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In mathematics, a ratio (/ ˈreɪʃ (i) oʊ /) shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ratio 4:3). Similarly, the ratio of lemons to oranges is 6:8 (or 3:4) and the ...
A ratio is often converted to a fraction when it is expressed as a ratio to the whole. In the above example, the ratio of yellow cars to all the cars on the lot is 4:12 or 1:3. We can convert these ratios to a fraction, and say that 4 / 12 of the cars or 1 / 3 of the cars in the lot are yellow.
Mole fraction is numerically identical to the number fraction, which is defined as the number of particles (molecules) of a constituent Ni divided by the total number of all molecules Ntot. Whereas mole fraction is a ratio of amounts to amounts (in units of moles per moles), molar concentration is a quotient of amount to volume (in units of ...
A finite regular continued fraction, where is a non-negative integer, is an integer, and is a positive integer, for . A continued fraction is a mathematical expression that can be writen as a fraction with a denominator that is a sum that contains another simple or continued fraction. Depending on whether this iteration terminates with a simple ...
Mass fraction (chemistry) In chemistry, the mass fraction of a substance within a mixture is the ratio (alternatively denoted ) of the mass of that substance to the total mass of the mixture. [1] Expressed as a formula, the mass fraction is: tot {\displaystyle w_ {i}= {\frac {m_ {i}} {m_ {\text {tot}}}}.} Because the individual masses of the ...
Cross-multiplication. In mathematics, specifically in elementary arithmetic and elementary algebra, given an equation between two fractions or rational expressions, one can cross-multiply to simplify the equation or determine the value of a variable. The method is also occasionally known as the "cross your heart" method because lines resembling ...
In order to convert a rational number represented as a fraction into decimal form, one may use long division. For example, consider the rational number 5 / 74 : 0.0 675 74 ) 5.00000 4.44 560 518 420 370 500 etc. Observe that at each step we have a remainder; the successive remainders displayed above are 56, 42, 50.
Proportion of the total volume of a constituent part. In chemistry and fluid mechanics, the volume fraction is defined as the volume of a constituent Vi divided by the volume of all constituents of the mixture V prior to mixing: [1] {\displaystyle \varphi _ {i}= {\frac {V_ {i}} {\sum _ {j}V_ {j}}}.} Being dimensionless, its unit is 1; it is ...
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