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
Step-2: Write each number as a product of primes, matching primes vertically when possible
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)
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
Step-2: Write each number as a product of primes, matching primes vertically when possible
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)
3. Find `3/4 + 5/4`
Solution:
`=(3)/(4) + (5)/(4)`
`=(3 + 5)/(4)`
`=(8)/(4)`
Reduce fractions
`=2`
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)
This material is intended as a summary. Use your textbook for detail explanation.
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