Why do you need to change a mixed number to an improper fraction?

Answer 1

When you are adding, subtracting, multiplying, or especially dividing fractions and mixed numbers, it is much easier to use improper fraction forms. You do not have to worry about borrowing, or separate calculations for the wholes and fractions.

Examples:

(4 2/3 - 1 5/6)

Convert the mixed numbers to 14/3 - 11/6 ,

then into common denominators 28/6 - 11/6

and you can find the answer is 17/6 which is also the mixed number 2 5/6

(1 3/5 x 3 3/4)

Converting, these are 8/5 x 15/4, and

multiplying numerators and denominators gives you 120/20 = 6

which is a simple result that was not immediately obvious.

(3 3/4 divided by 1 5/8)

Converting, these become 15/4 divided by 13/8 and you divide

by multiplying by the reciprocal (invert the second fraction)

which gives you 15/4 x 8/13 which is 120/52 = 2 16/52 = 2 4/13