Simplify 11/12+5/18-4/9
Please give answer fast step by step
Answers
Answer:
3 / 4 or 0.75
Step-by-step explanation:
in the question 11/12+5/18-4/9, the denominators are 12, 18 and 9
finding LCM of 12, 18 and 9 :
doing prime factorisation of 12, 18 and 9 :
12 = 2 x 2 x 3 = 2² x 3¹
18 = 2 x 3 x 3 = 2¹ x 3²
9 = 3 x 3 = 3²
LCM of given numbers = product of the greatest powers of each prime factor of the numbers
the prime factors in 12, 18 and 9 are 2 and 3
greatest power of 2 in the prime factorisation is 2²
greatest power of 3 in the prime factorisation is 3²
so LCM of 12, 18 and 9 = 2² x 3² = 4 x 9 = 36
coming to question -
11/12 + 5/18 - 4/9
we must convert each denominator to 36
11 / 12 = 33 / 36 ( multiplying numerator and denominator by 3 so that denominator becomes 36 )
5/18 = 10/36 (multiplying numerator and denominator by 2 so that denominator becomes 36 )
4/9 = 16/36 ( multiplying numerator and denominator by 4 so that denominator becomes 36 )
so 11/12 + 5/18 - 4/9 = 33/36 + 10/36 - 16/36
= ( 33 + 10 - 16 ) / 36
= 27 / 36
= 3/4 ( divide numerator and denominator by 9 ) or 0.75
therefore the answer of 11/12+5/18-4/9 is 3/4 or 0.75