# Questions tagged [fractional-part]

For questions related to the fractional part of a number.

331 questions
Filter by
Sorted by
Tagged with
35 views

### Understanding why a fraction is the same as a division problem

I am trying to understand why fractions are another way to write division. I haven't seen a satisfying explanation for this yet. I know that division when we say for example a divided by b is like ...
130 views

• 2,088
443 views

• 63
114 views

### Solve the equation: $\frac{x^2 - 2x + 3}{\lbrace x\rbrace} + \frac{2023}{2}{\lbrace x\rbrace} = 2\lfloor x \rfloor + 88$

Problem Solve the equation $\frac{x^2 - 2x + 3}{\lbrace x\rbrace} + \frac{2023}{2}{\lbrace x\rbrace} = 2\lfloor x \rfloor + 88$, where $\lfloor x \rfloor$ and $\{x\}$ are the greatest integer less ...
• 167
82 views

### Why is $\{x/2\}$ always either $\{x\}/2$ or $\{x\}/2 + 1/2$?

I was working on a problem involving floor functions and fractional parts. The question is to prove that $\lfloor x \rfloor - 2 \cdot \lfloor \frac{x}{2} \rfloor$ is either $0$ or $1$. In one of the ...
1 vote
49 views

### Question regarding finding domain .. want to know is there any better method

We need to find the domain of $$\dfrac{1}{[x]^2-x-2\{x\}}$$ I tried to find where the denominator is becoming $0$, then I will remove those value of real numbers and I will have my domain. Simplifying ...
• 159
92 views

• 123
1 vote
55 views

### Upper limit of sequence involving the fractional part

In the survey "The Problems Submitted by Ramanujan to the Journal of the Indian Mathematical Society", the lower limit of the sequences $n\{n\sqrt 2\}, n\{n\sqrt 3\}$, where $\{\cdot\}$ ...
60 views

1 vote
106 views

### Find the real numbers $x$ such that $\{x\} =\frac {x-3}{2\lfloor x\rfloor-5}.$

Determine the real numbers that verify the relation $$\{x\} =\frac {x-3}{2\lfloor x\rfloor-5}$$ where $\{x\}$ represents the fractional part, respectively $\lfloor x\rfloor$ represents the whole part ...