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
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How to remove square roots from denominator in $\frac{\sqrt{x}+\sqrt{y}}{\sqrt{x}-\sqrt{y}}$?

I have this math problem: Remove all square roots in the denominator of $\frac{\sqrt{x}+\sqrt{y}}{\sqrt{x}-\sqrt{y}} = ?$ The obvious solution is to multiply the fraction with…
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Calculating the difference between Numerator and Denominator - a feasible way of determining the smallest/largest fraction

Building on this question on SO, when comparing positive fraction to determine which is the largest/smallest, is it safe to consider the absolute difference between the Numerator and Denominator, assuming the fractions are in the lowest forms?…
Abrar
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Reducing fractions

How can I get [if it's possible]: $$ 2- \frac{1}{n+1} $$ from this: $$2- \frac{1}{n} + \frac{1}{n(n+1)} $$ EDIT: I started like this: $$2- \frac{1}{n} + \frac{1}{n(n+1)}= 2-\frac{n+1}{n(n+1)}+\frac{1}{n(n+1)} =2-\frac{n+2}{n(n+1)} $$ How do I…
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Stuck on candy bowl fraction

I am really stuck on this problem because I'm not even sure where to start. Larissa has a bowl of candies. On the first day, she eats 1/2 of the candies plus one more. On the second day, she eats 1/3 of the remaining candies plus one more. On the…
sug123
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Basic division problem: dividing a fraction by a fraction

I thought I clearly knew how to divide fractions by fractions until I came across this problem. Please can somebody let me know where I am going wrong? Here is what we start with. $(1-2x)/(2x^1/2)/e^x$ It then becomes $(1-2x)/(2e^x)*(x^1/2)$ I…
JKong
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Help with fractions

I have attached an image of which I have a question about. I don’t understand how you can get from equation 1 to equation 2. Could someone please explain…
David777
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Confusion Dividing A Fraction with a Whole Number...

In the lesson I am doing, I divide fractions. Here is my problem: 28/55 / 7 I had to look up how to do this problem. According to Math Is Fun, you divide the denominator by the whole number and then simplify if possible. I did this, and…
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Fractions swapped

I am following an electronics tutorial (slide 23 here) and at some point, he shows the formula: $\frac{Vs}{Ri} + \frac{Vo}{Rf} = 0$ Vs, Ri, Vo and Rf are just variables for voltage and resistance. After some rearanging, it becomes: $\frac{Vo}{Vs} =…
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Correct way of displaying different base equality

Given any fractional number in any base, for example $0.5_{10} = 0.8_{16}$, pretty simple as this gives no recurring fractional numbers. However, given $0.255_{10} = \overline{\text{4147AE}_{_{16}}}$ is a conversion that has a recurring fractional…
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How to divide and set an increment within a total?

I have total=90. I want to divide this number between 5 employees. For each employee from the second, I want to add an increment of 30% but the sum must remain 90. Variables: employees=5; total=90; increment=30% E.g. Employee Partial 1st …
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Can I cancel the factor $\ n-1$'s in $\frac{n-1}{n(n-1)(n-2)}$?

In the equation $$\frac{n-1}{n(n-1)(n-2)!} = \frac{1}{n(n-2)!} $$ can I cancel out the factors $(n-1)$'s in the numberator and denominator, so the equation is equal? I've learned that you can't cross anything if there is a + or - sign in the…
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If there is a negative sign beside the fraction bar, does that mean the numerator and denominator are both negative?

In math, sometimes I see a negative symbol beside the fraction bar. Does that mean both the numerator and the denominator are negative, or just the numerator?
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Interpreting the "bar" in an expression like $x=2.\left[1/2+\{4-(3\times\overline{2+3}\}\right]$

In the mathematics book of 6th grade, there is a chapter about fractions and grouping operators like (), {}, [] and fourth - the horizontal bar ________ which is placed over a math expression like the example given…
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Problem with getting variable by itself in fraction.

I have a problem that looks something like this: The difference of the quotient of a number and $-2$ from $12$ is $15$. So I started off like this: $12-\displaystyle\frac{x}{-2}=15$ Then I subtracted the $12$ from both sides to…
user60161
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One-step equations with negatives (Fractions)

I am solving the one-step equation: $$-\frac{3}{4}\alpha = \frac{5}{4}$$ In the answer sheet it says to multiply both sides by the "reciprocal" $-\dfrac{4}{3}$. In one step equations you are supposed to do the opposite on both sides and in this…
user549013