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# Fill in the blank to make the statement true

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

### 2 Answers by Expert Tutors

Steve S. | Tutoring in Precalculus, Trig, and Differential CalculusTutoring in Precalculus, Trig, and Diffe...
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1 3/4 + 1/6 + x = 7 1/2

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
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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