CONFIDENTIAL1 Good Afternoon! Today we will be learning about Review of Expressions, Variables, equations & Functions Let’s warm up : 1) Simplify: 4 x 5 + (18 ÷ 2) 2) Is (15 ÷ 5) + 9 equal to ? Evaluate the given expressions: 3) 5 + 2n when n = 3. 4) n + 7 = 16 5) Find the value of y = 7x + 3, when x = 4. 1) 29 2) < 3) 11 4) n = 9 5) 31

CONFIDENTIAL2 Order of Operations Evaluate x x 2 = 7 x 2 = 14 or x 2 = = 11 Two people may interpreted the problem differently this problem like Here, the correct answer is 11. Let’s see how.

CONFIDENTIAL3 ARITHMETIC EXPRESSION: It is an expression consisting of numbers, grouping symbols and arithmetic operation symbols. To evaluate these expressions, a specific Order of Expressions is followed.  When a numerical expression involves two or more operations, there is a specific order in which these operations must be performed. 4 – (3 + 2) is an arithmetic expression. Parenthesis, Exponents, (Multiplication/Division) then (Add/Subtract) OR that is, PEMDAS for short. Please Excuse (My Dear) (Aunt Sally). This phrase will help you understand the order.

CONFIDENTIAL4 To solve an expression you need to follow the rules for the Order of Operation. Evaluate: 3 + (3 x 4) - 1 Rule 1: First, do operations inside the parenthesis ( ). 3 + (3 x 4) - 1 Rule 2: Then do multiplication and division in order from left to right Rule 3: Finally, do addition and subtraction in order from left to right There is no more multiplicatio n or division. Evaluate: 2 x

CONFIDENTIAL5 Is 8 x (3 + 6) equal to 7 x (17 - 6) ? The value 8 x (3 + 6) = 72 is less than 7 x (17 - 6) = 77. Hence, not equal. First of all, we evaluate 8 x (3 + 6) = 8 x 9 = 72 Then, we evaluate 7 x (17 - 6) = 7 x 11 = 77

CONFIDENTIAL6 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) Number stories & expressions

CONFIDENTIAL7 Evaluating an Expression You can evaluate an expression by replacing the variable with the given number and performing the indicated operation Value of an Expression When you are asked to find the value of an expression, that means you are looking for the result that you get when you evaluate the expression. Evaluate simply means that we want to find an answer.

CONFIDENTIAL8 Evaluate the expression 12 – n for n = 4 Given the expression 12 – n. Here we will replace the occurrence of n with the number 4 Hence, 12 – n becomes = 12 – 4 = 8 n is replaced by 4. Evaluate the expression 3 x m for m = 5 15

CONFIDENTIAL9 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.

CONFIDENTIAL10 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.

CONFIDENTIAL11 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

CONFIDENTIAL12 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 3. n -3

CONFIDENTIAL13 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 Variables & equations

CONFIDENTIAL14  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)

CONFIDENTIAL15 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)

CONFIDENTIAL16 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

CONFIDENTIAL17 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

CONFIDENTIAL18 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.

CONFIDENTIAL19 BREAK

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CONFIDENTIAL21 FUNCTION : It is a relationship in which one quantity depends upon another quantity. In other words, Functions are rules that describe the relationship between two variables. For example, y = x + 4.  The two variables in a function have names that explain how they relate to one another.  One variable, usually x, is known as the input or independent variable. This is the variable upon which the operation or operations are performed.  The other variable, usually y, is called the output or dependent variable. The value of this variable is dependent upon the value of the independent variable. Functions

CONFIDENTIAL22  Functions are also displayed or described in the form of function tables or graphs.  A Function Table is a table of ordered pairs that follow the rule for that function. Function tables can be made up of an infinite number of ordered pairs. A Function Table for the equation y = 2x + 6 is shown below. ORDERED PAIR : Two numbers that give the location of a point on a graph or map are called the Ordered Pair. x1234 y independent variable dependent variable Rule  y = 2x + 6

CONFIDENTIAL23 Solve the problem with the help of a function table. Then write the equation. One number is 2 more than 3 times another number. You can write the equation with the help of the given statement. We are given that One number is 2 more than 3 times another number. Let the smaller number be ‘x’ and, greater number be ‘y’. Then the equation will be: y = 3x + 2 We will now solve the problem with the help of Function Table. STEP1:

CONFIDENTIAL24 STEP2: We find the values of ‘y’ by putting the values of ‘x’ in the equation. When x = 1, y = 3 x 1 + 2, y = = 5 When x = 2, y = 3 x 2 + 2, y = = 8 When x = 3, y = 3 x 3 + 2, y = = 11 When x = 4, y = 3 x 4 + 2, y = = 14 Input (x)1234 Output (Y) Rule  y = 3x + 2 STEP3: We now make the function table’ by putting the values of ‘x’ and ‘y’.

CONFIDENTIAL25 Assignments Simplify: 1) (24 ÷ 6) + (2 x 3) - 8 2) 9 x ) Is 2 x 7 -6 equal to 25 ÷ ? 1) 2 2) 14 3) Yes

CONFIDENTIAL26 4) 8a - 3 when a = 5. 5) 7 + 9b when b = 4. Evaluate the given expressions: 6) c ÷ when c = 35. 4) 37 5) 43 6) 14

CONFIDENTIAL27 7) 8d = 48 8) 4e + 7 = 63 Evaluate the given equation: 7) 68) 14

CONFIDENTIAL28 Question number Rule: y = x - 3 Input (x)Output (y) 9)6 10)2 11)8 12)4 Complete the function tables according to the given rules: 9) 3 10) 5 11) 5 12) 7

CONFIDENTIAL29 13) The sum of thrice a number and 2 is 44. Find the number. 14) Sean has twice as many pencils than the number of pens. He has 7 pencils. He gave 3 pens to his friend. Write the equation. How many pens does he have now? 13) 3n + 2 = 44 n = 14 14) y = 2x pens

CONFIDENTIAL30 You have done a nice job. See you in the next session.