Theory question 101
Fractions, Decimals and Approximation(a) Without using Mathematical tables or calculators, simplify: 34/9 ÷ (5⅓ − 2¾) + 59/10
(b) A number is selected at random from each of the sets {2, 3, 4} and {1, 3, 5}. Find the probability that the sum of the two numbers is greater than 3 and less than 7.
Show the model answer
Model answer
(a) 5⅓ − 2¾ = 16/3 − 11/4 = 31/12
31/9 ÷ 31/12 = 31/9 × 12/31 = 4/3
4/3 + 59/10 = 40/30 + 177/30 = 217/30 = 77/30
(b) There are 3 × 3 = 9 equally likely pairs; sums: 3, 5, 7, 4, 6, 8, 5, 7, 9
Sums greater than 3 and less than 7: 5, 4, 6, 5 → 4 outcomes
Probability = 4/9
Explanation
Do the bracket first, then the division, then the addition.