<p><a target="_blank" href="https://www.prepswift.com/quizzes/quiz/prepswift-remainders-and-addition">Remainders and Addition Exercise</a></p><p>To find the overall remainder in a <strong><span style="color:#27ae60;">Remainders and Addition</span></strong> problem, find the remainder of each term separately and then add them together. For example, what is the remainder of the following problem below:</p>
<p>$$\frac{17+9}{5}$$</p>
<p>This remainder is equal to the remainder of each term added together:</p>
<p>$$\frac{17}{5} + \frac{9}{5} = 2 \ (remainder) + 4 \ (remainder) = 6$$</p>
<p>If the resulting remainder sum is less than $5$ in this case, say $0$, $1$, $2$, $3$, or $4$, then that's simply the remainder because all of those values are less than $5$. If however, the remainder sum is equal to or greater than the divisor, then the final remainder is equal to the remainder sum minus $5$:</p>
<p>$$6-5=1 = \ final \ remainder$$</p>
<p>Of course you wouldn't solve this problem this way because it's so obvious that $(17+9) \div 5$ has a remainder of $1$, but you could use this trick in a problem like the one below that asks you to find the remainder:</p>
<p>$$\frac{7^{30}+6^{45}}{3}$$</p>