Mathematics Questions and Answers

\(m*n = \frac{m}{n}-\frac{n}{m}

= \frac{-3}{4} - \frac{4}{-3}

= \frac{-3}{4} + \frac{4}{3}

= \frac{(-9+16)}{12}

= \frac{7}{12}\)

Multiply appropriately to remove decimals on both numerator and denominators.

Such that you have \(\sqrt{\frac{(23000 \times 750)}{(345 \times 125)}}\)

Dividing, => \(\sqrt{400} = 20\).

(2 x 9 \(^0\) ) (3 x 9 \(^1\)+ Y x 9\(^0\)) = (3 x 5 \(^0\))(3 x 5\(^1\) + Y x 5\(^0\)).

(2 * 1)(3 *9 + y) = (3 * 1)(3 * 5 + y)

2(27+y) = 3(15 + y)

54 + 2y= 45 + 3y

54 - 45 = 3y - 2y

y=9

Hint: Two methods can be used;

1. Direct division (if you know division in number bases)

2. Convert both sides to base 10, divide and convert your answer back to base 6. Your answer should be 356

2434\(_6\) to base 10

2 \(\times\) 6\(^3\) + 4 \(\times\) 6\(^2\) + 3 \(\times\) 6\(^1\) + 4 \(\times\) 6\(^0\)

2 \(\times\) 216 + 4 \(\times\) 36 + 3 \(\times\) 6 + 4 \(\times\) 1

432 + 144 + 18 + 4 = 598

And: 42\(_6\) to base 10

4 \(\times\) 6\(^1\) + 2 \(\times\) 6\(^0\)

4 \(\times\) 6 + 2 \(\times\) 1

24 + 2 = 26

Then divide 598 by 26 

= 23

Then convert 23\(_{10}\) to base 6

Cost price (cp) = (100/5) x N1.20 =N24.00
Selling price (sp) = 100-20 = 80
(80/4) x N1.50 = N30.00

Gain = SP-CP = N30.00-N24.00 = N6.00
Gain% = (gain/CP) x 100 = 25%