## FRACTIONS AND DECIMALS

Fractions and decimals BOTH are similar,the way of expressing is only different.

Imagine a birthday party. There are 4 of your friends who attended your bday party . After cutting the cake you will want to distribute to 4 of your friends. So what you do ? You ensure that the cake is cut into 4 pieces and give 1 piece of cake to each of your friends and they are enjoying the cake.

From the above example we understand the following

- 1 piece of cake
- No of your friends – 4
- Each friend gets 1 portion of 4.
- This 1 portion of 4 is expressed as 1 / 4.
- For confirmation, we have 4 friends so we need to add 4 friends portions of cake to ensure we get 1 piece of cake
- 1st Friend – 1/4
- 2nd Friend – 1/4
- 3rd Friend – 1/4
- 4th Friend – 1/4

Add four portions – 1/4 + 1/4 +1/4 +1/4 = 4/4 = 1 (LCM is 4 and 1+1+1+1 /4)

1/4 is called fraction and is expressed in “a” divided by “b” form i.e a/b . Here in our example 1 portion of cake =1/4 , a =1 and b=4. If we compare numerator and denominator , we understand that numerator is bigger than denominator.

All the fractions where numerator is bigger than denominator are called as “proper fractions”

Proper Fractions

In another case there are only 3 small cakes and your friends are four. The distribution here shall be 3 small cakes/ 4 friends i.e 3/4. Even if we cut the cake and distribute equally, we are left with small remainder of cake. we observed here numerator is smaller than denominator.

All the fractions where numerator is smaller than denominator are called as “Improper fractions”

Such improper fractions are expressed as mixed fractions .i.e Quotient – Remainder/Divisor = 1 1/3 = 3/4

Decimals – These are the fractions when expressed in * “0.number”* or “

*“.*

**number.number**Lets try dividing 3 / 4 .

4 ) 3 (

Now that we cannot have bigger number factor for smaller number to divide. We use dot or point in the quotient and add a zero next to 3. so the above division becomes like this.

4 ) 3 0 ( .

After inserting point , we can start dividing the same in conventional way

- 4 ) 30 ( 0. 75
- 28
- ————
- 20
- 20
- ————–
- 0
- Another 1
- 10 ) 1 (
- 10 ) 10 ( 0.
- 10) 10 ( 0.1
- 10
- ————–
- 0
- Answer is 0.1

Some of the decimals we generally use in day to day activities.

- Half – 1/2 = 0.5
- Quarter – 1/4 = 0.25
- 1Kg – 1000 gms – 1/1000 = 0.001
- 1 kilometer – 1000 m = 1/1000 = 0.001
- 2500 gms – 2500/1000 =2.5 kgs