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): "3.65" was replaced by "(365/100)". 4 more similar replacement(s)
Step 1 :
73
Simplify ——
20
Equation at the end of step 1 :
244 35 2536 73
((———+——)+————)+——
100 10 1000 20
Step 2 :
317
Simplify ———
125
Equation at the end of step 2 :
244 35 317 73
((——— + ——) + ———) + ——
100 10 125 20
Step 3 :
7
Simplify —
2
Equation at the end of step 3 :
244 7 317 73
((——— + —) + ———) + ——
100 2 125 20
Step 4 :
61
Simplify ——
25
Equation at the end of step 4 :
61 7 317 73
((—— + —) + ———) + ——
25 2 125 20
Step 5 :
Calculating the Least Common Multiple :
5.1 Find the Least Common Multiple
The left denominator is : 25
The right denominator is : 2
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 5 | 2 | 0 | 2 |
| 2 | 0 | 1 | 1 |
| Product of all Prime Factors | 25 | 2 | 50 |
Least Common Multiple:
50
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 = 25
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. 61 • 2 —————————————————— = —————— L.C.M 50 R. Mult. • R. Num. 7 • 25 —————————————————— = —————— L.C.M 50
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:
61 • 2 + 7 • 25 297
——————————————— = ———
50 50
Equation at the end of step 5 :
297 317 73
(——— + ———) + ——
50 125 20
Step 6 :
Calculating the Least Common Multiple :
6.1 Find the Least Common Multiple
The left denominator is : 50
The right denominator is : 125
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 1 | 0 | 1 |
| 5 | 2 | 3 | 3 |
| Product of all Prime Factors | 50 | 125 | 250 |
Least Common Multiple:
250
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 = 5
Right_M = L.C.M / R_Deno = 2
Making Equivalent Fractions :
6.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 297 • 5 —————————————————— = ——————— L.C.M 250 R. Mult. • R. Num. 317 • 2 —————————————————— = ——————— L.C.M 250
Adding fractions that have a common denominator :
6.4 Adding up the two equivalent fractions
297 • 5 + 317 • 2 2119
————————————————— = ————
250 250
Equation at the end of step 6 :
2119 73
———— + ——
250 20
Step 7 :
Calculating the Least Common Multiple :
7.1 Find the Least Common Multiple
The left denominator is : 250
The right denominator is : 20
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 1 | 2 | 2 |
| 5 | 3 | 1 | 3 |
| Product of all Prime Factors | 250 | 20 | 500 |
Least Common Multiple:
500
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 = 2
Right_M = L.C.M / R_Deno = 25
Making Equivalent Fractions :
7.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 2119 • 2 —————————————————— = ———————— L.C.M 500 R. Mult. • R. Num. 73 • 25 —————————————————— = ——————— L.C.M 500
Adding fractions that have a common denominator :
7.4 Adding up the two equivalent fractions
2119 • 2 + 73 • 25 6063
—————————————————— = ————
500 500
Final result :
6063
———— = 12.12600
500
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