We’ve already practiced long division, yet so much our answers have actually all come out even (in other words, our critical subtraction problem ended in solution of 0). However, sometimes our division problems will not come the end evenly, and also we will have an additional number (not 0) once we execute the last subtraction problem. This leftover number is dubbed a remainder, and also it is created as part of the quotient. Follow in addition to this example:

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The red circled number in ~ the bottom our remainder. You execute not have to circle the remainder; we simply circled ours so that you know which number it is. After you have your remainder, you compose it on optimal of the division bar, with an r in prior of it, prefer this: 25 r 3.

once your division ends v a remainder, you must make certain that your remainder is less than your divisor. If her remainder is an ext than her divisor, you need to go ago and check your division, since it is incorrect. We deserve to still use our multiplication technique to check our division; you will certainly multiply the quotient (25) by the divisor (5), and also then add our remainder come the answer come the multiplication problem, favor this:

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Let’s shot that one an ext time. Here’s a new example:

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

currently let’s examine our work, prefer this:

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there are likewise several different ways to compose remainders. The standard way is displayed above, v an r in former of the number. However, you can likewise write remainders as fractions and as decimals.

Long division with Remainders as Fractions

now that you recognize the basics of lengthy division, you may be inquiry to compose your remainder as a fraction. Don’t worry! it’s not hard at all. You’re walking to execute long department the exact same way—divide, multiply, subtract, carry down, and then you’re going to get a remainder. Instead of composing r and then the number, you are going come take her remainder and make that the numerator of a fraction. The denominator originates from the divisor—you use the very same number you’re separating by in her denominator.

stop look in ~ the complying with example:

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

Also, you would check this division problem the same method as a normal department problem; multiply the quotient (23) by the divisor (6) and then add the remainder (1). Do not do anything through the fraction in bespeak to inspect this problem.

Long division with Remainders together Decimals

Another way you might be asked to express a remainder is in the form of a decimal. Once you’re asked come express your remainder together a decimal, you first complete department as usual, until you obtain to the point you usually end at, whereby you have nothing rather to carry down. Rather of protecting against here, however, you are going to save going through division. Friend will include a decimal point (.) after the last number given in the dividend, and you will also place a decimal allude in the quotient after ~ the number you have actually so far. ~ the decimal in the dividend, girlfriend will add a zero (0) and continue division. You will keep including zeroes till your subtraction step outcomes in solution of 0 as well. Follow in addition to this example:

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notice that we added a decimal after ~ the 6 in the dividend, and a decimal after ~ the 5 in ours quotient. Then, us started adding zeroes to the dividend. This time, it only took united state one included zero prior to our remainder to be zero.


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Now, let’s look at a difficulty where you’d need to add more than one zero to the dividend:

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once you have actually your quotient v a decimal, you inspect the answer in different way than if it had a remainder together a portion or just a remainder written with r. Instead of including the remainder separately, you just multiply the quotient (including decimal) through the divisor, favor this: