1. Simple Fractions Questions:

so im taking an online algebra course:
and when its reached the subject of adding fraction (in this case three)
the instructor explains that we need to find the lowest common denominator.
And he shows to ways to do it the first one is simply to make a list of all the multiples
of each denominator and then find locate the lowest common multiple.

The second is is to multiply all the denominators and then use the result as the common denominator,

it gave me somewhat of a head scratchier.
Witch time is the best to use each method?

Multiplication

can any one provide me with a good way to multiply big fractions without a calculator?
Thanks!

2. Re: Simple Fractions Questions:

Both methods will, eventually, give the correct answer- but the first method is almost always simplest.

For example, suppose the problem is to add $\displaystyle \frac{3}{14}+ \frac{2}{15}+ \frac{1}{6}$. I note that 14= 2(7), 15= 3(5), and 6= 2(3). The least common denominator must have factors of 2, 3, 5, and 7: 2(3)(5)(7)= 210. 14= 2(7) divides into 210 3(5)= 15 times so to get a denominator of 210 for the fraction $\displaystyle \frac{3}{14}$ we must multiply both denominator and numerator by 15: [tex]\frac{3(15)}{14(15)}= \frac{45}{210}. Similarly multiplying both denominator and numerator of $\displaystyle \frac{2}{15}$ by 2(7)= 14 gives $\displaystyle \frac{28}{210}$ and multiplying both denominator and numerator of $\displaystyle \frac{1}{6}$ by 3(15)= 45 gives [tex]\frac{45}{210}.

So $\displaystyle \frac{3}{14}+ \frac{2}{15}+ \frac{1}{6}= \frac{45}{210}+ \frac{28}{210}+ \frac{45}{210}= \frac{45+ 28+ 45}{210}= frac{118}{210}$. Both numerator and denominator are even so divisible by 2: that fraction can be reduced to $\displaystyle \frac{59}{105}$.

Now, if you prefer "tedious computation" to "thinking" you can do away with factoring the denominators to get the least common denominator-210 you can just get a common denominator by multiplying all the denominators together: $\displaystyle (14)(15)(6)= 1260$. To get the first fraction, $\displaystyle \frac{3}{14}$, to that denominator, multiply denominator and numerator by the other denominators, 15(6)= 90: $\displaystyle \frac{270}{1260}$. To get the second fraction, $\displaystyle \frac{2}{15}$, to that denominator multiply denominator and numerator by the other denominators, 6(14)= 84: $\displaystyle \frac{168}{1260}$. To get the third fraction, $\displaystyle \frac{1}{6}$, to that denominator multiply denominator and numerator by the other denominators, 14(15): $\displaystyle \frac{210}{1260}$.

So now we have $\displaystyle \frac{3}{14}+ \frac{2}{15}+ \frac{1}{6}= \frac{270}{1260}+ \frac{168}{1260}+ \frac{210}{1260}$. I will leave that for you to work out- if you want to!

3. Re: Simple Fractions Questions:

To multiply fractions that have larger numbers, you could reduce the fractions, if possible, before you multiply.