Theory question 106
Fractions, Decimals and Approximation(a) Simplify: (3 1/12 + 7/8)/(2 1/4 − 1/6)
(b) If p = m/2 − n2/5m, (i) make n the subject of the relation; (ii) find, correct to three significant figures, the value of n when p = 14 and m = −8.
Show the model answer
Model answer
(a) Numerator: 37/12 + 7/8 = 74/24 + 21/24 = 95/24. Denominator: 9/4 − 1/6 = 27/12 − 2/12 = 25/12.
95/24 ÷ 25/12 = 95/24 × 12/25 = 19/10 = 1 9/10.
(b)(i) n2/5m = m/2 − p, so n2 = 5m(m − 2p)/2 and n = ±√[5m(m − 2p)/2].
(ii) n2 = 5(−8)(−8 − 28)/2 = (−40)(−36)/2 = 720, so n = ±26.8.
Explanation
Isolate the n2 term first, then take the square root.