Mathematics Questions and Answers

\(\frac{0.00275 \times 0.0064}{0.025 \times 0.08}\)

Removing the decimals = \(\frac{275 \times 64}{2500 \times 800}\)

= \(\frac{88}{10^4}\)

\(88 x 10^{-4} = 88 x 10^{1} x 10^{-4} = 8.8 x 10^{-3}\)

You can use any whole numbers (eg. 1. 2. 3) to represent all the mangoes in the basket.

If the first child takes \(\frac{1}{4}\) it will remain 1 - \(\frac{1}{4}\) = \(\frac{3}{4}\)

Next, the second child takes \(\frac{3}{4}\) of the remainder

which is \(\frac{3}{4}\) i.e. find \(\frac{3}{4}\) of \(\frac{3}{4}\)

= \(\frac{3}{4}\) x \(\frac{3}{4}\)

= \(\frac{9}{16}\)

the fraction remaining now = \(\frac{3}{4}\) - \(\frac{9}{16}\)

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

= \(\frac{3}{16}\)

Interest I = \(\frac{PRT}{100}\)

∴ R = \(\frac{100 \times 1}{100 \times 5}\)

= \(\frac{100 \times 7.50}{500 \times 5}\)

= \(\frac{750}{500}\)

= \(\frac{3}{2}\)

= 1.5%

first work out the expression and then correct the answer to 4 s.f = 241.34..............(A)

(3 x 10-\(^3\))\(^2\)............(B)

= 3\(^2\)x\(^2\)

= \(\frac{1}{10^3}\) x \(\frac{1}{10^3}\)

(Note that x\(^2\) = \(\frac{1}{x^3}\))

= 24.34 x 3\(^2\) x \(\frac{1}{10^6}\)

= \(\frac{2172.06}{10^6}\)

= 0.00217206

= 0.002172(4 s.f)

a²bx + ab²x; a²b - b²

abx(a + b); b(a² - b²)

b(a + b)(a + b)

∴ H.C.F. = (a + b)