Addition and Subtraction of Fractions
So far in our study we have learnt about natural numbers, whole numbers and then integers. In the present chapter, we are learning about fractions, a different type of numbers.
Whenever we come across new type of numbers, we want to know how to operate with them. Can we combine and add them? If so, how? Can we take away some number from another i.e., can we subtract one from the other? and so on. Which of the properties learnt earlier about the numbers hold now? Which are the new properties? We also see how these help us deal with our daily life situations.
My mother divided an apple into 4 pieces and gave me two pieces while my brother got one piece. How much of the total apple did my mother give away to us?
- The apple was cut into
pieces - I got x =
of the whole (1) apple - My brother got y =
of the whole (1) apple - Adding (x + y)
- Total amount of apple given away
Mother asked Neelu and her brother to pick stones from the wheat. Neelu picked one fourth of the total stones in it and her brother also picked up one fourth of the stones. What fraction of the stones did both pick up together?
- The given problem is regarding
of fractions. - Given that Neelu picked (x):
- The amount picked by her brother (y) :
- Adding both amounts (x+y) we get the fraction is
- simply the fraction is
Sohan was putting covers on his note books.He put one fourth of the covers on Monday. He put another one fourth on Tuesday and the remaining on Wednesday. What fraction of the covers did he put on Wednesday?
- Fractions of covers done on Monday =
- Fractions of covers done on Tuesday =
- Adding with sum being
- Subtracting from the whole number of notebooks
- we get the fraction is
and simplify the fraction is - Fractions of covers done on Wednesday
Look at the following examples: A tea stall owner consumes in her shop 2 x
Clearly, both the situations require the fractions to be added. Some of these additions can be done orally and the sum can be found quite easily.
Adding or subtracting like fractions
All fractions cannot be added orally. We need to know how they can be added in different situations and learn the procedure for it. We begin by looking at addition of like fractions.
Does this explain that
Sharmila had
- From the given problem, we can see that this is a
problem - Writing the equation is
- Keeping the denominator the same.
- Evaluating the numerator and we get the fraction is
- Simplifying the fraction is
Thus, we can say that the difference of two like fractions can be obtained as follows:
Step 1 : Subtract the smaller numerator from the bigger numerator.
Step 2 : Retain the (common) denominator.
Step 3 : Write the fraction as :