Examples of fraction in the following topics:
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- A complex fraction is one in which the numerator, denominator, or both are fractions, which can contain variables, constants, or both.
- A complex fraction, also called a complex rational expression, is one in which the numerator, denominator, or both are fractions.
- From previous sections, we know that dividing by a fraction is the same as multiplying by the reciprocal of that fraction.
- You'll find that the common denominator of the two fractions in the numerator is 6, and then you can add those two terms together to get a single fraction term in the larger fraction's numerator:
- Recall, again, that dividing by a fraction is the same as multiplying by the reciprocal of that fraction:
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- Mole fractions are dimensionless, and the sum of all mole fractions in a given mixture is always equal to 1.
- What is the mole fraction of nitrogen in the mixture?
- What is the mole fraction of NaCl?
- We can now find the mole fraction of the sugar:
- Mole fraction increases proportionally to mass fraction in a solution of sodium chloride.
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- A fraction represents a part of a whole.
- Find a common denominator, and change each fraction to an equivalent fraction using that common denominator.
- To subtract a fraction from a whole number or to subtract a whole number from a fraction, rewrite the whole number as a fraction and then follow the above process for subtracting fractions.
- To multiply a fraction by a whole number, simply multiply that number by the numerator of the fraction:
- The process for dividing a number by a fraction entails multiplying the number by the fraction's reciprocal.
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- Root rationalization is a process by which any roots in the denominator of an irrational fraction are eliminated.
- In mathematics, we are often given terms in the form of fractions with radicals in the numerator and/or denominator.
- This same principal can be applied to fractions: whatever we do to the numerator, we must also do to the denominator, and vice versa.
- You are given the fraction $\frac{10}{\sqrt{3}}$, and you want to simplify it by eliminating the radical from the denominator.
- Therefore, multiply the top and bottom of the fraction by $\frac{\sqrt{3}}{\sqrt{3}}$, and watch how the radical expression disappears from the denominator:$\displaystyle \frac{10}{\sqrt{3}} \cdot
\frac{\sqrt{3}}{\sqrt{3}}
= {\frac{10\cdot\sqrt{3}}{{\sqrt{3}}^2}} = {\frac{10\sqrt{3}}{3}}$
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- For example, are there certain contexts when fractions representations are easier to operate with than decimal fractions?
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- The value of money and the balance of the account may be different when considering fractional time periods.
- But what happens if we are dealing with fractional time periods?
- In the case of fractional time periods, the devil is in the details.
- You can plug in a fractional time period to the appropriate equation to find the FV or PV.
- Calculate the future and present value of an account when a fraction of a compounding period has passed
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- A fractional reserve system is one in which banks hold reserves whose value is less than the sum of claims outstanding on those reserves.
- This is called the fractional-reserve banking system: banks only hold a fraction of total deposits as cash on hand.
- Because banks are only required to keep a fraction of their deposits in reserve and may loan out the rest, banks are able to create money.
- Fractional-reserve banking ordinarily functions smoothly.
- Examine the impact of fractional reserve banking on the money supply
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- In algebra, partial fraction decomposition (sometimes called partial fraction expansion) is a procedure used to reduce the degree of either the numerator or the denominator of a rational function.
- We can then write $R(x)$ as the sum of partial fractions:
- We have rewritten the initial rational function in terms of partial fractions.
- We have solved for each constant and have our partial fraction expansion:
- There are some important cases to note, for which partial fraction decomposition becomes more complicated.
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- Then you rewrite the two fractions with this denominator.
- The denominator in the second fraction can not be factored.
- The first fraction has two factors: $y$ and $(x^2+2)$.
- The second fraction has one factor: $(x^2 + 2)$.
- We then rewrite both fractions with the common denominator.