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Fill in the blank to make the statement true

1 3/4 + 1/6 +_=7 1/2

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Steve S. | Tutoring in Precalculus, Trig, and Differential CalculusTutoring in Precalculus, Trig, and Diffe...
5.0 5.0 (3 lesson ratings) (3)
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1 3/4 + 1/6 + x = 7 1/2
 
Always put the + sign into mixed numbers:
 
1 + 3/4 + 1/6 + x = 7 + 1/2
 
A. Method 1: Fraction Manipulation
 
Subtract 1 + 3/4 + 1/6 from both sides:
 
x = 7 + 1/2 – 1 – 3/4 – 1/6
 
x = 7 + 1/2 – 2/2 – 3/4 – 1/6
 
x = 7 – 1/2 – 3/4 – 1/6
 
x = 7 – 2/4 – 3/4 – 1/6
 
x = 7 – 5/(2*2) – 1/(2*3)
 
x = 7 – (5*3/(2*2*3) + 2*1/(2*2*3))
 
x = 7 – (5*3 + 2*1)/(2*2*3)
 
x = 7 – 17/12 = 7 – (12+5)/12
 
x = 7 – 1 – 5/12 = 6 – 5/12
 
x = 5 + 12/12 – 5/12 = 5 + 7/12
 
B. Method 2: Clear Fractions First
 
1 + 3/4 + 1/6 + x = 7 + 1/2
 
Multiply both sides by 2*2*3:
 
2*2*3*1 + 2*2*3*3/4 + 2*2*3*1/6 + 2*2*3*x = 2*2*3*7 + 2*2*3*1/2
 
12 + 9 + 2 + 12x = 84 + 6
 
23 + 12x = 90
 
12x = 90 – 23 = 67
 
x = 67/12 = (60 + 7)/12
 
x = 5 + 7/12
 
Melissa M. | Upper Level Math, Sciences, and ACTUpper Level Math, Sciences, and ACT
5.0 5.0 (212 lesson ratings) (212)
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For this question it is best to find the least common denominator (LCD) for all terms. In this case that denominator is 12.
Using the LCD you would convert all of the fractions into the following equation and solve:
1 9/12 + 2/16 + __ = 7 6/12
1 11/12 + __ = 7 6/12
___ = 7 6/12 - 1 11/12
___ = 5 7/12