Solution - Adding, subtracting and finding the least common multiple
Step by Step Solution
Step by step solution :
Step 1 :
11
Simplify ——
9
Equation at the end of step 1 :
1 4 3 11
—+(—•((—•x)-——)) = 0
4 5 4 9
Step 2 :
3
Simplify —
4
Equation at the end of step 2 :
1 4 3 11
—+(—•((—•x)-——)) = 0
4 5 4 9
Step 3 :
Calculating the Least Common Multiple :
3.1 Find the Least Common Multiple
The left denominator is : 4
The right denominator is : 9
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 2 | 0 | 2 |
| 3 | 0 | 2 | 2 |
| Product of all Prime Factors | 4 | 9 | 36 |
Least Common Multiple:
36
Calculating Multipliers :
3.2 Calculate multipliers for the two fractions
Denote the Least Common Multiple by L.C.M
Denote the Left Multiplier by Left_M
Denote the Right Multiplier by Right_M
Denote the Left Deniminator by L_Deno
Denote the Right Multiplier by R_Deno
Left_M = L.C.M / L_Deno = 9
Right_M = L.C.M / R_Deno = 4
Making Equivalent Fractions :
3.3 Rewrite the two fractions into equivalent fractions
Two fractions are called equivalent if they have the same numeric value.
For example : 1/2 and 2/4 are equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are equivalent as well.
To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.
L. Mult. • L. Num. 3x • 9 —————————————————— = —————— L.C.M 36 R. Mult. • R. Num. 11 • 4 —————————————————— = —————— L.C.M 36
Adding fractions that have a common denominator :
3.4 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
3x • 9 - (11 • 4) 27x - 44
————————————————— = ————————
36 36
Equation at the end of step 3 :
1 4 (27x - 44)
— + (— • ——————————) = 0
4 5 36
Step 4 :
4
Simplify —
5
Equation at the end of step 4 :
1 4 (27x - 44)
— + (— • ——————————) = 0
4 5 36
Step 5 :
Equation at the end of step 5 :
1 (27x - 44)
— + —————————— = 0
4 45
Step 6 :
1
Simplify —
4
Equation at the end of step 6 :
1 (27x - 44)
— + —————————— = 0
4 45
Step 7 :
Calculating the Least Common Multiple :
7.1 Find the Least Common Multiple
The left denominator is : 4
The right denominator is : 45
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 2 | 0 | 2 |
| 3 | 0 | 2 | 2 |
| 5 | 0 | 1 | 1 |
| Product of all Prime Factors | 4 | 45 | 180 |
Least Common Multiple:
180
Calculating Multipliers :
7.2 Calculate multipliers for the two fractions
Denote the Least Common Multiple by L.C.M
Denote the Left Multiplier by Left_M
Denote the Right Multiplier by Right_M
Denote the Left Deniminator by L_Deno
Denote the Right Multiplier by R_Deno
Left_M = L.C.M / L_Deno = 45
Right_M = L.C.M / R_Deno = 4
Making Equivalent Fractions :
7.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 45 —————————————————— = ——— L.C.M 180 R. Mult. • R. Num. (27x-44) • 4 —————————————————— = ———————————— L.C.M 180
Adding fractions that have a common denominator :
7.4 Adding up the two equivalent fractions
45 + (27x-44) • 4 108x - 131
————————————————— = ——————————
180 180
Equation at the end of step 7 :
108x - 131
—————————— = 0
180
Step 8 :
When a fraction equals zero :
8.1 When a fraction equals zero ...Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.
Here's how:
108x-131
———————— • 180 = 0 • 180
180
Now, on the left hand side, the 180 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
108x-131 = 0
Solving a Single Variable Equation :
8.2 Solve : 108x-131 = 0
Add 131 to both sides of the equation :
108x = 131
Divide both sides of the equation by 108:
x = 131/108 = 1.213
One solution was found :
x = 131/108 = 1.213How did we do?
Please leave us feedback.