Transposing Equations What is Transposition Transposition is a

Transposing Equations

: What is Transposition? • Transposition is a skill you need to learn to solve most algebra equations. • All equations have two sides- a Left Hand Side (LHS) and a Right Hand Side (RHS). • For example in the equation below 2 x + 5 is on the Left Hand Side of the equation and 29 is on the Right Hand Side of the equation:

How do I transpose? • transposition means changing the subject of the formula. . • This requires rearranging the terms so that the variable you require is isolated on the LHS of the equation. • This means you need to move everything on the same side as the subject to the other side using INVERSE OPERATIONS

What are inverse operations? • Inverse operations are opposite operations that undo each other. • Addition and subtraction are inverse operations • Multiplication and division are inverse operations. • Squaring and square rooting are inverse operations • When we transpose, we use inverse operations to move terms to the other side in order to leave the subject on its own. • Always move the term FURTHEST from the subject 1 st and work our way in (the onion skin method) • NOTE: think about how you READ the equation…. . . The term you read last is the first you move

Rearrange the formula to make a the subject This means we want to rearrange the formula so it says a= b = 5 a + 21 -21 ÷ 5 b – 21 = 5 a b – 21 = a 5 Our answer should say. . . a = b – 21 5

Rearrange the formula to make t the subject This means we want to rearrange the formula so it says t= h = 13 + 7 t -13 ÷ 7 h – 13 = 7 t h – 13 = t 7 Our answer should say. . . t = h – 13 7

Exercise One Rearrange each formula to make s the subject 1. u = 11 s + 3 2. w = 8 s + p 3. q = 3 s + 4 t 4. 7 s + m + t = l 5. a = 3(s + 4) Hint: You need to expand the brackets first 6. 4 = g(s – 7) 7. 22 + 5 s = g 8. r = q – 3 s

Rearrange each formula to make s the subject 1. u = 11 s + 3 2. w = 8 s + p 3. q = 3 s + 4 t 4. 7 s + m + t = l 5. a = 3(s + 4) 6. 4 = g(s – 7) 7. 22 + 5 s = g 8. r = q – 3 s s=u-3 11 s=w–p 8 s = q – 4 t 3 s=l–m–t 7 s = a - 12 3 s = 4 + 7 g g s = g - 22 5 s=q-r 3

Rearrange the formula to make v the subject This means we want to rearrange the formula so it says v= e = 3 v + t x 5 5 e = 3 v + t -t -t 5 e – t = 3 v ÷ 3 5 e – t = v 3 Our answer should say. . . v = 5 e – t 3

Rearrange the formula to make p the subject This means we want to rearrange the formula so it says p= m=p+n -n 2 -n m-n=p x 2 2(m – n) = p Our answer should say. . . p = 2(m – n)

Make x the subject in each of these formulae: 1. 2. 3. 4. 5. 6. 7. 8. 9.