Number Operations and Properties

We have,

$587\times 999=587\times (1000-1)$
$=587\times 1000-587\times 1$
$=587000-587$
$=586413$

$93521\times 625=935421\times {5}^{4}=935421\times {(\cfrac{10}{2})}^{4}$
$\cfrac{935421\times{10}^{4}}{{2}^{4}}=\cfrac{9354210000}{16}$
$=584638125$

$2056\times 987=2056\times (1000-13)$
$=2056\times 1000-2056\times 13$
$=2056000-26728$
$=2029272$.

$72519\times 9999=72519\times(10000-1)$
$=72519\times 10000-72519\times1$
$=725190000-72519$
$=725117481$

$12345679\times 72=123456789\times (70+2)$
$=12345679\times 70+123445679\times 2$
$=864197530+24691358$
$=888888888$

$(112\times {5}^{4})=112\times { \left( \cfrac { 10 }{ 2 }  \right)  }^{ 4 }=\cfrac { 112\times { 10 }^{ 4 } }{ { 2 }^{ 4 } } =\cfrac { 1120000 }{ 16 } =70000$

$5358\times 51=5358\times (50+1)$
$=5358\times 50+5358\times 1$
$=267900+5358$
$=273258$

1397×1397=13972.

12 * 14 = 168. This is a standard multiplication.

32 * 24 = 768. This is calculated using the Urdhva Tiryakbhyam method.

28 * 22 = 616. Using the Nikhilam formula or standard multiplication, the result is 616.

Dhwajanka method calculations: 3987/28 gives Q=142, R=11; 5786/78 gives Q=74, R=14; 7396/82 gives Q=90, R=16.

46 * 4 = 184. The vinculum method represents 46 as 5(bar 4), and the multiplication follows standard arithmetic.