Our Lesson Solve equations by Addition and subtraction

Confidential2 1. Write 36/24 in its simplest form 3/4 2.Are 49/58 and 7/8 equivalent fractions? No Find the LCD for the following pair of fractions 3.7/12, 3/ /48, 17/ Replace the blanks with >,=,< 5. 6/13_____ 7/15 < Warm up

Confidential3 Simplest form of Fraction A fraction is in its simplest form when the GCF of the numerator and the denominator is 1 There is no other common factor except 1 Example ,, Lets review what we have learned in the last lesson

Confidential4 If the cross products of two fractions are equal then they are equivalent fractions a c b d If ad = bc then a/b = c/d = 30 Equivalent Fractions

Confidential5 To compare fractions Rewrite each fraction using the same denominator Now you need only to compare the numerators Comparing and Ordering Fractions Fractions

Confidential6 Improper Fraction A fraction in which the numerator is greater than the denominator A mixed number (fraction) is a number that has a part that is a whole number and a part that is a fraction Mixed Number Mixed Numbers and Improper Fractions

Confidential7 Conversion from an improper fraction in to a mixed fraction Divide the numerator by the denominator The remainder you get put it over the denominator (i.e. in the numerator) The quotient in the place of the whole number Multiply the whole number times the denominator Add your answer to the numerator Put your new number over the denominator Conversion from a mixed fraction in to a improper fraction

Confidential8 The mixed fraction will look like Quotient Remainder Divisor (Whole number x Denominator) + Numerator Denominator The improper fraction will be written as

Confidential9 Addition of Fractions When the denominators are co-prime, we need to multiply the two denominators to get the common denominator When the two denominators have a common factor we find the least common denominator by factoring When one denominator is a multiple of the other denominator the multiple is the denominator Different denominators Equal Denominators Same denominator for both fractions so just add the numerators

Confidential = = x 9 4 x x 9 9 x = - == Lets see some examples Do same as in Addition Multiple Take the multiple Common Factors Take LCM Prime Multiply the two Subtraction of fractions Equal Denominators Different denominators

Confidential11 To multiply two fractions,multiply the numerators and then multiply the denominators a c b d x = ac bd b,d = 0 Multiplying fractions Division of Fractions To divide fractions, multiply by its multiplicative inverse a c b d ÷ = a d b c x b,d = 0

Confidential12 1. Convert the mixed fraction in to an improper fraction or add the whole numbers and fractions separately 2.Find a common denominator 3. Add/Subtract as required 4.Simplify, then if it is an improper fraction then again convert in to a mixed fraction Addition/Subtraction of mixed numbers Steps:

Confidential13 Multiplication of mixed fractions and fractions First convert the mixed fraction in to an improper fraction Then multiply, numerator x numerator and denominator x denominator x 1515 = x = If the answer is an improper fraction then again convert answer in to mixed number 9 35 = 9 35

Confidential14 Division of Mixed Fractions and Fractions To divide mixed fractions and fractions, multiply by its multiplicative inverse a c b d ÷ = a d b c x Where b, c and d = 0 First convert the mixed fraction in to an improper fraction

Confidential15 EXPRESSIONS & EQUATIONS What is the difference between an expression and an equation??? Expression: 3 + x does not have an equal sign; it is just a phrase Equation: 3 + x = - 9 always has an equal sign; it is a complete thought

Confidential16 SOLVE AN EQUATION To solve an equation means to find the values of the variable that make the equation true. The values of the variable are called the SOLUTIONS of the equation. 18 is a solution of: a + 2 = 20 because: a = 18

Confidential17 1) Isolate the variable term you wish to solve for 2) Substitute your answer into the original equation and check that it works Steps for Solving Equations

Confidential18 The numerical coefficient of any variable which does not have any other number in front of it is 1 x + 3 = 2 y - 6 = 54, z + 6 = 34 Here all these variables have a coefficient of 1 5x = 25, 4y + 7 = 35 here the coefficient of x is 5 and y is 4

Confidential19 If a = b, then a + c = b + c If a = b, then a – d = b – d Adding the same quantity to both sides of an equation produces an equivalent equation Subtraction is simply adding a negative number, this rule applies when subtracting the same quantity from both sides The Addition Property of Equality and Its Inverse Property of Subtraction

Confidential20 1)Isolate variable term y 2) It is important that we subtract 3 from both sides of the equation, otherwise we will lose equality Subtract 3 from both sides (y + 3) – 3 = 15 – 3 y = 12 Example: y+ 3 = 15 Isolating the variable term

Confidential21 Substitution is a process of replacing variables with numbers or expressions For example, a + 12 = b, and a = 9, find the value for b = b 21 = b Substitute Your Answer into the Original Equation By substituting, we switch or exchange values, often replacing a variable with a numerical value We substitute to minimize the number of variables in an expression, or to actually evaluate the expression or equation

Confidential22 Given x + 5 = 45, find x Find the basic operation and use the inverse operation on both sides of the equation x = x = 40 In the equation x is added to 5 so we will do the inverse operation and subtract 5 from both sides

Confidential23 Check by substitution + 5 = = = 45 x We know that the value of x = 40

Confidential24 Find the value of the variable in the following:  1. m - 2 = 5 m = 7  2. 4 = a -10 a = 14  3. f + 6 = 7 f = 1  4. p + 8= -11 p =-19  = k + 3 k = 18

Confidential25 Find the value of the variable in the following:  x = 88.9 x = 10  – y = y=  9. p + 1/2 = 1/8 p = -3/8  10. m – 12/24 = 6/36 m = 2/3  w = 3 w = 5

Confidential26 Break Time

Confidential27 Lets play a Game

Confidential28 1) Sally spent $15 at a restaurant for a lunch for herself and a friend. The bill came to $11.75 and tax was $.83.How much tip did she leave. Write an equation and solve it. $ $ t = $ 15 Lets make t = tip $ t = $15 t + $ $12.58 = $15 -$12.58 t = $2.42

Confidential29 2) Tom ran 5 Km less than Charlie. Had Charlie ran 6 more Kms he would have reached the town Hall. If the distance to the town hall from the start point is 15 Km, find the distance ran by Tom. 4 Km

Confidential30 3) The sum of the measures of the angles of a triangle is 180°. Find the missing measure. a = 180° 50°75° a a = 180 – ( ) a = 180 – 125 a = 55

Confidential31 SOLVE AN EQUATION To solve an equation means to find the values of the variable that make the equation true. The values of the variable are called the SOLUTIONS of the equation. 18 is a solution of: a + 2 = 20 because: a = 18 Lets Recap our today’s lesson

Confidential32 1) Isolate the variable term (numerical coefficient of 1) you wish to solve for 2) Substitute your answer into the original equation and check that it works Steps for Solving Equations

Confidential33 1)Isolate term with the variable a 2) It is important that we subtract 7 from both sides of the equation, otherwise we will lose equality. We now have: Subtract 7 from both sides (a + 7) – 7 = 15 – 7 a = 8 Here we solved for a by isolating by using opposite operations Example: a + 7 = 23 Isolating the variable term

Confidential34 Substitution is a process of replacing variables with numbers or expressions For example, a + 12 = b, and a = 9, find the value for b = b 21 = b Substitute Your Answer into the Original Equation By substituting, we switch or exchange values, often replacing a variable with a numerical value. We substitute to minimize the number of variables in an expression, or to actually evaluate the expression or equation

Confidential35 You did great in your lesson today! Be sure to practice what we have learned today