Compound Fractions

Solving compound fractions is the important topic in algebra. Compound fractions are nothing but a mixed fraction. It is also known as the mixed number.  Compound fractions are the combination of whole number and the proper fraction. We have to write the improper fractions in the form of compound fractions. In this we have to discuss about the solving compound fractions problems.


General discussion about fractions

Definition of fraction:

Dividing two numbers is known as fractions. It takes the original form of a/b. Here we can called a as a numerator value and b as a denominator value.

Definition of proper fraction:

When the numerator value is lesser than the denominator value. Then the fraction is denoted as proper fraction.

Definition of Improper fraction:

When the numerator  is greater than the denominator value. Then the fraction is denoted as Improper fraction.

Definition of compound fraction:

We can write the improper fraction is the combination of the whole number and then the proper fraction. This fraction is known as compound fraction.

Solving compound fraction problems

Addition of compound fractions:

Example 1:

Solving 2 (1)/(2) + 3 (1)/(2)

Solution:

First we can convert the compound fractions into improper fraction. It can be converted in the following manner

(((2*2)+1))/(2)+ (((3*2)+1))/(2)

That is (5)/(2)+(7)/(2)

Here the denominators are same so we can directly add the numerators otherwise we can take the L.C.D and then add the numerator values.

Adding this we can get, (12)/(2)

Divided by 2 we can get 6

This is the solution of the given fraction.

Subtraction of compound fraction:

Subtraction of compound fractions is similar to addition instead of + we can use the sign -.

Multiplication of compound fractions:

Example 2:

Solving 1 (1)/(3) x 2 (5)/(4)

Solution:

First we can convert the compound fractions into improper fraction. It can be converted in the following manner

(((1*3)+1))/(3) x (((2*4)+5))/(4)

that is (4)/(3) x (13)/(4)

Now we can multiply the numerator and denominator terms separately. Then we can simplify the fraction.

then we can get (13)/(3)

This is the solution of the given fraction.


Division of compound fractions:

Here we can convert the mixed numbers into improper fraction and then take the reciprocal of the second fraction. Now we have to multiply the fractions.