Theory question 101
Fractions, Decimals and Approximation(a) Simplify: (1¼ + 7/9)/(1 4/9 − 2⅔ × 9/64)
(b) Given that sin x = 2/3, evaluate, leaving your answer in surd form and without using tables or calculator, tan x − cos x.
Show the model answer
Model answer
(a) Numerator: 5/4 + 7/9 = (45 + 28)/36 = 73/36.
Denominator: 8/3 × 9/64 = 3/8; 13/9 − 3/8 = (104 − 27)/72 = 77/72.
73/36 × 72/77 = 146/77 = 1 69/77.
(b) Opposite 2, hypotenuse 3, adjacent √(9 − 4) = √5.
tan x = 2/√5, cos x = √5/3.
tan x − cos x = 2/√5 − √5/3 = (6 − 5)/(3√5) = 1/(3√5) = √5/15.
Explanation
Do the multiplication in the denominator before subtracting.