now we will take a look at how variables are used in algebraic expressions Click Here to Continue Correct Return Sorry! 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