CONFIDENTIAL1 Good Afternoon! Today we will be learning about Variables & equations Let’s warm up : Write an algebraic expression for the following: 3) The sum of 9 and a number. 4) 3 more than twice of a number. 1) 6a + 7 when a = 5. Evaluate the given expressions: 2) ( b + 9 ) x 2 when b = 3.

CONFIDENTIAL2 Let’s first review what we learnt in the previous sessions before proceeding further. We learnt about the following terms: Variable: It is a letter that represents a number.  Since a variable represents a number, it is treated just like a number when doing various mathematical operations. x is a very common variable that is used in algebra, but you can use any letter (a, b, c, d,....) to be a variable. Algebraic expression: It is a mathematical statement which contains at least one number and at least one variable along with at least one arithmetic operation. The following are examples of expressions: 2 × y + 5 z + 3 × (8 - z)

CONFIDENTIAL3 Evaluate the expression 3a for a = 4 STEP 1: Write the expression. 3a. STEP 2: Replace a with 4. 3 x 4. STEP 3: Simplify the expression. 3 x 4. = 12. So, the value of the expression is 12. Review

CONFIDENTIAL4 Translating an English Phrase Into an Algebraic Expression Sometimes, you will be having to write out your own algebraic expression based on the wording of a problem. In that situation, you should:  read the problem carefully,  pick out key words and phrases and determine their equivalent mathematical meaning,  replace any unknowns with a variable, and  put it all together in an algebraic expression. Review

CONFIDENTIAL5 Review When converting word problems to equations, certain "key" words tell you what kind of operations to use. WordOperation sumaddition differencesubtraction productmultiplication timesmultiplication less thansubtraction totaladdition more thanaddition

CONFIDENTIAL6 Review Write an algebraic expression for the sum of n and 5. The word sum means add. So the algebraic expression would be ( n + 5 ). This is an algebraic expression because it contains at least one number (5), at least one variable (n), and at least one arithmetic operation (subtraction). Write an algebraic expression for the difference of n and 5.

CONFIDENTIAL7 Let’s start with Variables & equations We know that variable is a letter that represents a number. Equation: It is a mathematical statement that has an expression on the left side of the equals sign (=) with the same value as the expression on the right side. The examples of an equation is: 5 + x = 12 2t - 29 = 7

CONFIDENTIAL8  One of the terms in an equation may not be known and needs to be determined.  The unknown term may be represented by a letter such as “x”. (e.g. 2 + x = 4).  The equation is solved by finding the value of the unknown “x” that makes the two sides of the equation have the same value.  Use the Inverse Operations to find the value of the variable in the addition equations. Solution A value, such that, when you replace the variable with it, it makes the equation true. (the left side comes out equal to the right side)

CONFIDENTIAL9 The equality of two expressions gives an equation. If two expressions are not equal, an inequality is created. The inequality symbols used at this grade level are ≠ (is not equal to), > (is greater than), and < (is less than). It may also be stated that an equation is ‘two expressions set equal to each other’. Solution A value, such that, when you replace the variable with it, it makes the equation true. (the left side comes out equal to the right side)

CONFIDENTIAL10 Solve: n + 5 = 9 WAY 1: WAY 2: There are different ways of to solve a problem. Use an addition fact. n + 5 = 9 n = 4 n + 5 = 9 n = 9 – 5 n = 4 Use the Inverse Operations. Subtract 5 from each side. Think: = 9 So ‘n’ must be 4.

CONFIDENTIAL11 Solve: 3m = 18 WAY 1: WAY 2: Use a related multiplication fact. 3m = 18 m = 6 3m = 18 3 x m ÷ 3 = 18 ÷ 3 m = 6 Use the Inverse Operations. Divide each side by 3. Think: 3 x 6 = 18 So ‘m’ must be 6.

CONFIDENTIAL12 We need to use the Inverse Operations to find the value of the variable in the equations. If the problem has Addition, use Subtraction to solve. a + 4 = 7 a = a = 3 If the problem has subtraction, use Addition to solve. b - 4 = 5 b = b = 9 If the problem has Multiplication, use Division to solve. 5c = 15 5c ÷ 5 = 15 ÷ 5 c = 3 If the problem has Division, use Multiplication to solve. d ÷ 4 = 4 d ÷ 4 x 4 = 4 x4 d = 16 Remember to Use Inverse Operations

CONFIDENTIAL13 The sum of twice a number and 13 is 75. Find the number. Translating a Sentence into an Equation Here the word is means equals. The word and means plus. Therefore, you can rewrite the problem like the following: The sum of twice a number plus 13 equals 75. Using numbers and a variable, you can write an equation that means the same thing as the original problem.

CONFIDENTIAL14 STEP1: Let the number be denoted by “n”. So, the equation will be as follows: 2n + 13 = 75 STEP2: Solve the equation. 2n + 13 = 75 2n = n = 622 n = 31 Divide both sides by 2. Subtract 13 from both sides. Hence, the number is 31.

CONFIDENTIAL15 BREAK

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CONFIDENTIAL17 Assignments Evaluate: 1) a + 10 = 27 2) b - 11 = 5 3) c × 7 = 63 4) 15 = 3 d

CONFIDENTIAL18 5) Three times a number is 15. 6) 20 is ten more than the number. 7) A number divided by 3 is 24. 8) A number subtracted from 10 is 6. Write the equations and then solve it.

CONFIDENTIAL19 9) Oliver made 6 sweaters. This is half as many as Sam made. How many sweaters did Sam make. Write and solve an equation.

CONFIDENTIAL20 10) In Mrs. Roman’s class, there are 35 students. There are 19 boys in the class. How many girls are in the class?

CONFIDENTIAL21 Very Good! Let's Review We know that variable is a letter that represents a number. Equation: It is a mathematical statement that has an expression on the left side of the equals sign (=) with the same value as the expression on the right side. The examples of an equation is: 5 + x = 12 2t - 29 = 7

CONFIDENTIAL22 The equality of two expressions gives an equation. If two expressions are not equal, an inequality is created. The inequality symbols used at this grade level are ≠ (is not equal to), > (is greater than), and < (is less than). It may also be stated that an equation is ‘two expressions set equal to each other’. Solution A value, such that, when you replace the variable with it, it makes the equation true. (the left side comes out equal to the right side) Review

CONFIDENTIAL23 Solve: n + 5 = 9 WAY 1: WAY 2: There are different ways of to solve a problem. Use an addition fact. n + 5 = 9 n = 4 n + 5 = 9 n = 9 – 5 n = 4 Use the Inverse Operations. Subtract 5 from each side. Think: = 9 So ‘n’ must be 4. Review

CONFIDENTIAL24 Review We need to use the Inverse Operations to find the value of the variable in the equations. If the problem has Addition, use Subtraction to solve. a + 4 = 7 a = a = 3 If the problem has subtraction, use Addition to solve. b - 4 = 5 b = b = 9 If the problem has Multiplication, use Division to solve. 5c = 15 5c ÷ 5 = 15 ÷ 5 c = 3 If the problem has Division, use Multiplication to solve. d ÷ 4 = 4 d ÷ 4 x 4 = 4 x4 d = 16 Remember to Use Inverse Operations

CONFIDENTIAL25 Review The sum of twice a number and 13 is 75. Find the number. STEP1: Let the number be denoted by “n”. So, the equation will be as follows: 2n + 13 = 75 STEP2: Solve the equation. 2n + 13 = 75 2n = n = 622 n = 31 Divide both sides by 2. Subtract 13 from both sides. Hence, the number is 31.

CONFIDENTIAL26 You have done a nice job. See you in the next session.