Remainder

Calculator Use Divide two numbers, a dividend and a divisor, and find the answer as a quotient with a remainder. Learn how to solve long division with remainders, or practice your own long division problems and use this calculator to check your answers. Long division with remainders is one of two methods of doing long division by hand. It is somewhat easier than solving a division problem by finding a quotient answer with a decimal. If you need to do long division with decimals use our What Are the Parts of Division For the division sentence 487 ÷ 32 = 15 R 7 • 487 is the dividend • 32 is the divisor • 15 is the quotient part of the answer • 7 is the remainder part of the answer How to do Long Division With Remainders From the example above let's divide 487 by 32 showing the work. Divide 48 by the divisor, 32. The answer is 1. You can ignore the remainder for now. 48 ÷ 32 = 1 Note that you could skip all of the previous steps with zeros and jump straight to this step. You just need to realize how many digits in the dividend you need to skip over to get your first non-zero value in the quotient answer. In this case you could divide 32 into 48 straight away. Since 7 is less than 32 your long division is done. You have your answer: The quotient is 15 and the remainder is 7. So, 487 ÷ 32 = 15 with a remainder of 7 For longer dividends, you would continue repeating the division and multiplication steps until you bring down every digit from the divdend and solve the problem. Fur...

Remainder as a whole number Often the remainder in division is expressed as a whole number. Example Floyd had 14 gumballs. He gave them to 4 friends. How many gumballs did each person receive? 14 ÷ 4 = 3, with a remainder of 2 Therefore each person received 3 gumballs, and there were 2 gumballs remaining. (Cutting gumballs into parts does not work very well!) Remainder as a common fraction or decimal fraction In many division problems, the remainder is expressed as a common fraction or a decimal fraction. Example Jamie and Roger went on a 10-mile hike. If the trip lasted 4 hours, about how many miles did they hike per hour? 10 ÷ 4 = 2½ or 2.5 Thus, Jamie and Roger hiked about 2½ miles (or 2.5 miles) per hour. In this situation, the remainder is expressed as as ½ or 0.5. Remainder ignored In some problems, the remainder is ignored. Example Bobbi was making bookshelves for her room. she had 8 feet of lumber for shelves, and each bookshelf was 3 feet long. How many shelves could she make? 8 ÷ 3 = 2, with 2 feet of shelving remaining. She could make 2 shelves. The lumber she would have remaining after that is not enough for her to make another bookshelf. Remainder as the next highest whole number Sometimes a remainder requires the problem solution to be the next highest whole number. Example Ken bought hot dog buns for the picnic. He needed 60 buns in all. The buns were packaged in bags containing 8 each. How many packages of buns did he need to buy? 60 ÷ 8 = 7, with a remaind...

• Your answer should be • an integer, like 6 6 6 6 • a simplified proper fraction, like 3 / 5 3/5 3 / 5 3, slash, 5 • a simplified improper fraction, like 7 / 4 7/4 7 / 4 7, slash, 4 • a mixed number, like 1 3 / 4 1\ 3/4 1 3 / 4 1, space, 3, slash, 4 • an exact decimal, like 0.75 0.75 0 . 7 5 0, point, 75 • a multiple of pi, like 12 pi 12\ \text 2 / 3 pi 2, slash, 3, space, start text, p, i, end text penguins Check • Your answer should be • an integer, like 6 6 6 6 • a simplified proper fraction, like 3 / 5 3/5 3 / 5 3, slash, 5 • a simplified improper fraction, like 7 / 4 7/4 7 / 4 7, slash, 4 • a mixed number, like 1 3 / 4 1\ 3/4 1 3 / 4 1, space, 3, slash, 4 • an exact decimal, like 0.75 0.75 0 . 7 5 0, point, 75 • a multiple of pi, like 12 pi 12\ \text R start text, R, end text • Your answer should be • an integer, like 6 6 6 6 • a simplified proper fraction, like 3 / 5 3/5 3 / 5 3, slash, 5 • a simplified improper fraction, like 7 / 4 7/4 7 / 4 7, slash, 4 • a mixed number, like 1 3 / 4 1\ 3/4 1 3 / 4 1, space, 3, slash, 4 • an exact decimal, like 0.75 0.75 0 . 7 5 0, point, 75 • a multiple of pi, like 12 pi 12\ \text 2 / 3 pi 2, slash, 3, space, start text, p, i, end text Check • Your answer should be • an integer, like 6 6 6 6 • a simplified proper fraction, like 3 / 5 3/5 3 / 5 3, slash, 5 • a simplified improper fraction, like 7 / 4 7/4 7 / 4 7, slash, 4 • a mixed number, like 1 3 / 4 1\ 3/4 1 3 / 4 1, space, 3, slash, 4 • an exact decimal, like 0.75 0.75 0 . 7 5 ...

According to the Merriam-Webster Dictionary, the remainder is, “a remaining group, part, or trace/ the number left after a subtraction/ the final undivided part after the Understanding Remainder in Maths in Detail The remainder refers to the portion of the Suppose you have 23 chocolates and you want to divide it equally among 4 of your friends. So, how many will each friend get? How many chocolates will remain after distributing the chocolates equally? The answer is: Each friend will get 5 chocolates, so 20 chocolates can be distributed equally among 4 friends and 3 chocolates will remain which cannot be distributed. So, here, 23 is the dividend, 4 is the divisor, 5 is the quotient and 3 is the remainder. Remainder Formula As we know, Dividend = Divisor × Quotient + Remainder Accordingly, the remainder formula is given as: Remainder = Dividend - (Divisor × Quotient) In the above remainder formula, • The dividend is the number or value that is being divided. • The divisor is the number that divides another number. • The quotient is the result that is obtained after the division of two numbers. • The remainder is the value that is left after the division. How to Find the Remainder After a Division? We can't always show in pictures how we divide the number of things equally among the groups to find the remainder. Instead, we can use the Does McDonald’s Sell Cheeseburgers Daily? Step I: Does - D ivide the dividend by the divisor. Step II: McDonald’s - M ultiply the Step III: S...

Division and Remainders Sometimes when dividing there is something left over. It is called the remainder. Example: There are 7 bones to share with 2 pups. But 7 cannot be divided exactly into 2 groups, so each pup gets 3 bones, and there is 1 left over: We say: "7 divided by 2 equals 3 with a remainder of 1" And we write: 7 ÷ 2 = 3 R 1 As a Fraction It is also possible to cut the remaining bone in half, so each pup gets 3½ bones: 7 ÷ 2 = 3 R 1 = 3 ½ " 7 divided by 2 equals 3 remainder 1 equals 3 and a half" Play with the Idea Try changing the values here ... sometimes there will be a remainder: 19 cannot be divided exactly by 5. The closest we can get ( without going over) is: 3 x 5 = 15 which is 4 less than 19. So the answer of 19 ÷ 5 is: 19 ÷ 5 = 3 R 4 Check it by multiplying: 5 × 3 + 4 = 19 As a Fraction We can also make a fraction with: • the remainder on top, and • the number you are dividing by on the bottom, so we also have: 19 ÷ 5 = 3 R 4 = 3 4/ 5

Computational operation In modulo operation returns the Given two positive numbers a and n, a modulo n (often abbreviated as a mod n) is the remainder of the a by n, where a is the n is the For example, the expression "5 mod 2" would evaluate to 1, because 5 divided by 2 has a Although typically performed with a and n both being n is 0 to n − 1 inclusive ( a mod 1 is always 0; a mod 0 is undefined, possibly resulting in a When exactly one of a or n is negative, the naive definition breaks down, and programming languages differ in how these values are defined. Variants of the definition [ ] In least positive residue, the smallest non-negative integer that belongs to that class (i.e., the remainder of the In nearly all computing systems, the quotient q and the remainder r of a divided by n satisfy the following conditions: ( 1) However, this still leaves a sign ambiguity if the remainder is non-zero: two possible choices for the remainder occur, one negative and the other positive, and two possible choices for the quotient occur. In number theory, the positive remainder is always chosen, but in computing, programming languages choose depending on the language and the signs of a or n. n or a is negative (see the table under a modulo 0 is undefined in most systems, although some do define it as a. Quotient ( q) and remainder ( r) as functions of dividend ( a), using truncated division Many implementations use truncated division, for which the quotient is defined by q = [ a n ]...

• • • • • • What Is a Remainder in Math? A remainder is something which is “left over” or “remaining.” So, What does remainder mean in a division problem? The meaning of remainder is the leftover value or the remaining part after a division problem is called a remainder. In a division problem, there are two cases. • When a number is completely divisible by another number: In this case, we are not left with anything at the end of the division. • When a number is not divisible by another number: In this case, we are left with some value at the end of the division. We call it the “remainder” of the division. Definition of Remainder The definition of remainder in math can be given as the leftover number in a division problem . If the number is not completely divisible by another number, then we are left with a value, which is called remainder. A remainder is always less than the divisor. Parts of a Division The four important parts of any division problem are: • Dividend • Divisor • Quotient • Remainder In a division problem, the number that is being divided is called dividend. The number that divides the dividend is called divisor. The result of the division is called a “quotient.” When the dividend is not completely divided by the divisor, the leftover value is called “remainder.” Example: Divide 25 by 6. We know that $6\times4 = 24$ Thus, quotient $= 4$ and we are left with the remainder of 1. We can write this as $25 \div 6 \rightarrow 4 R 1$, where 4 is the quotient and 1...