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Home > Pre-Algebra calculators > Simplify fraction expression example
21. Simplify fraction expression example ( Enter your problem )
( Enter your problem )
  1. Example-1
 		Other related methods
  1. Numerator and Denominator
  2. Proper and Improper Fractions
  3. Like and Unlike fractions
  4. Model Fractions (Visual Fractions)
  5. Simplify Fraction
  6. Equivalent Fractions
  7. How many eighths are equivalent to 1/2
  8. Fraction to Decimal (Mixed Number to Decimal)
  9. Decimal to Fraction (Decimal to Mixed Number)
  10. Fraction to Percentage (Mixed Number to Percentage)
  11. Improper fraction to Mixed number
  12. Mixed Number to Improper Fraction
  13. Reciprocal of a fraction
  14. LCD of fractions
  15. Convert unlike fraction to like fraction
  16. Comparing fractions
  17. Ascending and descending order of fractions
  18. Add, subtract, multiply and divide of Fractions
  19. Add, subtract, multiply and divide of Mixed numbers
  20. Visual Model for Adding, Subtracting of Fractions
  21. Simplify fraction expression
20. Visual Model for Adding, Subtracting of Fractions
(Previous method)

1. Example-1


1. Simplify `1/2+3/4-7/6`

Solution:
`1/2+3/4-7/6`

`=(1)/(2) + (3)/(4) - (7)/(6)`

LCM of `2,4,6` is `12`


Step-1: Prime factorization of `2,4,6` using factor by division method

22
 1
 
24
22
 1
 
26
33
 1

Step-2: Write each number as a product of primes, matching primes vertically when possible
2=2
4=2 × 2
6=2 × 3

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) - (7 xx 2)/(6 xx 2)` (Change into equivalent fractions with the LCD 12)

`=(6)/(12) + (9)/(12) - (14)/(12)` (Simplify the numerators and denominators)

`=(6 + 9 - 14)/(12)`

`=(1)/(12)` 2. Simplify `8/9*35/12-7/15`

Solution:
`8/9*35/12-7/15`

`=(8)/(9) xx (35)/(12) - (7)/(15)`

`=(8xx35)/(9xx12) - (7)/(15)`

`=(2*2*2xx5*7)/(3*3xx2*2*3) - (7)/(15)` (Find factors)

`=(cancel{(2)}*cancel{(2)}*2xx5*7)/(3*3xxcancel{(2)}*cancel{(2)}*3) - (7)/(15)` (Remove common factors)

`=(70)/(27) - (7)/(15)`

LCM of `27,15` is `135`


Step-1: Prime factorization of `27,15` using factor by division method

327
39
33
 1
 
315
55
 1

Step-2: Write each number as a product of primes, matching primes vertically when possible
27=3 × 3 × 3
15=3 × 5

Step-3: Bring down the primes in each column. The LCM is the product of these factors
27=3 × 3 × 3
15=3 × 5
LCM = 3 × 3 × 3 × 5 = 135

`:.` LCM of `27,15` is `135`


`=(70 xx 5)/(27 xx 5) - (7 xx 9)/(15 xx 9)` (Change into equivalent fractions with the LCD 135)

`=(350)/(135) - (63)/(135)` (Simplify the numerators and denominators)

`=(350 - 63)/(135)`

`=(287)/(135)` 3. Simplify `3 1/2+1 3/4-7/6`

Solution:
`3 1/2+1 3/4-7/6`

`=3 (1)/(2) + 1 (3)/(4) - (7)/(6)`

Converting mixed number to improper fraction
`=(3xx2+1)/(2) + (1xx4+3)/(4) - (7)/(6)`

`=(7)/(2) + (7)/(4) - (7)/(6)`

LCM of `2,4,6` is `12`


Step-1: Prime factorization of `2,4,6` using factor by division method

22
 1
 
24
22
 1
 
26
33
 1

Step-2: Write each number as a product of primes, matching primes vertically when possible
2=2
4=2 × 2
6=2 × 3

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`


`=(7 xx 6)/(2 xx 6) + (7 xx 3)/(4 xx 3) - (7 xx 2)/(6 xx 2)` (Change into equivalent fractions with the LCD 12)

`=(42)/(12) + (21)/(12) - (14)/(12)` (Simplify the numerators and denominators)

`=(42 + 21 - 14)/(12)`

`=(49)/(12)`

`=4 1/12` (Converting improper fraction to mixed number) 4. Simplify `2 3/4-1 5/7*1 3/4`

Solution:
`2 3/4-1 5/7*1 3/4`

`=2 (3)/(4) - 1 (5)/(7) xx 1 (3)/(4)`

Converting mixed number to improper fraction
`=(2xx4+3)/(4) - (1xx7+5)/(7) xx (1xx4+3)/(4)`

`=(11)/(4) - (12)/(7) xx (7)/(4)`

`=(11)/(4) - (12xx7)/(7xx4)`

`=(11)/(4) - (2*2*3xx7)/(7xx2*2)` (Find factors)

`=(11)/(4) - (cancel{(2)}*cancel{(2)}*3xxcancel{(7)})/(cancel{(7)}xxcancel{(2)}*cancel{(2)})` (Remove common factors)

`=(11)/(4) - 3`

LCM of `4,1` is `4`


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

24
22
 1
 
11
 1

Step-2: Write each number as a product of primes, matching primes vertically when possible
4=2 × 2
1=

Step-3: Bring down the primes in each column. The LCM is the product of these factors
4=2 × 2
1=
LCM = 2 × 2 = 4

`:.` LCM of `4,1` is `4`


`=(11)/(4) - (3 xx 4)/(1 xx 4)` (Change into equivalent fractions with the LCD 4)

`=(11)/(4) - (12)/(4)` (Simplify the numerators and denominators)

`=(11 - 12)/(4)`

`=(-1)/(4)`

This material is intended as a summary. Use your textbook for detail explanation.
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20. Visual Model for Adding, Subtracting of Fractions
(Previous method)


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