Operations on Fractions in Grade V

Hello Friends, in today's session we all are going to discuss about one of the most interesting and a bit complex topic of mathematics,Order of Operations  on fractions and mixed numbers, which are usually studied in grade V of board of secondary education andhra pradesh. Here I am going to tell you the best way of understanding these topics.
Now we will first start with fraction:
math fractions is represented as a part of whole number. Fractions have numerator and denominator. Some examples of fractions are ¼, ¾. Fraction are of three types proper fraction, improper fraction, and mixed fractions. Let’s see some operations on fractions:

1.    Addition of fractions:

While adding two fractions we must take care that the denominators of the fractions to be added must be same. If the denominators are different then find the LCM of the denominators and put each one in its equivalent form. Then simply add the numerators.

                     p/q + r/q = (p + r)/q

2.    Subtraction of fractions:

While subtracting two fractions we must take care that the denominators of the fractions to be subtracted must be same. If the denominators are not same, find the LCM of the denominators and put each one in its equivalent form. Then simply subtract the numerators.

                     p/q - r/q = (p - r)/q

3.    Multiplication of fractions:

While multiplying two fractions simply multiply the numerators together and then multiply the denominators together and simplify them.

                     p/q x r/s = (p x r)/(q x s)

4.    Division of fractions:

While dividing the fractions, simply take the reciprocal of the second fraction and multiply both the fractions together.

           p/q ÷ r/s = p/q x s/r = (p x s)/(q x r)

Now let’s move to the second topic i.e. Mixed numbers:
A mixed number is represented as the integer number followed by the proper function. Let’s see some operations on mixed numbers and to know more about mixed fractions click here:

1.    Addition of mixed numbers:

          Steps for addition

1. Convert mixed number to improper fraction.
2. Now take the LCM by multiplying the numerator and denominator of fractions by a factor to obtain the lowest possible common denominator for the two fractions.
3. Perform the addition of the numerators
4. Reduce the answer if possible.
5. If the answer is an improper fraction convert it to a mixed number.

2.    Subtraction of mixed numbers:

          Steps for subtraction

1. Convert mixed number to improper fraction.
2. Take the LCM by multiplying the numerator and denominator of fractions by a factor to obtain the lowest possible common denominator for the two fractions.
3. Perform the subtraction of the numerators
4. Reduce the answer if possible.
5. If the answer is an improper fraction convert it to a mixed number.

1. Multiplication of mixed numbers:

          Steps for multiplying

1. Convert mixed number to improper fraction.
2. Multiply the numerators and multiply the denominators of the fractions.
3. Reduce the answer if possible.
4. If the answer is an improper fraction convert it to a mixed number.

4. Division of mixed numbers:

         Steps for division

1. Convert mixed number to improper fraction.
2. Take the reciprocal of the second fraction.
3. Multiply the numerators and multiply the denominators of the fractions.
4. Reduce the answer if possible.
5. If the answer is an improper fraction convert it to a mixed number.

This is all about the operations of fractions and mixed numbers in grade V
and if you want to get details on Multistep Problems in Grade VI then you can refer to the internet and text books.