Prove that 4.6×(0.8×10.5)= (4.6×0.8))×10.5

1.	Prove that 4.6×(0.8×10.5)= (4.6×0.8))×10.5
Answer» $\sf\huge\bold{\underline{\underline{{Solution}}}}$ The above question is given in the form of associative law: A(BC)=(AB)C =>4.6×(0.8×10.5)=(4.6×0.8)×10.5 Step by step explanation First we solve value inside the brackets then multiply with outside. Values are in decimal so,we SIMPLY multiply as whole number and then put decimal points. Calculation : 4.6×(0.8×10.5) simply multiply as whole number 105 ×8 ____ 840 ____ Count the number of digits after decimal in 0.8×10.5 there are 2 digits Place POINT 2 from right to left in the RESULTANT. =>8.40 =>4.6×(8.40) Simple multiply as whole numbers: 840 ×46 _______ 5040 3360x _______ 38640 Now ,count the number of digits after decimal in 4.6×8.40 =>1+2=3 place decimal 3 digits forward from right =38.640(LHS) Solving RHS =>(4.6×0.8)×10.5 Normally Multiply as whole numbers: $\:$ 46 ×08 _______ 368 00x ______ 368 two digits after decimal so,368=3.68 =>3.68×10.5 $\:\:\:$ 368 $\:\:$ x105 $\text{[math]}$ _________ $\:\:\:\:\:$ 1840 $\:\:\:\:$ 000x $\:\:\:$ 368xx $\text{[math]}$ __________ $\:\:\:\:$ 38640 Now,count digits after decimal in 3.68×10.5 There are 3 digits so,place decimal after 3 PLACES from right . =>38.640(RHS) ∴LHS=RHS=38.64

Answer»

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

The above question is given in the form of associative law:

A(BC)=(AB)C

=>4.6×(0.8×10.5)=(4.6×0.8)×10.5

Step by step explanation

First we solve value inside the brackets then multiply with outside.
Values are in decimal so,we SIMPLY multiply as whole number and then put decimal points.

Calculation :

4.6×(0.8×10.5)

simply multiply as whole number

105

×8

____

840

____

Count the number of digits after decimal in 0.8×10.5 there are 2 digits

Place POINT 2 from right to left in the RESULTANT.

=>8.40

=>4.6×(8.40)

Simple multiply as whole numbers:

840

×46

_______

5040

3360x

_______

38640

Now ,count the number of digits after decimal in 4.6×8.40 =>1+2=3

place decimal 3 digits forward from right

=38.640(LHS)

Solving RHS

=>(4.6×0.8)×10.5

Normally Multiply as whole numbers:

$\:$ 46

×08

_______

368

00x

______

368

two digits after decimal

so,368=3.68

=>3.68×10.5

$\:\:\:$ 368

$\:\:$ x105

$\text{[math]}$ _________

$\:\:\:\:\:$ 1840

$\:\:\:\:$ 000x

$\:\:\:$ 368xx

$\text{[math]}$ __________

$\:\:\:\:$ 38640

Now,count digits after decimal in 3.68×10.5

There are 3 digits so,place decimal after 3 PLACES from right .

=>38.640(RHS)

∴LHS=RHS=38.64