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): "2.75" was replaced by "(275/100)". 5 more similar replacement(s)
Step 1 :
11
Simplify ——
4
Equation at the end of step 1 :
189 25 135 135 11
(((———+——)+———)+———)+——
100 10 100 100 4
Step 2 :
27
Simplify ——
20
Equation at the end of step 2 :
189 25 135 27 11
(((———+——)+———)+——)+——
100 10 100 20 4
Step 3 :
27
Simplify ——
20
Equation at the end of step 3 :
189 25 27 27 11
(((———+——)+——)+——)+——
100 10 20 20 4
Step 4 :
5
Simplify —
2
Equation at the end of step 4 :
189 5 27 27 11
(((——— + —) + ——) + ——) + ——
100 2 20 20 4
Step 5 :
189
Simplify ———
100
Equation at the end of step 5 :
189 5 27 27 11
(((——— + —) + ——) + ——) + ——
100 2 20 20 4
Step 6 :
Calculating the Least Common Multiple :
6.1 Find the Least Common Multiple
The left denominator is : 100
The right denominator is : 2
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 2 | 1 | 2 |
| 5 | 2 | 0 | 2 |
| Product of all Prime Factors | 100 | 2 | 100 |
Least Common Multiple:
100
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 = 50
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. 189 —————————————————— = ——— L.C.M 100 R. Mult. • R. Num. 5 • 50 —————————————————— = —————— L.C.M 100
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:
189 + 5 • 50 439
———————————— = ———
100 100
Equation at the end of step 6 :
439 27 27 11
((——— + ——) + ——) + ——
100 20 20 4
Step 7 :
Calculating the Least Common Multiple :
7.1 Find the Least Common Multiple
The left denominator is : 100
The right denominator is : 20
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 2 | 2 | 2 |
| 5 | 2 | 1 | 2 |
| Product of all Prime Factors | 100 | 20 | 100 |
Least Common Multiple:
100
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 = 5
Making Equivalent Fractions :
7.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 439 —————————————————— = ——— L.C.M 100 R. Mult. • R. Num. 27 • 5 —————————————————— = —————— L.C.M 100
Adding fractions that have a common denominator :
7.4 Adding up the two equivalent fractions
439 + 27 • 5 287
———————————— = ———
100 50
Equation at the end of step 7 :
287 27 11
(——— + ——) + ——
50 20 4
Step 8 :
Calculating the Least Common Multiple :
8.1 Find the Least Common Multiple
The left denominator is : 50
The right denominator is : 20
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 1 | 2 | 2 |
| 5 | 2 | 1 | 2 |
| Product of all Prime Factors | 50 | 20 | 100 |
Least Common Multiple:
100
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 = 2
Right_M = L.C.M / R_Deno = 5
Making Equivalent Fractions :
8.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 287 • 2 —————————————————— = ——————— L.C.M 100 R. Mult. • R. Num. 27 • 5 —————————————————— = —————— L.C.M 100
Adding fractions that have a common denominator :
8.4 Adding up the two equivalent fractions
287 • 2 + 27 • 5 709
———————————————— = ———
100 100
Equation at the end of step 8 :
709 11
——— + ——
100 4
Step 9 :
Calculating the Least Common Multiple :
9.1 Find the Least Common Multiple
The left denominator is : 100
The right denominator is : 4
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 2 | 2 | 2 |
| 5 | 2 | 0 | 2 |
| Product of all Prime Factors | 100 | 4 | 100 |
Least Common Multiple:
100
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 = 1
Right_M = L.C.M / R_Deno = 25
Making Equivalent Fractions :
9.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 709 —————————————————— = ——— L.C.M 100 R. Mult. • R. Num. 11 • 25 —————————————————— = ——————— L.C.M 100
Adding fractions that have a common denominator :
9.4 Adding up the two equivalent fractions
709 + 11 • 25 246
————————————— = ———
100 25
Final result :
246
——— = 9.84000
25
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