1. Find `3/4 - 2/4`
Solution:
We will use fraction circles
| `(3)/(4)` | | 3 parts of `1/4` |
| - `(2)/(4)` | | - 2 parts of `1/4` |
| `1/4` | | 1 parts of `1/4` |
So, `(3)/(4) - (2)/(4)=1/4`
2. Find `3/4 - 5/6`
Solution:
We will use fraction circles
Here, LCM of 4 and 6 is 12. Convert each fractions into like fractions. So multiply numerator and denominator by the ratio of LCM and denominator of the fraction
`(3)/(4)=(3xx3)/(4xx3)=(9)/(12)`
`(5)/(6)=(5xx2)/(6xx2)=(10)/(12)`
| `(9)/(12)` | | 9 parts of `1/12` |
| - `(10)/(12)` | | - 10 parts of `1/12` |
| `-1/12` | Answer is negative | |
Directly simplify fraction expression (without model)
`=(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 `1 3/4 - 1 2/4`
Solution:
We will use fraction circles
| `1(3)/(4)` | | 7 parts of `1/4` |
| - `1(2)/(4)` | | - 6 parts of `1/4` |
| `1/4` | | 1 parts of `1/4` |
So, `1 (3)/(4) - 1 (2)/(4)=1/4`
4. Find `1 1/4 - 2/3`
Solution:
We will use fraction circles
Here, LCM of 4 and 3 is 12. Convert each fractions into like fractions. So multiply numerator and denominator by the ratio of LCM and denominator of the fraction
`1 (1)/(4)=1 (1xx3)/(4xx3)=1 (3)/(12)`
`(2)/(3)=(2xx4)/(3xx4)=(8)/(12)`
| `1(3)/(12)` | | 15 parts of `1/12` |
| - `(8)/(12)` | | - 8 parts of `1/12` |
| `7/12` | | 7 parts of `1/12` |
So, `1 (1)/(4) - (2)/(3)=7/12`
This material is intended as a summary. Use your textbook for detail explanation.
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