Questions tagged [fractions]

Questions on fractions, i.e. expressions (not values) of the form $\frac ab$, including arithmetic with fractions. Not to be confused with the tag (rational-numbers): fractions denote rational numbers, but the same rational number may be written in different ways as a fraction.

A fraction is simply an expression $\frac{a}{b}$, where $a$ and $b$ are typically integers (where $b\neq 0$). This tag may be used, when $a$ and $b$ are more general expressions or algebraic objects; however, consider adding a more specific tag also:

Fractions are distinct from rational numbers because they are a representation: $\frac 34$ and $\frac{30}{40}$ are different fractions that happen to represent the same rational number.

For arithmetic with fractions, this tag is appropriate along with .

2981 questions
1
vote
1 answer

What fraction of smarties are brown?

If I have 26 smarties and 2 of them are brown, what fraction is that?
1
vote
1 answer

How to separate denominator?

I am sorry, it's probably very basic question, but I have great hole in head and can't figure it out. I need to separate denominator, like that: $ \frac { 1 } { n _ { 0 } + n _ { 1 } + n _ { 2 } + \ldots } = \frac { A } { n _ { 0 } } + \frac { B } {…
pajczur
  • 463
1
vote
1 answer

Want to Confirm Answer for the Sum of Fractions with Triangular Number Sequence as the Denominators

I am trying to compute the sum of these fractions: $$\frac{3}{1}+\frac{3}{1+2}+\frac{3}{1+2+3} + \dots + \frac{3}{1+2+3+\dots+100}.$$ I believe the denominators are a triangular number sequence, therefore the expression should convert to…
RC Wong
  • 57
1
vote
3 answers

fractions with negative numerators and denominators

I've been having this doubt in my mind.. I really don't get the concept behind fractions with negative numerators and denominators being equal to there positive form. For eg.: $\frac{-2}{-3} = \frac{2}{3}$. I tried to google it but there were no…
1
vote
1 answer

How can you predict the number of recurring digits when a rational recurring fraction is converted to a decimal?

How can you predict the number of recurring digits when a rational recurring fraction is converted to a decimal? For example how could I predict the number of recurring digits in 1/9 based off a rule for its denominator? If possible can you please…
Bunga
  • 21
1
vote
3 answers

How to illustrate "one divided by four"?

I was trying to create a video illustrating "one divided by four" by showing a circle being cut into four slices. However, I ran into a problem--namely once the circle had been cut into four slices, there were 4 one-fourths left on the screen. My…
1
vote
3 answers

Fraction and simplification

solve: $\frac{1}{x(x-1)} + \frac{1}{x} = \frac{1}{x-1}$ What are the possible answers ? (A) -1 (B) Infinitely Many Solutions (C) No solution (D) 0 The answer from where i've referred this is (B), but when i simplify it I get (D) My…
1
vote
2 answers

How solve the nedeed value of $t$ in this statement

What conditions must the parameter $t$ fulfill so that the equation: $x(1+4t) - 24 = 3xt - \frac{x}{2}$, have a unique solution ? I resolve it, but I think it was coincidence. This was: $x + 4xt - 24 = 3xt - \frac{x}{2}$ $3x - 48 = -2xt$ $3x + 2xt =…
ESCM
  • 3,161
1
vote
4 answers

Incorrect in solving $\frac{a}{b} - \frac{a}{c} = 1$ for $c$

I have this: $$\frac{a}{b} - \frac{a}{c} = 1$$ Solve for $c$. Then, $$\frac{a}{b} - \frac{a}{c} = 1 \cdot bc$$ $$ = ac - ab = bc$$ $$ = a(c - b) = bc$$ $$ c = \frac{bc}{a} + b$$ This is my final result. But the correct result…
ESCM
  • 3,161
1
vote
2 answers

Difference between fractions and rational numbers?

What is the difference between fractions and rational numbers? is $\frac{\pi}{1}$ a fraction?
rain
  • 9
1
vote
1 answer

Repeated division until the result is greater than a given number

I have a problem of repeated multiplication with a fraction (strictly less than 1), until the result is greater than a given number. For example: Let's say the given two numbers are 3 and 1.5. We have to multiply 3 repeatedly with 0.667 (say)…
Raghav
  • 65
1
vote
1 answer

finite fractions density (represented with 2 finite integers)

I'm trying to compare 2 types of data in programs: floating point decimals ($doubles$) and fractions (let's say $pair$), but it doesn't really matter for the question. So here is what I can't find nor do: I would like a exact expression,…
1
vote
3 answers

In a fraction between integers, what denominators produce a periodic result?

I'm trying to remember something that a math teacher told me many years ago about fractions. If I remember correctly he said that, in a fraction between integers, when the denominator is a multiple of $3$ or $7$, the result is a periodic number. Is…
Ither
  • 113
1
vote
1 answer

Relationships between denominator constants from fractional decomposition

Performing fractional decomposition on the fraction $\frac{a(x-c)+b}{(x-y_1)(x-y_2)}=\frac{A}{x-y_1} + \frac{B}{x-y_2}$ $\space$(1) where $x$ is a variable and the rest are constants, you find $A = \frac{a(y_1-c)+b}{y_1-y_2}$ $B =…
Andy
  • 45
1
vote
2 answers

In partial fractions, why must the degree of the numerator be lower than the denominator?

Specifically, it must be one degree lower. But why must it be smaller?