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Find the product 80×22

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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

User Tina Chen
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