1. Find `3/4 - 1/2`
Solution:
`=(3)/(4) - (1)/(2)`
LCM of `4,2` is `4`
Step-1: Prime factorization of `4,2` 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 | |
| 2 | = | 2 | | |
|
| LCM | = | 2 | × 2 | = 4 |
`:.` LCM of `4,2` is `4`
`=(3)/(4) - (1 xx 2)/(2 xx 2)` (Change into equivalent fractions with the LCD 4)
`=(3)/(4) - (2)/(4)` (Simplify the numerators and denominators)
`=(3 - 2)/(4)`
`=(1)/(4)`
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)`
`=(-1)/(12)`
3. Find `5/6 - 1/6`
Solution:
`=(5)/(6) - (1)/(6)`
`=(5 - 1)/(6)`
`=(4)/(6)`
Reduce fraction
`=(2)/(3)`
4. Find `1/2 + 3/4 - 5/6`
Solution:
`=(1)/(2) + (3)/(4) - (5)/(6)`
LCM of `2,4,6` is `12`
Step-1: Prime factorization of `2,4,6` 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
| 2 | = | 2 | | | |
| 4 | = | 2 | × 2 | | |
| 6 | = | 2 | | × 3 | |
|
| LCM | = | 2 | × 2 | × 3 | = 12 |
`:.` LCM of `2,4,6` is `12`
`=(1 xx 6)/(2 xx 6) + (3 xx 3)/(4 xx 3) - (5 xx 2)/(6 xx 2)` (Change into equivalent fractions with the LCD 12)
`=(6)/(12) + (9)/(12) - (10)/(12)` (Simplify the numerators and denominators)
`=(6 + 9 - 10)/(12)`
`=(5)/(12)`
This material is intended as a summary. Use your textbook for detail explanation.
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