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

Equation transposition

I am struggling to see how an equation has been transposed. It is probably pretty easy, so apologies in advance. If possible; please show the transposition stages: $V_{out} = V1 . \frac{R2}{R1 + R2} (\frac{R3 + R4}{R3}) - V2 . \frac {R4} {R3}$ this…
martin
  • 11
1
vote
1 answer

Fast way to calculate Fraction

I want to solve this problem not by using common denominator. Is there any innovative and fast way ?. $$ {1 \over 6} + {4 \over 21} + {5 \over 84} + {7 \over 228} + {9 \over 532} =\ {\large ?} $$
1
vote
1 answer

Advanced GCSE Indices

At school, we've been asked to simplify the following: $$\left(\frac{S^{9/10}}{S^{3/5}}\right)^{-4}$$ I've given it a go but haven't been taught this yet. Could someone please explain the process which one would use?
Sylith
  • 111
1
vote
3 answers

Reduce a fraction

Given the function $f(x)=\frac{x^2-5}{x+\sqrt{5}}$ If I draw this function in maple, I will get a line. How can that be true? I should expect a line except in area of $x = -\sqrt{5}$, where $f(x) \rightarrow \infty$ or $f(x) \rightarrow -\infty $.…
Hamid Mohammad
  • 161
  • 1
  • 1
  • 7
1
vote
2 answers

If $a +b $,= 5 and $ab = 6$ . Find $\frac{1}{a}$ + $\frac{1}{b}$

$a +b $ = 5 and $ab = 6$ . Find $\cfrac{1}{a}$ + $\cfrac{1}{b}$ Any Ideas on how to begin? Many Thanks
1
vote
1 answer

can someone explain rates to me? (spec. question inside)

i noticed that i've been getting this type of question consistently wrong, in the new sat prep. i'm not sure what kind of problem it exactly is either, so i could not find an explanation. i would really appreciate it if you could explain this whole…
erin
  • 13
1
vote
3 answers

A fraction problem

$$a = x + \frac1x \\b =y + \frac1y \\ c = xy +\frac1{xy} $$ Express $c$ in terms of $a$ and $b$
sidt36
  • 261
1
vote
1 answer

Auto loan calculator website widget

I was going to try my luck on StackOverflow, but I have a feeling my issue here is on order of operations. I'm using the loan calculation found here to build a loan calculator for a clients…
Joe
  • 11
1
vote
2 answers

find a value of x in a fraction

Can anyone help me with this? I don't know where to start. I assume there is a trick. Fine the value of x if $$ \frac{1}{1 + \frac{1}{2 + \frac{1}{3 + \frac{1}{4 + \frac{1}{x}}} } } \ \ = \ \ \frac{67}{96} \ \ , $$
user321645
1
vote
1 answer

Is there a positive integer n such that the fraction $(9n+5)/(10n+3)$ is not in the lowest term?

Is there a positive integer n such that the fraction $(9n+5)/(10n+3)$ is not in the lowest term? Please explain. I found $n=2$ be a solution. Is it correct?
Raj
  • 69
1
vote
3 answers

fraction division understanding

Want to visualize rule division of fraction. For example 1) 2 2 4 _ * _ = _ 2 3 6 in this case we "split" each piece of cake in numerator to the 2 "first fraction" and apply the same operation for the denominator. Could you please…
student
  • 183
1
vote
1 answer

Fraction involving Surds

Fraction involving Surds. Can anyone please show me the working out? $$ \frac{(\sqrt{6}-1)}{\sqrt{3}} + \frac{(\sqrt{6}+2)}{2\sqrt{3}} $$ I did this and it was incorrect: $$ 2\sqrt{3}(\sqrt{6}-1) + \frac{\sqrt{3}(\sqrt{6} + 2)}{\sqrt{3}\times…
Enzo
  • 13
1
vote
1 answer

simple multiplication question: multiplying radial fractions

I'm having a bit of brain block right now. In order to multiply any fractions you simply reduce to lowest form, then multiply num., then denom. When I tried with fractions in radian form it didn't work out so well. consider: $(6 \pi/5)(2 \pi/3$) If…
1
vote
2 answers

KhanAcademy nested fractions problem

So I was given a problem at KA today. They offer you a choice among possible simplified versions of this expression: $$\frac{1+\frac{x}{y}}{\frac{x}{y}}$$ My solution…
wswld
  • 115
1
vote
5 answers

How to raise a fraction to a fractional exponent?

I am trying to simplify this but I'm not sure how to approach it.
123
  • 807