Pre algebra fractions

Question

I wanted to know why I couldn't cancel out the common factors in 14/15 / 7/12, I did flip them 14/15 * 12/7 when I did it the informal way I got 1 3/5 which was right but when I did it the formal way just to check I got 2 2/3? So my question is why couldn't or shouldn't I cancel out the common factor.

Thanks in Advance!

Answer 1

Hi Senib,

You are correct to multiply the first fraction (14/15) by the reciprocal of the second fraction (12/7).

And, you can cross-cancel the common factors between the denominator 15 and the numerator 12 because they are located diagonally across from one another in the equation.

3 is the greatest common factor of 12 and 15. Cross-cancel those two numbers with 3, and the 12 becomes 4 while the 15 becomes 5.

You can also cross-cancel the common factors between the numerator 14 and the denominator 7 because they are located diagonally across from one another in the same equation.

7 is the greatest common factor of 7 and 14. Cross-cancel those two numbers with 7, and the 14 becomes 2 while the 7 becomes 1.

Upon cross-cancelling all around, you now have 2/5 x 4/1.

Multiply the two reduced-simplified fractions by one another and you get 8/5 (1 3/5 as a converted mixed number from the given improper fraction) for your final answer!

I hope this helps!

Answer 2

I am not sure what you are referring to as the informal/formal ways of doing this arithmetic.

Problem: (14/15) / (7/12)

Both fractions are already in simplest form...so there is no reducing the original fractions (14/15) and (7/12).

However, when you flip and multiply, you can cancel a common factor.

Method:

(14/15) / (7/12)

(14/15) * (12/7)

[ 14/ (5*3) ] * [ (4*3) / 7] <------ here, you can cancel a factor of 3.

(14/5 ) * (4 / 7)

56 / 35

Common factors are cancelled in order to reduce the fraction. In order to reduce a fraction, one needs to divide the numerator and denominator by the same factor. (ie 3/6 becomes 1/2 when you divide the numerator and denominator by 3.... notice that 3 is a common factor here because 3/6 can also be written as (3*1) / (3*2).

Lets look at the original problem again.

(14/15) * (12/7)

[ 14/ (5*3) ] * [ (4*3) / 7]

[14(4*3)] / [ (5*3)7 ] <----- you can cancel a factor of 3 because it ends of being in the numerator and denominator.

14(4) / 5(7)

56 / 35

Also, unless your teacher requires you to use proper fractions, improper fractions are more than okay to use (just be sure to simplify final answers).