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# Rearranging Formulas

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Rearranging algebra formulas using the Onion Skin Method

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### Rearranging Formulas

1. 1. Image Source: http://www.juicing-for-health.com
2. 2. In a previous lesson we showed how toSolve Equations using the work downthrough the “Onion Skins” Method.In this lesson we will review the use of the“Onion Skin” method, and show how it canbe applied to Transposing (or rearranging)Algebra Formula Equations.
3. 3. • Turn the whole equation into an “onion”, building skinsoutwards from the letter variable in the center.• These onion skins are created by first drawing a centreskin around the letter variable we are solving for.• We then create skins outwards from here, following theBODMAS/PEMDAS order of operations.• The outermost skin should enclose the entire equation.• Now “Peel” inwards doing opposite operations.• Apply these opposites, starting from the single numberitem which is contained in the outermost onion skin.• Keep applying opposites until we reach the lettervariable, that is in the center of the Onion.
4. 4. Solving Equations Using Onion SkinsSolve the Equation : n + 5 = 7To solve the Equation work from the biggest outerskin, inwards through the smaller skins, applyingopposites, until we reach the letter variable center.n + 5 = 7Solution for n is: n = 7 - 5 = 2 n = 2Draw the first skin around “n”,and then draw more skinsradiating outwards, until thewhole algebra equation iscircled by the final outer skin.
5. 5. Transposing a Formula Using Onion SkinsTranspose : n + m = k to make “n” the subjectTo rearrange the Formula, work from the biggest outerskin, inwards through the smaller skins, applyingopposites, until we reach the required subject letter “n” at thecenter.n + m = kn = k - m so “n” formula is : n = k - mEg. We need to rearrange n + m = k to convert it to an n = ? formulaBecause “n” is the desired subject,draw a skin around “n” first,and then draw more skinsradiating outwards, untilthe whole formula equation iscircled by the final outer skin.
6. 6. Solving a 2 Step Equation Using Onion SkinsSolve the Equation : 2h + 3 = 11To solve the Equation work from the biggest outerskin, inwards through the smaller skins, applyingopposites, until we reach the letter variable.2h + 3 = 11Solution for h is: h = 11 - 3 2 h = 4Draw the first skin around “h”,and then draw more skinsradiating outwards, until thewhole algebra equation iscircled by the final outer skin.
7. 7. Transposing a Formula Using Onion SkinsTranspose : v = u + at to make “a” the subjectEg. We need to rearrange v = u + at to convert it to an a = ? formulav = u + atBecause “a” is the desired subject,draw a skin around “a” first,and then draw more skinsradiating outwards, untilthe whole formula equation iscircled by the final outer skin.To rearrange the Formula, work from outer skin, inwards, applyingopposites, until we reach the required subject letter “a” at the center.a = v - u t a = v - utv - uta =
8. 8. Л hTransposing a Squared FormulaTranspose to make “r” the subjectV = Л r2hBecause “r” is the desired subject,draw the skins radiating outwardsfrom “r”.Note that the squaring of “r” is askin whose opposite is square root.r = V Л h r = VV = Лr2hЛ hVr =
9. 9. v2Transposing a Formula with a FractionRearrange to make “m” the subjectE = m v2 Make the 1/2 a “2”in the bottom line ofthe algebra fraction.m = E x 2 v2E = ½ mv22E2m =
10. 10. 2EmTransposing an Exponent and a FractionRearrange to make “v” the subjectE = m v 2Make the 1/2 a “2”in the bottom line ofthe algebra fraction.Note that the squaring of“r” is a skin whose oppositeis square root.m = E x 2 mE = ½ mv22m =
11. 11. (100-D)100STransposing Selling Price to Marked PriceRearrange to an “M”= FormulaS = M (100 – D)M = S x 100 (100-D)S = M(100-D) / 100100M =
12. 12. 3hk - nTransposing a Multi-Variable FormulaRearrange to make an “c” the subjectc = k x h - n 3(3c + n) / h = k3c + n = khc =
13. 13. h 23Transposing a Square Root FormulaRearrange to make “k” the subjecth = 3 kNote that the square rootis a skin whose opposite issquaring.k = h 3 Squared x Lh = 3 k/LLk = L
14. 14. DTransposing a Subject DenominatorRearrange to make “v” the subjectD = mWhen our Subject is in the bottom, Flip both sides first.v = 1 x mD = m/vmvv =11 = vmDD
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