Solution - Adding, subtracting and finding the least common multiple
Step by Step Solution
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
5/12*d+1/6*d+1/3*d+1/12*d-(6)=0
Step by step solution :
Step 1 :
1
Simplify ——
12
Equation at the end of step 1 :
5 1 1 1
((((——•d)+(—•d))+(—•d))+(——•d))-6 = 0
12 6 3 12
Step 2 :
1
Simplify —
3
Equation at the end of step 2 :
5 1 1 d
((((——•d)+(—•d))+(—•d))+——)-6 = 0
12 6 3 12
Step 3 :
1
Simplify —
6
Equation at the end of step 3 :
5 1 d d
((((——•d)+(—•d))+—)+——)-6 = 0
12 6 3 12
Step 4 :
5
Simplify ——
12
Equation at the end of step 4 :
5 d d d
((((—— • d) + —) + —) + ——) - 6 = 0
12 6 3 12
Step 5 :
Calculating the Least Common Multiple :
5.1 Find the Least Common Multiple
The left denominator is : 12
The right denominator is : 6
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 2 | 1 | 2 |
| 3 | 1 | 1 | 1 |
| Product of all Prime Factors | 12 | 6 | 12 |
Least Common Multiple:
12
Calculating Multipliers :
5.2 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 = 1
Right_M = L.C.M / R_Deno = 2
Making Equivalent Fractions :
5.3 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. 5d —————————————————— = —— L.C.M 12 R. Mult. • R. Num. d • 2 —————————————————— = ————— L.C.M 12
Adding fractions that have a common denominator :
5.4 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:
5d + d • 2 7d
—————————— = ——
12 12
Equation at the end of step 5 :
7d d d
((—— + —) + ——) - 6 = 0
12 3 12
Step 6 :
Calculating the Least Common Multiple :
6.1 Find the Least Common Multiple
The left denominator is : 12
The right denominator is : 3
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 2 | 0 | 2 |
| 3 | 1 | 1 | 1 |
| Product of all Prime Factors | 12 | 3 | 12 |
Least Common Multiple:
12
Calculating Multipliers :
6.2 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 = 1
Right_M = L.C.M / R_Deno = 4
Making Equivalent Fractions :
6.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 7d —————————————————— = —— L.C.M 12 R. Mult. • R. Num. d • 4 —————————————————— = ————— L.C.M 12
Adding fractions that have a common denominator :
6.4 Adding up the two equivalent fractions
7d + d • 4 11d
—————————— = ———
12 12
Equation at the end of step 6 :
11d d
(——— + ——) - 6 = 0
12 12
Step 7 :
Adding fractions which have a common denominator :
7.1 Adding fractions which have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
11d + d 12d
——————— = ———
12 12
Reducing to Lowest Terms :
7.2 The above result can still be reduced :
12d
——— = d
12
Equation at the end of step 7 :
d - 6 = 0
Step 8 :
Equation at the end of step 8 :
d - 6 = 0
Step 9 :
Solving a Single Variable Equation :
9.1 Solve : d-6 = 0
Add 6 to both sides of the equation :
d = 6