# Unlike fractions

If denominators of the given fractions are different then those fractions are unlike fractions.

## How to convert unlike fractions into like fractions

1. Find LCM (lowest common multiple) for the given fractions denominators.
2. For each of the unlike fractions do the following steps.
New Denominator = LCM of the denominators
New Numerator = Multiply the numerator by the quotient from Dividing the LCM by the denominator of the unlike fraction.
3. After step 2 all the unlike fractions will have the same denominator (LCM)(Or unlike fractions are converted to like fractions).

### Example: Convert 1⁄6 and 3⁄8 into like fractions.

LCM for 6 and 8 = 24
Adjust numerator to the LCM (24):
Convert 1/6:
Numerator to be multiplied by: 246 = 4
New numerator = 1 * 4 = 4
16 = 424
Convert 38 :
Numerator to be multiplied by: 248 = 3
New numerator = 3 * 3 = 9
38 = 924
Result: 16 and 38 = 424 and 924

## How to compare unlike fractions - Using LCM

1. Convert unlike fractions into like fractions.
2. The fraction (after converting into like fractions) which has the biggest numerator is the biggest fraction among the given fractions.
3. If two or more fractions have same numerator then those fractions are equivalent fractions.

## How to compare two unlike fractions - Using cross multiplication

1. Multiply the numerator of the first fraction with the denominator of the second fraction, result is value 1.
2. Multiply the numerator of the second fraction with the denominator of the first fraction, result is value 2.
3. If the value 1 is greater than the value 2 then the first fraction is bigger than the second fraction.
4. If the value 2 is greater than the value 1 then the second fraction is bigger than the first fraction.
5. If value 1 and value 2 are same then both the fractions are equal.

### Example:Compare the fractions 2⁄3 and 4⁄5

Value 1: 2 * 5 = 10
Value 2: 4 * 3 = 12
Since 12 > 10 (Value 2 > Value 1), so 45 > 23

## How to add unlike fraction

1. Convert unlike fractions into like fractions.
2. Denominator of the result = The LCM of the denominators (Denominator of the new like fractions)
3. Numerator of the result = Sum of all the new numerators (add all the numerators)
4. To reduce to lowest term divide the numerator and denominator of the result by the HCF(GCD)

### Example: Add the unlike fractions 4⁄10 and 1⁄3

LCM for 10 and 3 = 30
Adjust numerator to the LCM (30):
410 = 1230
13 = 1030
410 + 13 = 1230 + 1030 = 2230
HCF the numerator and the denominator of the result fraction (22 and 30) = 2
Divide the numerator and the denominator by the HCF (2); Result = 1115

## How to subtract unlike fraction

1. Convert unlike fractions into like fractions.

2. Denominator of the result = The LCM of the denominators (denominator of the new like fractions)

3. Numerator of the result = Find the difference between the two numerators

4. To reduce to lowest term divide the numerator and denominator of the result by the HCF(GCD)

### Example: Find difference between 4⁄10 and 1⁄3

410 - 13 = 1230 - 1030 = 2230

HCF the numerator and the denominator of the result fraction (2 and 30) = 2

Divide numerator and the denominator by the HCF (2); Result = 115