Multiplication methods - class-IX

We know that amongst two consecutive natural numbers, one is even and one is odd.

$ The\quad units\quad place\quad numbers\quad are\quad 4,\quad 8,\quad 7\quad and\quad 3.\ 4\times 8=32\longrightarrow \quad units\quad place\quad number\quad is\quad 2\ 2\times 7=14\longrightarrow \quad units\quad place\quad number\quad is\quad 4\ 4\times 3=12\longrightarrow \quad units\quad place\quad number\quad is\quad 2\ Answer-\quad Option\quad A $

$(-1)\times$$(-1)\times$$(-1)$$.....1001$ times 

Unit digits of both numbers are $6$ and $8$. 

156 $\times$ 0 = 0

The resultant product of $3$ negative signs would be negative.

$(100 + 2) \times (100 + 3)$
           [Using $(x +a) (x+b)=x^2+(a+b)x+ ab$]
$ = (100)^2 + (2 + 3) \times 100 + 2 \times 3$
$ = 10000 + 5 \times 100 + 6 = 10000 + 500 + 6 = 10506$

Let the number is x

178*0=0

$7986$
$\underline {\times 548}$
63888
319440
$\underline {3993000}$
$\underline {4376328}$

$796\xrightarrow {\text {rounded to nearest tens}}800$
$19\xrightarrow {\text {rounded to nearest tens}}20$
$\therefore 800\times 20=16,000$

(98+ 14) $\displaystyle \times $ 0 = 0

Multiplying unit digit of each number we get 672 hence 2 is the unit digit of the product.

The value of $7.86 \times 4.6 $

$3897\times 999=3897\times (1000-1)$
$=3897\times 1000-3897\times1$
$=3897000-3897$
$=3893103$

$\ \ \ \ \ \ \ \ 34 \ \times\ \ \   56 \ ----$

$\ \ \ \ 12340\ \times \ \ \ \ \ \ 23 \ ---- \ \ \ \ \ \ \ 37020 \ + 246800 \ ---- \ \ \ \ \ 283820$

Any number multiplied by $0$ gives $0$ itself.

$959877\times 10=9598770$

$\Rightarrow$  Diesel consumes by generator in $1,hour$ = $2.875,liters.$

$132820\div 20=6641$
and $6641\times 16=106256$

A machine produces $2800$ screws in a day.

Given,
$6 \times 3 (3 - 1)$

Repeated addition is also known as multiplication. If the same number is repeated then in short we can write that in the form of multiplication.
For example : $3+3+3+3+3$

$B + C = B$

$C = 0$

AA.B $=$ BB $\Rightarrow $ (10 A + A) B $ = $BB= 10 B $+$ B

$AB = B,A = 1$

$ B+A = 3 $

$\Rightarrow B + 1 =3, \Rightarrow B = 2$

1 1 

11

12

22

110

132

Let $x $ be multiplied by $-23$ to get $575$

$4 \times 378 \times 25$

Now,

Consider whole number is $a$

odd Natural Number

a(b x c ) = (a x b) x c is an example of associative property.

We know that for any number $n$ multiplied by $0$ is always $0$ that is $n\times 0=0$.

$0$ should be replaced M because
$304\times 4 = 1216$

Now as $A \times B$ gives 2 in the product, the combinations could be

$2\times 1$ or $1 \times 2, 6 \times 2$ or $2\times 6, 3 \times 4$

or $4 \times 3, 6 \times 7$ or $7 \times 6$ or $8 \times 4$ or

$4\times 8, 9 \times 8$ or $8\times 9$. But to get 2 in hundred's

place and 5 in ten's place in the product, B has to be 6 and A has to be

7. Then $6\times 7=42$.
Write 2 and carry over 4. then $7\times 3= 21$ and add 4 to get 2 and 5 in the product.
The value of B is 6 and A is 7.

If a number is multiplied by 2 and 5 respectively. Then number should be divided by their L.C.M i.e  by 10.
Clearly, only number divisible by 10 is 30.
Hence, option D is correct.

$20\times 60\div 40-20+10=$
After putting the true sign, we get
$20+ 60- 40\times20\div10=$
$20+60-80=$
$0=0$
Answer (B) 0

$15\frac{2}{3}\times 3\frac{1}{6}+6\frac{1}{3}= 11\frac{7}{18}+x$
Or $\frac{47}{3}\times \frac{19}{6}+\frac{19}{3}= \frac{205}{18}+x$
Or $\frac{893}{18}+\frac{19}{3}= \frac{205}{18}+x$
Or 893+114=205+18x
Or 18x=893+114-205=$\frac{802}{18}=44\frac{5}{9}$

We know that any number multiplied by $0$ will always result in $0$. For example: The equation $0\times 2 = 0$ can be read as 'Zero times Two equals Zero'. That means, you are taking $'2'$ zero times, effectively taking nothing. So, multiplying any number by zero will always be zero.

Option $B$ is correct.
The multiplicative inverse will include $1$ as numerator.

We know that any number multiplied by $1$ will always result in that number itself. For example: The equation $2\times 1 = 2$ can be read as 'two times one equals one'. That means, you are taking $'2'$ one times, effectively taking nothing but multiplying by its unity. So, multiplying any number by one will always be the number itself.

By calculations,

We know that any number multiplied by $1$ will always result in that number itself. Therefore, we only multiply $44$ and $567$ as follows:

$15289$ is estimated as $15300$ and $587$ is estimated as $600$.