Question

Why does the quotient of 8 ÷ 1 not change when we add a place value in the dividend and the divisor to make 80 ÷ 10?

Answer 1

Basically this is because division can be thought of as how many times does the divisor have to be multiplied in order to produce the dividend.

So you would need to multiply 1 8 times in order to produce the dividend,

Similarly, 10 goes into 80 8 times. The zeros are simply cancelled out in the division.