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

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