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