How To Solve Fraction Problems Step By Step Contrast Compare Essay
In general, The quotient of two fractions equals the product of the dividend and the reciprocal of the divisor.
That is, to divide one fraction by another, we invert the divisor and multiply.
Thus, We subtract fractions with unlike denominators in a similar way that we add such fractions. We build each fraction to an equivalent fraction with this denominator to get Now, adding numerators yields Again, special care must be taken with binomial numerators.
However, we first write each fraction in standard form. Example 2 Write the difference of as a single term.
One case is In general, Example 3 When the fractions in a quotient involve algebraic expressions, it is necessary to factor wherever possible and divide out common factors before multiplying.
Example 4 The sum of two or more arithmetic or algebraic fractions is defined as follows: The sum of two or more fractions with common denominators is a fraction with the same denominator and a numerator equal to the sum of the numerators of the original fractions.
The product of two fractions is defined as follows.
The product of two fractions is a fraction whose numerator is the product of the numerators and whose denominator is the product of the denominators of the given fractions.
Thus, the LCD of the fractions because this is the simplest expression that is a multiple of each of the denominators.
This is precisely the same notion as that of dividing one integer by another; a ÷ b is a number q, the quotient, such that bq = a. To solve this equation for q, we multiply each member of the equation by .
Thus, In the above example, we call the number the reciprocal of the number .
Example 3 When the fractions contain algebraic expressions, it is necessary to factor wherever possible and divide out common factors before multiplying. Solution First, we must factor the numerators and denominators to get Now, dividing out common factors yields We now multiply the remaining factors of the numerators and denominators to obtain Note that when writing fractional answers, we will multiply out the numerator and leave the denominator in factored form.
Very often, fractions are more useful in this form.