###### INTRODUCTION

fraction is used to represent the part of the whole thing. Fraction can be write in the form of (Numerator /denominator).

ex. ½, ¾, ¼.

½ Means, we are cutting an apple in 2 equal part and taking only one part. The denominator will mention the whole thing is cutted in how much equal part. Here the apple is cutted in 2 equal part so the denominator become 2. And we are only taking one pice from that. So the numerator become 1 in this example. ½ can also be called as half.

**Like fractions:** fractions with same denominator is called like fractions. ex. 3/7, 5/7, 1/7.

**Unlike fractions : **Fractions with different denominator is called unlike fraction ex. 4/7, 5/10, 5/9.

**Proper fraction : **if the numerator less than denominator in a fraction, then it is called proper fraction. The value of proper fraction is always less than 1. ex. 1/8, 4/9,6/11.

**Improper fraction : **If the numerator is equal to or greater than denominator, then it is called improper fraction. The value of improper fraction is always equal or greater than 1. ex. 5/2, 12/7, 8/8.

**Mixed fractions: **This is the combination of a whole number and fraction. For example 3 apple and a half apple. ex 3½.

**Comparing the like fraction : **In Order to compare the like fractions we can just compare the numerator only and can decide which one is smaller, bigger or equal. Do some exercise. p-79

**Changing in to mixed fractions :** we can change an improper fraction into mixed fraction by divide the numerator with denominator. The whole part will be the quotient, numerator will be the remainder and divisor will be the denominator of the mixed fraction. do exercise in p-79.

Changing in to Improper fractions : We can change a mixed fraction into improper fraction. The numerator of the improper fraction can obtain by multiplying the whole part and denominator and add the numerator with the product. The denominator of the improper fraction is same as the denominator of the mixed fraction see exercise in p-79. See video

###### Equivalent fractions

Same fraction of a whole can represent with different fractional numbers. that means different fractional number can be same value. ex. 1/2 of an apple and 2/4 an apple. See activity on p-80. we can find the number of equivalent fraction of a fractional number by * multiplying the numerator and denominator by same number. *We can also find the equivalent fractions

**by dividing the numerator and denominator by same number.***see p-80*

###### checking the equivalent fraction

In order to check whether to fraction are same or not we can cross multiply them. Cross multiplication can be done by multiply the numerator of the first number and denominator of the second number. Then multiply the numerator of the second number and denominator of the first number. If both product are same then the two fractions are same. The product is the value of the fraction whose denominator is multiplied. By this we can find which one is big or small also. see p-81 for exercise

###### lowest form of the fraction

As we know same fraction can be write with different numerator and different denominator. ex 2/4, 4/8, 6/ 12. So in this section we will study how we can check whether the given fraction is in its lowest form. **If the given fraction number is in its lowest form then there will not be any common factor of numerator and denominator expect 1. ****(or the hcf will be 1). ** For ex. 6/12, the HCF of 6 na12 is 6so it is not 1. There for 6/12 is not in its lowest form. If we consider 1/6, then the HCF is 1 so it is in it lowest form.

To change a fraction in its lowest form, we can find the HCF of numerator and denominator and then we have to divide both numerator and denominator with HCF and we will get the lowest form of the fraction. ex 6/12 HCF is 6 so divide both numerator and denominator we will get 1/6 this is the lowest form. see exercise 6B in p-83. See video

###### Comparing the fractions

**Comparing the like fractions:** as the denominator of the like fractions are same just compare the numerator. The biggest numerator fraction is the bigger one.

**comparing the unlike fraction** : In this case all denominator will be different. In this case * if the numerator is same for all the biggest denominator fraction is the smallest one. *If denominator and numerator are different for fractions then we can find the LCM if the denominators and make all fraction with same denominator as LCM, then we can compare the numerator only. To do this we have to divide the LCM with denominator of each fraction. And multiply the quotient with numerator and denominator of each fraction respectively. See exercise 6c p-86 See video

###### Adding the fractions

**Adding the like fractions : **As the like fraction have the same denominator we have to add only the numerators of the fractions and the denominator is the same.ex. 2/12 + 4/12 = 6/12.

**Adding the unlike fractions:** In order to add two or more unlike fractions we have to make them like fractions. To do this we have to find the LCM of the all denominators, and convert the denominator of all the fractions to the LCM. Now all the fraction is in like fractions and we can add them. see examples and exercise in page 88. See video

**Adding the mixed numbers with like fractions :** For do this we have to add the whole part together first, and this will be the new whole part. Now add the two like fraction part. If the result is in improper fraction convert that in to mixed fraction and now we will get the proper fraction in the fraction part of the mixed fraction. Now we can add the previously obtained new whole part along with the whole part of the mixed fraction and keep the fraction part as it is. See ex. i page-89.

**Adding the mixed numbers with unlike fractions :** This one also we can do as per the above steps. But before doing that we have to covert the unlike fractions in like fractions. see ex. and exercise in page-89.

**Subtracting the fractions –**

To subtract any faction, we have to make them first in to the like fraction. To do this we can find LCM of all denominators, and make all the fractions denominator to the LCM. Then we can subtract the numerators and keep the denominator same. Like this we can subtract like fractions and unlike fractions. even it is proper or improper. see the exercise i page-90.

**Subtracting the mixed fractions: **