<p>Please give me a thorough explanation to solve this problem</p>
<p>When the positive integer n is divided by 6, the remainder is 2. What's the remainder when 24n is divided by 36 ?</p>
<p>The positive integer n is divided by 6, the remainder is 2 => does this mean n = 6j + 2 (j is a positive integer ) ?</p>
<p>Thanks a lot :D</p>
<p>( The answer is 12 )</p>
<p>Make it simple. When 8 is divided by 6, remainder is 2. </p>
<p>8 X 24 = 192</p>
<p>When 192 is divided by 36 = 5.3333. This means that 5 ‘36’ fit in 192. To find out what number the 0.3333 represents, you multiply 36 X 5. </p>
<p>36 X 5 = 180. Hence, to get 192, the remainder must be 12. Did that help in any way?</p>
<p>^That’s right. Some people find the remainders using very wrong methods!!!</p>
<p>Oh, I solved this problem like this:</p>
<p>( 8 x 24 ) / 36 = 5.3333 = 5 + 1/3</p>
<p>And I thought that 1/3 is the remainder :(( so what’s that 1/3 if it’s not the remainder ?</p>
<p>^ No, 1/3 is definitely NOT the remainder. It is the fractional part of your answer. But there is an easy way to get the remainder from the fractional part of the answer: multiply the fractional part by the divisor. So in this case, (1/3) x 36 = 12. !2 is the remainder.</p>
<p>@Miranda</p>
<p>What do you mean by the wrong way to solve it. How else would one do? Is there a way to do it without picking a number for n?</p>
<p>^After finding a number, some students would go check it by the calculator, turn the represented number (improper fraction) to a mixed fraction and the numerator would be their answer. That’s what I meant by a WRONG WAY, for this method works out for 10% of the time, in the other 90%, they get a wrong answer.</p>
<p>Remainders are always integers.</p>
<p>Also, you can solve this problem algebraically, although I think plugging in numbers is much easier and faster for most people. Here is how:</p>
<p>“The positive integer n is divided by 6, the remainder is 2” is the same as n = 6j + 2 where j is a positive integer. Then, 24n = (6<em>24)j + 48 = (6</em>6<em>4)j+48 = (36</em>4)j+(36+12) = 36<em>(4j+1) + 12 = 36</em>k + 12 where k = 4j+1 and k is just another integer. So, 24n = 36k + 12 so that the remainder is 12 when 24n is divided by 36.</p>
<p>^Indeed remainders are always integers. In my post above, I did oppose this fact. I said people take the whole number numerator, after converting their improper fraction to va mixed nuber.</p>
<p>Let D be the dividend, P the divisor, Q the quotient of integer division, R the remainder of integer division.</p>
<p>Then, D = Q*P + R
Which gives D/P = Q + R/P</p>
<p>Thus, Q + R/P is mixed fraction notation for D/P where P is the denominator of the fractional part.</p>
<p>So, Mirinda, as long as the fractional part of the mixed fraction has denominator as P, it should work. If not, it can be converted to have denominator P in the following way: Let X be the denominator given. Then, multiply both the numerator and denominator each by (P/X). This is equivalent to multiplying by 1, thus keeping the fraction value unchanged but changing the denominator to P.</p>
<p>^A blunder had occured while I was typing my previous post, and instead of typing ‘I didn’t oppose this fact’, I typed the opposite and notice that I mentioned the word, SOMETIMES.
I meant that the method you are describing is not always Authentic.</p>