2. Variables Tutorial 3c

3. variable 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

4. 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.

5. 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).

6. Example: x 2 6 6 + 2 = x x must be 8 for this open sentence to be true 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. Variables

7. Examples 6 + 2 = xx must be 8 for this equation to be true y = 12 - 6y must be 6

8. 1. A = 6 + 2 A = 8104 2. 23 - 6 = x x = 17813 3. G = 12 + 7 G = 19531 4. 21 - 7 = d d = 141728 Find the value of the variable that makes each equation true.

9. 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

10. 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

11. 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

12. 1. 9 + 0 = 9 CommutativeAssociativeIdentity 2. 7 + 8 = 8 + 7 CommutativeAssociativeIdentity 3. (2 + 4) + 3 = 3 + (2 + 4) CommutativeAssociativeIdentity 4. W + v = v + W CommutativeAssociativeIdentity Choose the correct property.

13. Addition & Subtraction In mathematics, subtraction is an operation that undoes addition. Subtraction is called the inverse(opposite) operation of addition. Example : 5 + 12 = 17 or 12 = 17 - 5 or 5 = 17 - 12 a + b = c or a = c - b or b = c - a An addition equation can be rewritten as a subtraction equation:

14. 1. Which equation to the right is is equivalent to 5 + 15 = 20 ? 5 = 20 - 15 20 = 15 - 5 15 = 5 - 20

15. 2. Which equation to the right is is equivalent to 8 + 9 = 17 ? 17 - 8 = 9 8 - 9 = 17 8 - 17 = 9

16. 3. Which equation to the right is is equivalent to 24 = 17 + 7 ? 24 - 7 = 17 17 - 24 = 7 17 - 7 = 24

17. 4. Which equation to the right is is equivalent to 55 = 26 + 29 ? 55 - 26 = 29 26 - 55 = 29 26 - 29 = 55

18. 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.

19. 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.

20. Review cont... 3 + x = 7 The variable x represents the numeral 4. 3 + x = 9 The variable x represents the numeral 6. 3 + x = 50The 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).

21. 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 3b.  In the expression 3b, the number “3” is the constant (also known as the coefficient) and the letter b is the variable.

22. Variables & Multiplication The letter a is a variable that could stand for any number. Lets work out a multiplication problem involving a variable.  5a = 30Think to yourself: “5 multiplied by what number is equal to 30? 5 multiplied by 6 equals 30. Therefore the variable a equals 6. a = 6

23. 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.  8  m = 4Think 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 m = 2

24. Variable Expressions Now we will take a look at how variables are used in algebraic expressions Click Here to Continue

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