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): "0.14" was replaced by "(14/100)". 4 more similar replacement(s)
Step 1 :
7
Simplify ——
50
Equation at the end of step 1 :
15 525 225 7
((————+————)+————)+——
1000 1000 1000 50
Step 2 :
9
Simplify ——
40
Equation at the end of step 2 :
15 525 9 7
((———— + ————) + ——) + ——
1000 1000 40 50
Step 3 :
21
Simplify ——
40
Equation at the end of step 3 :
15 21 9 7
((———— + ——) + ——) + ——
1000 40 40 50
Step 4 :
3
Simplify ———
200
Equation at the end of step 4 :
3 21 9 7
((——— + ——) + ——) + ——
200 40 40 50
Step 5 :
Calculating the Least Common Multiple :
5.1 Find the Least Common Multiple
The left denominator is : 200
The right denominator is : 40
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 3 | 3 | 3 |
| 5 | 2 | 1 | 2 |
| Product of all Prime Factors | 200 | 40 | 200 |
Least Common Multiple:
200
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 = 5
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. 3 —————————————————— = ——— L.C.M 200 R. Mult. • R. Num. 21 • 5 —————————————————— = —————— L.C.M 200
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:
3 + 21 • 5 27
—————————— = ——
200 50
Equation at the end of step 5 :
27 9 7
(—— + ——) + ——
50 40 50
Step 6 :
Calculating the Least Common Multiple :
6.1 Find the Least Common Multiple
The left denominator is : 50
The right denominator is : 40
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 1 | 3 | 3 |
| 5 | 2 | 1 | 2 |
| Product of all Prime Factors | 50 | 40 | 200 |
Least Common Multiple:
200
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 = 4
Right_M = L.C.M / R_Deno = 5
Making Equivalent Fractions :
6.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 27 • 4 —————————————————— = —————— L.C.M 200 R. Mult. • R. Num. 9 • 5 —————————————————— = ————— L.C.M 200
Adding fractions that have a common denominator :
6.4 Adding up the two equivalent fractions
27 • 4 + 9 • 5 153
—————————————— = ———
200 200
Equation at the end of step 6 :
153 7
——— + ——
200 50
Step 7 :
Calculating the Least Common Multiple :
7.1 Find the Least Common Multiple
The left denominator is : 200
The right denominator is : 50
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 3 | 1 | 3 |
| 5 | 2 | 2 | 2 |
| Product of all Prime Factors | 200 | 50 | 200 |
Least Common Multiple:
200
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 = 4
Making Equivalent Fractions :
7.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 153 —————————————————— = ——— L.C.M 200 R. Mult. • R. Num. 7 • 4 —————————————————— = ————— L.C.M 200
Adding fractions that have a common denominator :
7.4 Adding up the two equivalent fractions
153 + 7 • 4 181
——————————— = ———
200 200
Final result :
181
——— = 0.90500
200
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