Question

when n is divided by 14, the remainder is 10. what is the remainder when n is divided by 7?

Answer 1

The answer is a remainder of 3. Here's how I got the answer:

First, by definition the dividend is the number that is being divided; the divisor is the number that is dividing the dividend; and the quotient is the result. It is a fact that:

Dividend=(Divisor)(Quotient)+Rmainder

For example: 19/5=3 R4
where 19=Dividend, 5=Divisor, 3=Quotient, and 4=Remainder. Since we know that:
Dividend=(Divisor)(Quotient)+Remainder, we get:

Dividend=(5)(3)+4=15+4=19

We can now apply this to the problem using the following formula:

Dividend=(Divisor)(Quotient)+Remainder or using symbols to get:

N=(D)(Q)+R
where N=Dividend
where D=Divisor
where Q=Quotient
where R=Remainder

For N/14, we get:

N=(14)(Q)+10
Since Q (the Quotient) has to be a whole number because of what the problem states, Q can equal 1 or 2 or 3 or 4, etc.

If Q=1:

N/14: N=(14)(1)+10=24
24/14=1 R10

N/7=24/7 (the number 24 is from above)=3 R3

If Q=2:

N/14: N=(14)(2)+10=28+10=38
38/14=2 R10

N/7=38/7=5 R3

Therefore, in each case the remainders are the same: for N/14, the remainder=10, and for N/7, the remainder=3.

Consequently, the formula works and the remainder for N/7 is 3.