Respuesta :
We want to calculate the following product
[tex]80\cdot22[/tex]To do so, we will use some properties of the product. First, note that 22=20+2. So we have
[tex]80\cdot22=80\cdot(20+2)[/tex]Now, we will use the distributive property, so we get
[tex]80\cdot(20+2)=80\cdot20+80\cdot2[/tex]Now, this suggests that we can calculate 80*2 and 80*20 separately and then add the results together.
So now, we want to calculate first
[tex]80\cdot2[/tex]Note that 80=8*10. So we have
[tex]80\cdot2=8\cdot10\cdot2[/tex]We can rearrange the order of the product as follows
[tex]8\cdot10\cdot2=10\cdot(8\cdot2)[/tex]We know that 8*2=16. So we have
[tex]10\cdot(8\cdot2)=10\cdot16[/tex]NOw, recall that multiplying by 10 can be done by simply adding a 0 in the right end of the number, so we get
[tex]80\cdot2=10\cdot16=160[/tex]Now, we want to calculate 80*20. So we have
[tex]80\cdot20[/tex]Recall that 20=2*10. Then
[tex]80\cdot20=80\cdot2\cdot10[/tex]We already know that 80*2=160. Then
[tex]80\cdot2\cdot10=160\cdot10[/tex]By applying the same principle of multiplying by 10, we have
[tex]80\cdot20=160\cdot10=1600[/tex]Now, we add both solutions, so we have
[tex]80\cdot22=1600+160=1760[/tex]