We’ve currently practiced lengthy division, however so far our answers have all come out also (in other words, our last subtraction trouble ended in solution of 0). However, sometimes our division problems will not come out evenly, and also we will have an additional number (not 0) as soon as we carry out the last subtraction problem. This leftover number is dubbed a remainder, and also it is created as part of the quotient. Follow along with this example:

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The red circled number in ~ the bottom ours remainder. You perform not have to circle the remainder; we simply circled our so the you understand which number the is. After ~ you have actually your remainder, you create it on height of the division bar, through an r in former of it, like this: 25 r 3.

once your division ends v a remainder, you should make sure that your remainder is much less than your divisor. If her remainder is much more than her divisor, you need to go ago and examine your division, due to the fact that it is incorrect. We deserve to still use our multiplication an approach to check our division; you will multiply the quotient (25) by the divisor (5), and then include our remainder to the answer come the multiplication problem, prefer this:

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Let’s shot that one much more time. This is a brand-new example:

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ours answer to this difficulty is 23 r 1; note that we constantly write the remainder ~ the quotient, on height of the division bar. Also an alert that our remainder (1) is smaller than our divisor (6).

now let’s check our work, like this:

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over there are likewise several different ways to compose remainders. The standard way is displayed above, with an r in front of the number. However, friend can also write remainders together fractions and as decimals.

Long division with Remainders together Fractions

now that you understand the basics of long division, you might be request to create your remainder as a fraction. Nothing worry! the not difficult at all. You’re going to execute long division the same way—divide, multiply, subtract, carry down, and then you’re going to obtain a remainder. Rather of creating r and also then the number, you space going to take her remainder and also make that the molecule of a fraction. The denominator comes from the divisor—you usage the very same number you’re separating by in her denominator.

stop look in ~ the adhering to example:

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an alert that you carry out not usage the r at every in front of your remainder when you’re turning it into a fraction. However, you do still write the portion as component of the quotient (answer come your division problem).

Also, girlfriend would examine this division problem the same means as a normal division problem; main point the quotient (23) through the divisor (6) and also then include the remainder (1). Carry out not execute anything v the portion in order to examine this problem.

Long department with Remainders together Decimals

Another way you might be asked come express a remainder is in the type of a decimal. Once you’re asked to express your remainder as a decimal, you very first complete division as usual, till you gain to the suggest you usually end at, whereby you have nothing else to lug down. Rather of stopping here, however, you room going to save going through division. Girlfriend will add a decimal suggest (.) after ~ the last number given in the dividend, and you will also place a decimal suggest in the quotient after the number you have so far. After ~ the decimal in the dividend, you will add a zero (0) and also continue division. You will certainly keep including zeroes till your subtraction step outcomes in an answer of 0 as well. Follow in addition to this example:

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an alert that we included a decimal after ~ the 6 in the dividend, and also a decimal after the 5 in our quotient. Then, us started including zeroes come the dividend. This time, it just took united state one included zero prior to our remainder to be zero.


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Now, stop look in ~ a trouble where you’d have to add much more than one zero come the dividend:

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as soon as you have your quotient v a decimal, you examine the answer differently than if it had actually a remainder together a fraction or simply a remainder written through r. Instead of including the remainder separately, you just multiply the quotient (including decimal) by the divisor, favor this: