giancarlojr wrote:
I used the calculator just to try out and the results are somewhat misleading in terms of answering the question correctly:
135/7=19.285...
135/19=7.105263...
so in this case you would get differing remainders. How come the two methods result in different answers?
The explanation lies in how remainders, divisors and decimals are related through division.
Take as an example the expression 17 ÷ 5. We know through long division that the divisor 5 goes into the dividend 17 three times with 2 left over, so the quotient could be written as 3 remainder 2. However, the quotient were we to put 17 ÷ 5 in the calculator would be 3.4 as a decimal.
Why is this??
It's because the decimal leftover 0.4 = 2/5 as a fraction, which is also equal to the remainder 2 out of the divisor of 5.
So, for all division : remainder / divisor must = quotient decimal leftover as a fraction.
Let's now apply this concept to the decimals left over in the problem.
As already established, 135 ÷ 7 = 19 remainder 2 and if you take that remainder of 2 and divide it by the divisor of 7 you get a decimal leftover of 0.285714 repeating.
Then, since 135 ÷ 19 = 7 remainder 2 you would instead take that remainder of 2 and divide it by the divisor of 19 to get a decimal leftover of 0.105263...
Hope this sufficiently explains the relationship between remainders and decimals in division!
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