Answer: 5 & 2/3 yards of total fabric
whole part = 5
fractional part = 2/3
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Step-by-step explanation
The mixed number 3 & 1/4 converts to the improper fraction 13/4 through the use of this formula
a & b/c = (a*c+b)/c
Subtract the two fractions 13/4 and 5/6 to find out how much fabric is needed for the jacket only.
13/4 - 5/6
(13/4)*(3/3) - (5/6)*(2/2)
39/12 - 10/12
(39-10)/12
29/12
We need 13/4 yards of fabric for the dress and 29/12 yards of fabric for the matching jacket.
Add up those fractions to find the total amount of fabric needed.
13/4 + 29/12
39/12 + 29/12
(39+29)/12
68/12
(4*17)/(4*3)
17/3
Now convert that to a mixed number
17/3 = (15+2)/3
17/3 = 15/3 + 2/3
17/3 = 5 + 2/3
17/3 = 5 & 2/3
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Here's another approach
3 & 1/4 = 3 + 1/4 = amount needed for dress
3 + 1/4 - 5/6 = amount needed for jacket
Add those expressions to get the total amount of fabric needed.
(3 + 1/4) + (3 + 1/4 - 5/6)
(3+3) + (1/4 + 1/4 - 5/6)
6 + 2/4 - 5/6
6 + 1/2 - 5/6
6 + 3/6 - 5/6
6 - 2/6
6 - 1/3
5 + 1 - 1/3
5 + 3/3 - 1/3
5 + 2/3
5 & 2/3