1 Answer

Tina Chen · Answer 1 · 2023-02-22T15:12:01+0000

We want to calculate the following product

$80\cdot22$

To do so, we will use some properties of the product. First, note that 22=20+2. So we have

$80\cdot22=80\cdot(20+2)$

Now, we will use the distributive property, so we get

$80\cdot(20+2)=80\cdot20+80\cdot2$

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

$80\cdot2$

Note that 80=8*10. So we have

$80\cdot2=8\cdot10\cdot2$

We can rearrange the order of the product as follows

$8\cdot10\cdot2=10\cdot(8\cdot2)$

We know that 8*2=16. So we have

$10\cdot(8\cdot2)=10\cdot16$

NOw, recall that multiplying by 10 can be done by simply adding a 0 in the right end of the number, so we get

$80\cdot2=10\cdot16=160$

Now, we want to calculate 80*20. So we have

$80\cdot20$

Recall that 20=2*10. Then

$80\cdot20=80\cdot2\cdot10$

We already know that 80*2=160. Then

$80\cdot2\cdot10=160\cdot10$

By applying the same principle of multiplying by 10, we have

$80\cdot20=160\cdot10=1600$

Now, we add both solutions, so we have

$80\cdot22=1600+160=1760$

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