# How can we rewrite a modulus function?

• MHB
• Nousher Ahmed
In summary, a modulus function is a mathematical function that gives the remainder when one number is divided by another. It can be rewritten to make solving equations or graphing easier, and can also be rewritten as a piecewise function. To remove the absolute value, we can use the rule |x| = x for positive values of x and |x| = -x for negative values of x. Other methods, such as using the square root or floor function, can also be used to rewrite a modulus function.
Nousher Ahmed
We can rewrite |x-3|<10 in the following way.

-10<x-3<10

But can rewrite |x-3|+|x+1|+|x|<10 in the following way?

-10<x-3+x+1+x<10.

If we cannot, will anybody please explain why we cannot?

You can't write it that way because it's not in general correct.

You can write it as a union of such rules though.

In this case it appears to be

$(x < -\dfrac 8 3) \cup (4 < x)$

## 1. What is a modulus function?

A modulus function, also known as a modulo function, is a mathematical operation that calculates the remainder when one integer is divided by another integer.

## 2. How can we rewrite a modulus function using division and subtraction?

A modulus function can be rewritten using division and subtraction as follows: a % b = a - (a/b)*b. This formula calculates the remainder when a is divided by b.

## 3. What is the purpose of using a modulus function?

The purpose of using a modulus function is to find the remainder when dividing two integers. This can be useful in various mathematical calculations, such as determining if a number is even or odd, or in cryptography for generating random numbers.

## 4. Can a modulus function be used with decimal numbers?

No, a modulus function is typically used with integers. However, some programming languages have a "mod" operator that can be used with decimal numbers.

## 5. How can we use a modulus function to solve equations?

A modulus function can be used to solve equations by finding the remainder when dividing two integers. This remainder can then be used to determine the value of a variable in the equation.

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