1. Example-1
1. Find Convert unlike fraction to like fraction of `8/9,35/12,7/15`
Solution: Step-1 : `8/9,35/12,7/15`
Step-2 : Find the least common multiple (LCM) of denominators
Steps of LCM of 9,12,15Method-1 : Finding LCM of 9,12,15 using Division MethodStep-1: Divide the numbers by prime factors until the remainder is 12 | 9 | | 12 | | 15 | 2 | 9 | | 6 | | 15 | 3 | 9 | | 3 | | 15 | 3 | 3 | | 1 | | 5 | 5 | 1 | | 1 | | 5 | | 1 | | 1 | | 1 | Step-2: Multiply all the divisors to obtain the LCMLCM of `9,12,15=2 xx 2 xx 3 xx 3 xx 5=180` Method-2 : Finding LCM of 9,12,15 using Prime Factorization MethodStep-1: Prime factorization of `9,12,15` using factor by division method Step-2: Write each number as a product of primes, matching primes vertically when possible 9 | = | | | 3 | × 3 | | | 12 | = | 2 | × 2 | × 3 | | | | 15 | = | | | 3 | | × 5 | |
Step-3: Bring down the primes in each column. The LCM is the product of these factors 9 | = | | | 3 | × 3 | | | 12 | = | 2 | × 2 | × 3 | | | | 15 | = | | | 3 | | × 5 | |
| LCM | = | 2 | × 2 | × 3 | × 3 | × 5 | = 180 |
`:.` LCM of `9,12,15` is `180`
Here, LCM of `9,12,15 = 180`
Step-3 : `:.` LCD (Least common denominator) of `8/9,35/12,7/15` is `180`
Step-4 : Rewriting the original inputs as equivalent fractions with the LCD: `8/9=8/9xx20/20=160/180`
`35/12=35/12xx15/15=525/180`
`7/15=7/15xx12/12=84/180`
2. Find Convert unlike fraction to like fraction of `1/2,2/3,3/4`
Solution: Step-1 : `1/2,2/3,3/4`
Step-2 : Find the least common multiple (LCM) of denominators
Steps of LCM of 2,3,4Method-1 : Finding LCM of 2,3,4 using Division MethodStep-1: Divide the numbers by prime factors until the remainder is 1Step-2: Multiply all the divisors to obtain the LCMLCM of `2,3,4=2 xx 2 xx 3=12` Method-2 : Finding LCM of 2,3,4 using Prime Factorization MethodStep-1: Prime factorization of `2,3,4` 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 | | | | 3 | = | | | 3 | | 4 | = | 2 | × 2 | | |
| LCM | = | 2 | × 2 | × 3 | = 12 |
`:.` LCM of `2,3,4` is `12`
Here, LCM of `2,3,4 = 12`
Step-3 : `:.` LCD (Least common denominator) of `1/2,2/3,3/4` is `12`
Step-4 : Rewriting the original inputs as equivalent fractions with the LCD: `1/2=1/2xx6/6=6/12`
`2/3=2/3xx4/4=8/12`
`3/4=3/4xx3/3=9/12`
3. Find Convert unlike fraction to like fraction of `5/4,3/2,7/5`
Solution: Step-1 : `5/4,3/2,7/5`
Step-2 : Find the least common multiple (LCM) of denominators
Steps of LCM of 4,2,5Method-1 : Finding LCM of 4,2,5 using Division MethodStep-1: Divide the numbers by prime factors until the remainder is 1Step-2: Multiply all the divisors to obtain the LCMLCM of `4,2,5=2 xx 2 xx 5=20` Method-2 : Finding LCM of 4,2,5 using Prime Factorization MethodStep-1: Prime factorization of `4,2,5` 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 | | | | 5 | = | | | 5 | |
| LCM | = | 2 | × 2 | × 5 | = 20 |
`:.` LCM of `4,2,5` is `20`
Here, LCM of `4,2,5 = 20`
Step-3 : `:.` LCD (Least common denominator) of `5/4,3/2,7/5` is `20`
Step-4 : Rewriting the original inputs as equivalent fractions with the LCD: `5/4=5/4xx5/5=25/20`
`3/2=3/2xx10/10=30/20`
`7/5=7/5xx4/4=28/20`
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