1. Find `1/2 + 3/4`

Solution:
`=(1)/(2) + (3)/(4)`

LCM of `2,4` is `4`

Step-1: Prime factorization of `2,4` using factor by division method

2 2   1

2 4 2 2   1

Step-2: Write each number as a product of primes, matching primes vertically when possible

2	=	2
4	=	2	× 2

Step-3: Bring down the primes in each column. The LCM is the product of these factors

2	=	2
4	=	2	× 2
LCM	=	2	× 2	= 4

`:.` LCM of `2,4` is `4`

`=(1 xx 2)/(2 xx 2) + (3)/(4)` (Change into equivalent fractions with the LCD 4)

`=(2)/(4) + (3)/(4)` (Simplify the numerators and denominators)

`=(2 + 3)/(4)`

`=(5)/(4)`

`=1 (1)/(4)` (Converting improper fraction to mixed number)

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2. Find `3/4 + 5/6`

Solution:
`=(3)/(4) + (5)/(6)`

LCM of `4,6` is `12`

Step-1: Prime factorization of `4,6` using factor by division method

2 4 2 2   1

2 6 3 3   1

Step-2: Write each number as a product of primes, matching primes vertically when possible

4	=	2	× 2
6	=	2		× 3

Step-3: Bring down the primes in each column. The LCM is the product of these factors

4	=	2	× 2
6	=	2		× 3
LCM	=	2	× 2	× 3	= 12

`:.` LCM of `4,6` is `12`

`=(3 xx 3)/(4 xx 3) + (5 xx 2)/(6 xx 2)` (Change into equivalent fractions with the LCD 12)

`=(9)/(12) + (10)/(12)` (Simplify the numerators and denominators)

`=(9 + 10)/(12)`

`=(19)/(12)`

`=1 (7)/(12)` (Converting improper fraction to mixed number)

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3. Find `3/4 + 5/4`

Solution:
`=(3)/(4) + (5)/(4)`

`=(3 + 5)/(4)`

`=(8)/(4)`

Reduce fractions
`=2`

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4. Find `3/4 + 5/4 - 1/4`

Solution:
`=(3)/(4) + (5)/(4) - (1)/(4)`

`=(3 + 5 - 1)/(4)`

`=(7)/(4)`

`=1 (3)/(4)` (Converting improper fraction to mixed number)

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