Question

4 7/9 - 1 5/6 + 3 1/3

Answer 1

The expression is 4 7/9 - 1 5/6 + 3 1/3.

First write the mixed numbers as impoper fraction.

The improper fraction of a b/c = [a(c) + b]/c = (ac + b)/c, where a, b and c are real numbers.

The improper fraction of 4 7/9 = [4(9) + 7]/9 = (36 + 9)/9 = 43/9.

The improper fraction of 1 5/6 = [1(6) + 5]/6 = (6 + 5)/9 = 11/6.

The improper fraction of 3 1/3 = [3(3) + 1]/3 = (9 + 1)/3 = 10/3.

4 7/9 - 1 5/6 + 3 1/3 = 43/9 + 11/6 + 10/3.

To add fractions with unlike denominators, rename the fractions with a common denominator. Then add and simplify as with like fractions.

Next find the  least common denominator (LCD) of unlike denominators 9, 6 and 3.

multiples of 9 : 9, 18, 27, 36, 45, 54, 63, 72, …

multiples of 6 : 6, 12, 18, 24, 30, 36, 42, 48, …

multiples of 3 : 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, …

The least of the nonzero common multiples is called the least common multiple (LCM). So, the LCM of 9, 6 and 3 is 18.

4 7/9 - 1 5/6 + 3 1/3

= 43/9 - 11/6 + 10/3

= (43/9)*(2/2) - (11/6)*(3/3) + (10/3)*(6/6)

= (43*2)/(9*2) - (11*3)/(6*3) + (10*6)/(3*6)

= 86/18 - 33/18 + 60/18

= (86 - 33 + 60)/18

= 113/18.

The value of 4 7/9 - 1 5/6 + 3 1/3 = 113/18.