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Published byAnnie Elston Modified over 2 years ago

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Rearranging Equations

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Things to remember: Don’t rush it. You must go through each stage of your method and not try to skip any. If you are making x the subject it means that you want to end up with x = and this is the only x in your answer. Whatever you do to one side of the equals sign you must do to the other.

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

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

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Exercise One Rearrange each equation to make s the subject 1.u = 11s w = 8s + p 3.q = 3s + 4t 4.7s + m + t = l 5.a = 3(s + 4) 6.4 = g(s – 7) s = g 8.r = q – 3s Hint: You need to expand the brackets first

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Rearrange each equation to make s the subject 1.u = 11s + 3 s = u w = 8s + p s = w – p 3.q = 3s + 4t s = q – 4t 4.7s + m + t = l s = l – m – t 5.a = 3(s + 4) s = a – 12 = a = g(s – 7) s = 4 + 7g = s = g s = g r = q – 3s s = q - r g 5 3 g 3

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Rearrange the equation to make v the subject e = 3v + t 5e = 3v + t 5e – t = 3v 5e – t = v - t x5 This means we want to rearrange the equation so it says v = Our answer should say... v = 5e – t ÷3

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Rearrange the equation to make p the subject m = p + n m - n = p 2(m – n) = p - n x2 This means we want to rearrange the equation so it says p = Our answer should say... p = 2(m – n) 2 2

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Example more difficult Rearrange the equation a = x + to make x the subject. Method - multiply both sides by d rearrange to get x’s on the left factorise divide by (d + c) a = x + ad = dx + cx dx + cx = ad x(d + c) = ad x =

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Rearrange the equation a = + to make p the subject. Method - multiply both sides by pq rearrange to get p’s on the left factorise divide by (aq – 1) a = + apq = q + p apq – p = q p(aq – 1) = q p = Example more difficult

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Rearrange the equation a = b + to make p the subject. Method - multiply both sides by 1 + p expand brackets rearrange to get p’s on the left divide by (a – b) a = b + a(1 + p) = b(1 + p) + c a + ap = b + bp + c ap – bp = b + c – a p = p(a – b) = b + c – a factorise Example more difficult

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Rearrange the equation s = b + to make t the subject. Method - subtract b from both sides square both sides rearrange to get t on the left multiply by p s = b + s – b = (s – b)² = = (s – b)² t = p(s – b)² Example more difficult

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4. Rearrange the equation s = b + to make t the subject. Test Yourself 1. Rearrange the equation a = x + to make x the subject. 2. Rearrange the equation a = + to make p the subject. 3. Rearrange the equation a = b + to make p the subject. Check your answers on previous slides

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