Algebra

What is algebra? Used in everyday life e.g. splitting a bill in a restaurant. Cost (£) = Total Number of people. C = T P In science, e.g. finding the speed that an object is travelling. Speed = Distance Time

Simplifying equations Simplify these equations; Example: a + a + a simplified is 3a. c +c – f simplified is 2c – f 1. h + h + h + h = 2. 3 x f = 3. b + b + b = 4. g + g – g = 5. d + f + d + f = 6. a + b + a + 2b + a

Simplifying equations Simplify these equations; Example: a + a + a simplified is 3a. c +c – f simplified is 2c – f 1. h + h + h + h = 4h 2. 3 x f = 3f 3. b + b + b = 3b 4. g + g – g = g 5. d + f + d + f = 2d +2f 6. a + b + a + 2b + a =3a+3b

Solving simple formulae Example: Find the value of p 3p + 55 = 82 Move the numbers to one side of the equals sign and letters to the other. When you change the side, you change the sign. 3p = 82 – 55 3p = 27 p = 27/3 p = 9 Have a go! 3z – 12 = 168 3r + 14 = 47 4n + 1 = 1001 6q – 30 = 42 12a – 12 = 72

Solving simple formulae Example: Find the value of p 3p + 55 = 82 Move the numbers to one side of the equals sign and letters to the other. When you change the side, you change the sign. 3p = 82 – 55 3p = 27 p = 27/3 p = 9 Have a go! 3z – 12 = 168 z = 60 3r + 14 = 47 r = 11 4n + 1 = 1001 n =250 6q – 30 = 42 q = 12 12a – 12 = 72 a =7

Substituting with values. If a = 5, b = 3 and c = 1, solve these equations; Example: 3a + b = (3 x 5) + 3 = 18 Don’t forget BODMAS, which is Brackets, order, division, multiplication, addition, subtraction. 3a + b = 2. 2b – c = 3. a + 3b = 4. 2b – 2c = 5. a – b – c = 6. 5b + 7c = 7. 4a ÷ 2 = 8. 10c x 10 = 9. 6b + 3c + 8a

Substituting with values. If a = 5, b = 3 and c = 1, solve these equations; Example: 3a + b = (3 x 5) + 3 = 18 Don’t forget BODMAS, which is Brackets, order, division, multiplication, addition, subtraction. 2b – c = 5 a + 3b = 14 2b – 2c = 4 a – b – c = 1 5b + 7c = 22 4a ÷ 2 = 10 10c x 10 = 100 6b + 3c + 8a = 61

Combining like terms: Example: 22 – 4T = 10 + 8T group the like terms together 22-10 = 8T + 4T (change the side, change the sign) 12 = 12T Now, get T on its own. 12/12 = T 1 = T 5U + 7 = 56 – 2U  30 + 2V = 15 +7V 6W – 20 = 15 + W 62 + 7X = 152 – 8X 7Y + 12 – 5Y = 42 4Z + 27 = 30 + 2Z

Combining like terms: Example: 22 – 4T = 10 + 8T group the like terms together 22-10 = 8T + 4T (change the side, change the sign) 12 = 12T Now, get T on its own. 12/12 = T 1 = T 5U + 7 = 56 – 2U  U = 7 30 + 2V = 15 +7V V = 3 6W – 20 = 15 + W W = 7 62 + 7X = 152 – 8X X = 6 7Y + 12 – 5Y = 42 Y = 15 4Z + 27 = 30 + 2Z Z = 1.5

Solving equations involving brackets 5( x -4) = 30 First, expand the bracket 5x – 20 = 30 Now, it’s very much like our previous examples. 5x = 30 + 20 5x = 50 x = 10 Try these: 2(3x – 4) = 28 2(a – 3) = 15 3(t - 11) = 2(t + 8)

Solving equations involving brackets 5( x -4) = 30 First, expand the bracket 5x – 20 = 30 Now, it’s very much like our previous examples. 5x = 30 + 20 5x = 50 x = 10 Try these: 2(3x – 4) = 28 x = 6 2(a – 3) = 15 a = 10.5 3(t - 11) = 2(t + 8) T = 49

Any questions?