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.
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Fraction word problem that a total includes uneven groups
There are red, blue and yellow pens in a box.
The ratio of the number of red pens to blue pens is 2:3.
The ratio of the number of yellow pens to the total number of red and blue pens is 5:6.
What ...
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Which numbers are sums of finite numbers of reciprocal squares?
Question: Is there a “nice” characterization of rational numbers $q$ for which $q$ can be written as
$$q = \frac{1}{n_1^2} + \frac{1}{n_2^2} + \dots + \frac{1}{n_k^2}$$
for distinct natural numbers $...
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AMC 10 Math Question Using Algebraic Manipulation [closed]
What is the greatest integer less than or equal to $\frac{3^{100} + 2^{100}}{3^{96} + 2^{96}}?$
$({\rm A}) \, 80 \qquad ({\rm B}) \, 81 \qquad ({\rm C}) \, 96 \qquad ({\rm D}) \, 97 \qquad ({\rm E}) \,...
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question about fraction axioms,proofs of properties of fractions [duplicate]
I want to ask a question as a university student) I really love strict and complete mathematics. I don’t like to learn and cram something and I want to understand and axiomize. I want to ask a ...
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Properties of Nth roots and fractional powers
Context: I'm programming an arbitrary precision math library and created some weird algorithms to calculate a number raised to non-integer powers due to optimizations.
From my understanding, raising ...
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Simple question regarding fraction to ratio conversions
Supposed you have a ratio expressed
in the form 4:8 . How do we convert this to fraction?
One answer gives me 1/2 in its simplest form. Chatpt produces the same result
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How to combine divisions and fractions?
On my Facebook-account, regularly I see questions about calculations, like $1 \div \frac{1}{2}$, which makes me doubt if this equals $0.5$ or $2$.
I remember from my childhood that such notation was ...
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How to find x if its in the denominator and on the other side of equal sign. [duplicate]
$$\frac{a}{b+xc} = x $$
So I have $x$ in the denominator on the left side and also $x$ on the right.
$a$, $b$, and $c$ are known and I need to find out for $x$. How should I go about it?
Edit: Thanks ...
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Can i take the reciprocal of both sides of an equation?
I have the following equation, which i am supposed to solve for $s_{0,4}$:
$$P=\frac{C}{1+s_{0,1}}+\frac{C}{(1+s_{0,2})^2}+\frac{C}{(1+s_{0,3})^3}+\frac{C+F}{(1+s_{0,4})^4}$$
which I rearranged in the ...
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Dividing 4 individual numbers. [closed]
So obviously dividing (3/4)/(3/4) would be the same as (3/4) x (4/3) which is 1. Or dividing 3/5/5 would be like doing 3/5 x 1/5 which is 3/25. But, what if you have four individual numbers what's the ...
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If $u$, $v$ and $w$ are the digits of decimal system, then the rational number represented by $0.uw\overline{uv}$ is?
Context
I was recently giving a math test and encountered the following question:
If $u$, $v$ and $w$ are the digits of decimal system, then the rational number represented by $0.uw\overline{uv}$ is?
...
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Fraction word problem that dividing a whole into equal parts
Alice, Grace and Pauline shared the cost of a present for their father equally. Alice used $\frac{2}{3}$ of her money, Grace used $\frac{3}{4}$ of her money, Pauline used $\frac{2}{5}$ of her money.
...
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Converting $\frac{1}{s^3+a_2s^2+a_1s+a_0}$ to a product of second and first order terms
I am dealing with a transfer function of the form
$$H(s) = \frac{1}{s^3+a_2s^2+a_1s+a_0}$$
where the coefficients are real but unknown. Is it always possible to convert the transfer function to a ...
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Partial fractions with a repeated factor [duplicate]
I am looking to find a derivation, or a intuitive explanation as for why a partial fraction with a repeated factor needs to include a factor in the expansion for each power possible. How does one ...
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Determining denominator of partial fractions
Before, integrating, we can often split a fraction into its partial fractions to make the integration process significantly more simple. However, I have realised that this fraction we can split can ...
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