Algebra What is algebra Used in everyday life

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 simplified is 3 a. c +c – f simplified is 2 c – f 1. h + h + h = 2. 3 x f = 4. g + g – g = 5. d + f + d + f = 3. b + b = 6. a + b + a + 2 b + a

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

Solving simple formulae Example: Find the value of p 3 p + 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. 3 p = 82 – 55 3 p = 27/3 p = 9 Have a go! 3 z – 12 = 168 3 r + 14 = 47 6 q – 30 = 42 12 a – 12 = 72 4 n + 1 = 1001

Solving simple formulae Example: Find the value of p 3 p + 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. 3 p = 82 – 55 3 p = 27/3 p = 9 Have a go! 3 z – 12 = 168 z = 60 3 r + 14 = 47 r = 11 6 q – 30 = 42 q = 12 12 a – 12 = 72 a =7 4 n + 1 = 1001 n =250

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

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

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

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

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

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

Any questions?