Solution - Adding, subtracting and finding the least common multiple
Step by Step Solution
Step 1 :
5
Simplify —
6
Equation at the end of step 1 :
8 11 13 5
((—+——)+——)+—
9 18 27 6
Step 2 :
13
Simplify ——
27
Equation at the end of step 2 :
8 11 13 5
((— + ——) + ——) + —
9 18 27 6
Step 3 :
11
Simplify ——
18
Equation at the end of step 3 :
8 11 13 5
((— + ——) + ——) + —
9 18 27 6
Step 4 :
8
Simplify —
9
Equation at the end of step 4 :
8 11 13 5
((— + ——) + ——) + —
9 18 27 6
Step 5 :
Calculating the Least Common Multiple :
5.1 Find the Least Common Multiple
The left denominator is : 9
The right denominator is : 18
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 3 | 2 | 2 | 2 |
| 2 | 0 | 1 | 1 |
| Product of all Prime Factors | 9 | 18 | 18 |
Least Common Multiple:
18
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 = 2
Right_M = L.C.M / R_Deno = 1
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. 8 • 2 —————————————————— = ————— L.C.M 18 R. Mult. • R. Num. 11 —————————————————— = —— L.C.M 18
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:
8 • 2 + 11 3
—————————— = —
18 2
Equation at the end of step 5 :
3 13 5
(— + ——) + —
2 27 6
Step 6 :
Calculating the Least Common Multiple :
6.1 Find the Least Common Multiple
The left denominator is : 2
The right denominator is : 27
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 1 | 0 | 1 |
| 3 | 0 | 3 | 3 |
| Product of all Prime Factors | 2 | 27 | 54 |
Least Common Multiple:
54
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 = 27
Right_M = L.C.M / R_Deno = 2
Making Equivalent Fractions :
6.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 3 • 27 —————————————————— = —————— L.C.M 54 R. Mult. • R. Num. 13 • 2 —————————————————— = —————— L.C.M 54
Adding fractions that have a common denominator :
6.4 Adding up the two equivalent fractions
3 • 27 + 13 • 2 107
——————————————— = ———
54 54
Equation at the end of step 6 :
107 5
——— + —
54 6
Step 7 :
Calculating the Least Common Multiple :
7.1 Find the Least Common Multiple
The left denominator is : 54
The right denominator is : 6
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 1 | 1 | 1 |
| 3 | 3 | 1 | 3 |
| Product of all Prime Factors | 54 | 6 | 54 |
Least Common Multiple:
54
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 = 1
Right_M = L.C.M / R_Deno = 9
Making Equivalent Fractions :
7.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 107 —————————————————— = ——— L.C.M 54 R. Mult. • R. Num. 5 • 9 —————————————————— = ————— L.C.M 54
Adding fractions that have a common denominator :
7.4 Adding up the two equivalent fractions
107 + 5 • 9 76
——————————— = ——
54 27
Final result :
76
—— = 2.81481
27
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