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**The remainder operator can be used with negative integers**. The rule is: Perform the operation as if both operands were positive. If the left operand is negative, then make the result negative.**Remainder can never be a negative number**. Consider this — 12/7=1+(5/7), and not 2-(2/7). Hence, the remainder is 5 and not -2. Remainder is something you get when you divide a number by another number and the number isn’t a multiple of the other number.This means that **n is 15 less than a multiple of 13** i.e. actually 2 less than a multiple of 13 because when you go back 13 steps, you get another multiple of 13. This gives us a negative remainder of -2 which means the positive remainder in this case will be 11.

Table of Contents

## Is it possible for a remainder to be negative?

**Remainder can never be a negative number**. Consider this — 12/7=1+(5/7), and not 2-(2/7). Hence, the remainder is 5 and not -2. Remainder is something you get when you divide a number by another number and the number isn’t a multiple of the other number.

## What does it mean to have a negative remainder?

This means that **n is 15 less than a multiple of 13** i.e. actually 2 less than a multiple of 13 because when you go back 13 steps, you get another multiple of 13. This gives us a negative remainder of -2 which means the positive remainder in this case will be 11.

### Remainder Theorem (Using Negative Remainders)

### Images related to the topicRemainder Theorem (Using Negative Remainders)

## Can a remainder be negative in synthetic division?

You can write the final answer in two ways. The first one is **using the minus or subtraction symbol to indicate that the remainder is negative**. The second one is using the + symbol but attaching a negative symbol to the numerator. They mean the same thing!

## Is the remainder always positive?

We indeed often want uniqueness of q and r. But long division algorithm is only practical if q is rounded towards zero (truncated) and that leads to negative (non-positive) remainder for negative numerator. But **Euclidean division defines remainder as positive (non-negative)**.

## Is a divided by a positive?

…

Summary.

Expression | Quotient | Example |
---|---|---|

positive ÷ positive | positive | 6 ÷ 2 = 3 6\div 2=3 6÷2=3 |

negative ÷ negative | positive | − 6 ÷ ( − 2 ) = 3 -6\div (-2)=3 −6÷(−2)=3 |

## What will be the remainder when is divided by 5?

No. 31) 31. On dividing a number by 5, we get **3** as remainder.

## Can a remainder be greater than the divisor?

Properties of Remainder:

The remainder is always less than the divisor. **If the remainder is greater than the divisor, it means that the division is incomplete**. It can be greater than or lesser than the quotient. For example; when 41 is divided by 7, the quotient is 5 and the remainder is 6.

## See some more details on the topic can a remainder be negative here:

### All About Negative Remainders on the GMAT | Veritas Prep

Generally speaking, if n is divided by m and it leaves a remainder r, the negative remainder in this case is -(m – r). When n is divided by 7, …

### Finding the remainder when dividing negative numbers

Just like in multiplication, when one but not both numbers are negative, the answer will be negative. If both numbers are negative, the answer will be positive.

### Dividing by Binomials and Polynomials

You can write the remainder using the symbol R, or as a fraction added to the rest of the quotient with the remainder in the numerator and the divisor in the …

### Can the remainder be negative? – 1200Artists

The remainder operator can be used for negative integers. The rules are:… Make the result negative if the left operand is negative.

## What is the remainder theorem formula?

The remainder theorem formula is: **p(x) = (x-c)·q(x) + r(x)**. The basic formula to check the division is: Dividend = (Divisor × Quotient) + Remainder.

## What is remainder and factor theorem?

Remainder Theorem states that if polynomial ƒ(x) is divided by a linear binomial of the for (x – a) then the remainder will be ƒ(a). Factor Theorem states that if ƒ(a) = 0 in this case, then the binomial (x – a) is a factor of polynomial ƒ(x).

### Concept of a NEGATIVE Remainder

### Images related to the topicConcept of a NEGATIVE Remainder

## What is the difference between factor theorem and remainder theorem?

Basically, **the remainder theorem links remainder of division by a binomial with the value of a function at a point, while the factor theorem links the factors of a polynomial to its zeros**.

## Can negative numbers divisible?

Rule 3: **a negative number divided by a negative number equals a positive number**. Two negatives make a positive, so a negative number divided by a negative number equals a positive number. For example, -8 / -2 = 4.

## What is a negative divide by a negative?

Like a negative divided by a negative will **always be positive**.

## Do two negatives divided make positive?

**When you divide two negative numbers, the answer is always a positive number**. For example, -4 divided by -2 equals 2. When both numbers are negative, the negatives cancel out, resulting in the answer always being a positive number.

## Which is quotient and remainder?

3.1 Quotients and Remainders

The number of times we have subtracted is called the quotient (of the division of by ) The number that is leftover from after subtracting as often as possible is called the remainder (of the division of by ).

## What does mod 7 mean?

a X b (mod 7), **equals the**. **obtained when the ordinary**. **and b is divided by 7**.

## Is positive times negative positive?

**When you multiply a negative number to a positive number, your answer is a negative number**. It doesn’t matter which order the positive and negative numbers are in that you are multiplying, the answer is always a negative number. The answer is -2 x 4 = -8.

### How to Find the Remainder and Quotient when Dividing a Negative Integer by a Positive One

### Images related to the topicHow to Find the Remainder and Quotient when Dividing a Negative Integer by a Positive One

## Is zero a whole number?

The whole numbers are the numbers 0, 1, 2, 3, 4, and so on (the natural numbers and zero). Negative numbers are not considered “whole numbers.” All natural numbers are whole numbers, but not all whole numbers are natural numbers since **zero is a whole number but not a natural number**.

## Why is a negative divided by a negative a positive?

Any negative number divided by negative then it’ll be positive **because the negative signs will be canceled** that’s the reason you’ll get a positive number. , former Taught Math & Science for Over 25 Years. Originally Answered: Why does dividing a negative by a negative equal a positive?

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