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): "3.997" was replaced by "(3997/1000)". 4 more similar replacement(s)
Step 1 :
3997
Simplify ————
1000
Equation at the end of step 1 :
8948 3587 6643 3997
((————+————)+————)+————
10 10 10 1000
Step 2 :
6643
Simplify ————
10
Equation at the end of step 2 :
8948 3587 6643 3997
((———— + ————) + ————) + ————
10 10 10 1000
Step 3 :
3587
Simplify ————
10
Equation at the end of step 3 :
8948 3587 6643 3997
((———— + ————) + ————) + ————
10 10 10 1000
Step 4 :
4474
Simplify ————
5
Equation at the end of step 4 :
4474 3587 6643 3997
((———— + ————) + ————) + ————
5 10 10 1000
Step 5 :
Calculating the Least Common Multiple :
5.1 Find the Least Common Multiple
The left denominator is : 5
The right denominator is : 10
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 5 | 1 | 1 | 1 |
| 2 | 0 | 1 | 1 |
| Product of all Prime Factors | 5 | 10 | 10 |
Least Common Multiple:
10
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. 4474 • 2 —————————————————— = ———————— L.C.M 10 R. Mult. • R. Num. 3587 —————————————————— = ———— L.C.M 10
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:
4474 • 2 + 3587 2507
——————————————— = ————
10 2
Equation at the end of step 5 :
2507 6643 3997
(———— + ————) + ————
2 10 1000
Step 6 :
Calculating the Least Common Multiple :
6.1 Find the Least Common Multiple
The left denominator is : 2
The right denominator is : 10
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 1 | 1 | 1 |
| 5 | 0 | 1 | 1 |
| Product of all Prime Factors | 2 | 10 | 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 = 5
Right_M = L.C.M / R_Deno = 1
Making Equivalent Fractions :
6.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 2507 • 5 —————————————————— = ———————— L.C.M 10 R. Mult. • R. Num. 6643 —————————————————— = ———— L.C.M 10
Adding fractions that have a common denominator :
6.4 Adding up the two equivalent fractions
2507 • 5 + 6643 9589
——————————————— = ————
10 5
Equation at the end of step 6 :
9589 3997
———— + ————
5 1000
Step 7 :
Calculating the Least Common Multiple :
7.1 Find the Least Common Multiple
The left denominator is : 5
The right denominator is : 1000
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 5 | 1 | 3 | 3 |
| 2 | 0 | 3 | 3 |
| Product of all Prime Factors | 5 | 1000 | 1000 |
Least Common Multiple:
1000
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 = 200
Right_M = L.C.M / R_Deno = 1
Making Equivalent Fractions :
7.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 9589 • 200 —————————————————— = —————————— L.C.M 1000 R. Mult. • R. Num. 3997 —————————————————— = ———— L.C.M 1000
Adding fractions that have a common denominator :
7.4 Adding up the two equivalent fractions
9589 • 200 + 3997 1921797
————————————————— = ———————
1000 1000
Final result :
1921797
——————— = 1921.79700
1000
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