How do you solve #a+ 1\frac { 2} { 3} = 2\frac { 5} { 6}#?

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Answer 1 · 2018-01-21T13:31:54

See a solution process below:

First, to make the problem easier to work with, convert each of the mixed numbers into improper fractions:

#1 2/3 = 1 + 2/3 = (3/3 xx 1) + 2/3 = 3/3 + 2/3 = (3 + 2)/3 = 5/3#

#2 5/6 = 2 + 5/6 = (6/6 xx 2) + 5/6 = 12/6 + 5/6 = (12 + 5)/6 = 17/6#

Next, rewrite the equation using the improper fractions as:

#a + 5/3 = 17/6#

Now, subtract #color(red)(5/3)# from each side of the equation to solve for #a# while keeping the equation balanced:

#a + 5/3 - color(red)(5/3) = 17/6 - color(red)(5/3)#

#a + 0 = 17/6 - (2/2 xx color(red)(5/3))#

#a = 17/6 - color(red)(10/6)#

#a = (17 - color(red)(10))/6#

#a = 7/6#

If necessary, we can convert this improper fraction into a mixed number:

#7/6 = (6 + 1)/6 = 6/6 + 1/6 = 1 + 1/6 = 1 1/6#

Therefore, the solution can also be written as:

#a = 1 1/6#