question_answer

(a) Find \[4x\times 5y\times 7z\]

(b) First find 4x x 5y and multiply it by 7z; or first find \[5y\text{ }\times \text{ }7z\]and multiply it by 4x.

(c) Is the result the same? What do you observe?

(d) Does the order in which you carry out the multiplication matter?

Answer:

(a) \[4x\times 5y\times 7z\]

\[=\left( 4\times 5\times 7 \right)\times \left( x\times y\times z \right)\]

= 140 xyz

(b) \[4x\text{ }\times \text{ }5y\]

\[=\left( 4\times 5 \right)\times \left( x\times y \right)\]

= 20 xy

\[20xy\times 7z\]

\[=\left( 20\times 7 \right)\times \left( xy\times z \right)\]

= 140xyz                                 ...(i)

Now, \[5y\times 7z\]

\[=\left( 5\times 7 \right)\times \left( y\times z \right)\]

= 35 yz

Secondly\[,35yz\times 4x\]

\[=\left( 35\times 4 \right)\times \left( yz\times x \right)\]

\[=\text{ }140\text{ }yzx\text{ }or\text{ }140\text{ }xyz\]                  ... (ii)

(c) Yes, the result is same.

(d) No, the order in which we carry out the multiplication does not matter.