Mixed fractions can be multiplied and divided just like standard fractions once they are rewritten into the form of improper fractions. This article will explain how this process works.

Fractions include two parts: a numerator and a denominator. Improper fractions also include the same two parts except that the numerator is greater than the denominator. Mixed fractions on the other hand include an integer term along with the numerator and denominator. Mixed fractions are essentially the same thing as improper fractions, they are just written differently. An improper fraction can be transformed into the mixed fraction form by dividing the denominator into the numerator. Since the numerator is greater than the denominator, the denominator will divide evenly into the numerator some number of times, this is the integer term. The remainder that is left over after the division will result in a fraction with a new numerator and the original denominator. An example shows this quite clear. The fraction, ^{17}/_{4} is an improper fraction and to rewrite this into a mixed fraction, we will divide the denominator of 4 into the numerator of 17. 4 can be divided into 17, 4 times, so 4 is our integer term. Since 4 times 4 is 16, we are left with a remainder of 1 which is the numerator of our new fraction that also includes the old denominator, so we have 4 ^{1}/_{4}.

To rewrite mixed fractions into improper fractions, we must simply do the opposite of the procedure above. Recognizing that in a mixed number, the integer term is the number of times the denominator goes evenly into a large numerator, we realize that multiplying the integer term by the denominator and adding the remainder in the numerator will give us the numerator of the improper fraction, whereas the denominator remains unchanged. An example will further explain this. Consider we want to rewrite the mixed number of 4 ^{2}/_{9} into the form of an improper fraction. We see that 4 (the integer term) x 9 (the denominator) gives 36 and we add the remainder of 2 which yields 38. So the improper fraction is ^{38}/_{9}. If we rewrite this back into the mixed fraction form, we get that 9 divides into_{}38, 4 times and leaves a remainder of 2 and so as expected we have 4 ^{2}/_{9}.

Now once we have rewritten our mixed numbers, we can multiply and divide them just like we would with any fraction.

Some examples will clarify these points.

1.) 2 ^{5}/_{7 }x 6 ^{3}/_{7 }= [((2 x 7) + 5)/7][((6 x 7) + 3)/7] = (^{19}/_{7})(^{45}/_{7})_{}

(19 x 45)/(7 x 7) = ^{855}/_{49}

We will further reduce this answer into the mixed fraction form.

^{855}/_{49} = 17 ^{22}/_{49}

2.) 10 ^{2}/_{9} divided by 4 ^{5}/_{8 }= ?

10 ^{2}/_{9} = ((10 x 9) + 2)/9 = ^{92}/_{9}

4 ^{5}/_{8 }= ((4 x 8) + 5)/8 = ^{37}/_{8 }

So we have (^{92}/_{9}) / (^{37}/_{8}) = (^{92}/_{9}) (^{8}/_{37}) = (92 x 8)/(9 x 37) = ^{736}/_{333} = 2 ^{70}/_{333}

To perform this division, we found the reciprocal of ^{37}/_{8} and multiplied it by (^{92}/_{9}) and then reduced the product to a mixed fraction.