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Model 1 :

When the numerators are same and the denominators are different, the fraction with the largest denominator is the smallest. Have a look at the following example.

- Here, 13 is the largest denominator, so, (3/13) is the smallest fraction. 5 is the smallest denominator, hence (3/5) is the largest fraction.
- Here logic is very simple,
- Situation 1 : Assume that you are 5 Children in your family. Your Dad brought an Apple and mom cut it into 5 pieces and distributed among all the children including you. (1/5)
- Situation 2 : Assume that you are 8 Children in your family. Your Dad brought an Apple and mom cut it into 8 pieces and distributed among all the children including you. (1/8)
- In which Situation will you get the BIG Piece of the Apple??? ;). Obviously in the Situation 1. Thats it.........

### Model 2 :

When the numerators are different and the denominators are same, the fraction with the largest numerator is the largest. Have a look at the following example.

**Which of the following fractions is the smallest?****(7/5) , (9/5), (4/5), (11/5)**

- As 4 is the smallest numerator, the fraction 4/5 is the smallest.
- As 11 is the largest numerator, the fraction 11/5 is the largest.
- Here too logic is very simple,
- Situation 1 : Assume that you are 4 Children in your family. Your Dad brought 8 Apples and mom distributed them among all the children including you. (8/4)
- Situation 2 : Assume that you are 4 Children in your family. Your Dad brought 12 Apples and mom distributed them among all the children including you. (12/4)
- In which situation will you get more apples? Obviously in the second. So, 12/4 is the Biggest.. Thats it ;)

### Model 3 :

The fraction with the largest numerator and the smallest denominator is the largest.

**Which of the following fractions is the largest?****(19/16), (24/11), (17/13), (21/14), (23/15)**

- As 24 is the largest numerator and 11 is the smallest denominator, 24/11 is the largest fraction.
- Logic??? Cutting the More fruits into Less pieces is more beneficial for you than cutting the Less fruits into More pieces :P

### Model 4 :

When the numerators of two fractions are unequal, we try and equate them by suitably cancelling factors or by suitably multilplying the numerators. Thereafter we compare the denominators as in

**Model 1**. Have a look at the following examples.**Which of the following fractions is the largest?****(64/328), (28/152), (36/176), (49/196)**

- 64/328 = 32/164 = 16/82 = 8/41 this is approximately equal to 1/5
**Note :**In these type of problems, approximate values will be enough. No need to get EXACT values.- 25/152 = 14/76 = 7/38 this is approximately equal to 1/5.5
- 36/176 = 18/88 = 9/44 this is approximately equal to 1/5
- 49/196 = 7/28 = 1/4
- As all the numerators are 1 and the least denominator is 4, the fraction 49/196 is the largest
**Which of the following fractions is the largest?****(71/181), (214/519), (429/1141)**

- (71/181) = (71 X 6) / (181 X 6) = 426/1086
- (214/519) = (214 X 2) / (519 X 2) = 428/1038

- The numerators are now all ALMOST equal (426, 428 and 429). The smallest denominator is 1038.
- So, the largest fraction must be 428/1038 that is 214/519 :)

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* *Click Here to read Mental Maths (Comparison of Fractions) - Part 2

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break it down

= 1/1.16 1/1.125 1/1.25

here 1.125 is smallest

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