Solution - Adding, subtracting and finding the least common multiple
Step by Step Solution
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "0.5" was replaced by "(5/10)". 5 more similar replacement(s)
Step 1 :
1
Simplify —
2
Equation at the end of step 1 :
34 75 2 155 1
(((——+——)+——)+———)+—
10 10 10 10 2
Step 2 :
31
Simplify ——
2
Equation at the end of step 2 :
34 75 2 31 1
(((——+——)+——)+——)+—
10 10 10 2 2
Step 3 :
1
Simplify —
5
Equation at the end of step 3 :
34 75 1 31 1
(((——+——)+—)+——)+—
10 10 5 2 2
Step 4 :
15
Simplify ——
2
Equation at the end of step 4 :
34 15 1 31 1
(((—— + ——) + —) + ——) + —
10 2 5 2 2
Step 5 :
17
Simplify ——
5
Equation at the end of step 5 :
17 15 1 31 1
(((—— + ——) + —) + ——) + —
5 2 5 2 2
Step 6 :
Calculating the Least Common Multiple :
6.1 Find the Least Common Multiple
The left denominator is : 5
The right denominator is : 2
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 5 | 1 | 0 | 1 |
| 2 | 0 | 1 | 1 |
| Product of all Prime Factors | 5 | 2 | 10 |
Least Common Multiple:
10
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 = 2
Right_M = L.C.M / R_Deno = 5
Making Equivalent Fractions :
6.3 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. 17 • 2 —————————————————— = —————— L.C.M 10 R. Mult. • R. Num. 15 • 5 —————————————————— = —————— L.C.M 10
Adding fractions that have a common denominator :
6.4 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:
17 • 2 + 15 • 5 109
——————————————— = ———
10 10
Equation at the end of step 6 :
109 1 31 1
((——— + —) + ——) + —
10 5 2 2
Step 7 :
Calculating the Least Common Multiple :
7.1 Find the Least Common Multiple
The left denominator is : 10
The right denominator is : 5
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 1 | 0 | 1 |
| 5 | 1 | 1 | 1 |
| Product of all Prime Factors | 10 | 5 | 10 |
Least Common Multiple:
10
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 = 2
Making Equivalent Fractions :
7.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 109 —————————————————— = ——— L.C.M 10 R. Mult. • R. Num. 2 —————————————————— = —— L.C.M 10
Adding fractions that have a common denominator :
7.4 Adding up the two equivalent fractions
109 + 2 111
——————— = ———
10 10
Equation at the end of step 7 :
111 31 1
(——— + ——) + —
10 2 2
Step 8 :
Calculating the Least Common Multiple :
8.1 Find the Least Common Multiple
The left denominator is : 10
The right denominator is : 2
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 1 | 1 | 1 |
| 5 | 1 | 0 | 1 |
| Product of all Prime Factors | 10 | 2 | 10 |
Least Common Multiple:
10
Calculating Multipliers :
8.2 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 = 5
Making Equivalent Fractions :
8.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 111 —————————————————— = ——— L.C.M 10 R. Mult. • R. Num. 31 • 5 —————————————————— = —————— L.C.M 10
Adding fractions that have a common denominator :
8.4 Adding up the two equivalent fractions
111 + 31 • 5 133
———————————— = ———
10 5
Equation at the end of step 8 :
133 1
——— + —
5 2
Step 9 :
Calculating the Least Common Multiple :
9.1 Find the Least Common Multiple
The left denominator is : 5
The right denominator is : 2
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 5 | 1 | 0 | 1 |
| 2 | 0 | 1 | 1 |
| Product of all Prime Factors | 5 | 2 | 10 |
Least Common Multiple:
10
Calculating Multipliers :
9.2 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 = 5
Making Equivalent Fractions :
9.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 133 • 2 —————————————————— = ——————— L.C.M 10 R. Mult. • R. Num. 5 —————————————————— = —— L.C.M 10
Adding fractions that have a common denominator :
9.4 Adding up the two equivalent fractions
133 • 2 + 5 271
——————————— = ———
10 10
Final result :
271
——— = 27.10000
10
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