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): "13458.537" was replaced by "(13458537/1000)". 3 more similar replacement(s)
Step 1 :
13458537
Simplify ————————
1000
Equation at the end of step 1 :
1074 10495 13458537
(———— + —————) + ————————
10 1000 1000
Step 2 :
2099
Simplify ————
200
Equation at the end of step 2 :
1074 2099 13458537
(———— + ————) + ————————
10 200 1000
Step 3 :
537
Simplify ———
5
Equation at the end of step 3 :
537 2099 13458537
(——— + ————) + ————————
5 200 1000
Step 4 :
Calculating the Least Common Multiple :
4.1 Find the Least Common Multiple
The left denominator is : 5
The right denominator is : 200
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 5 | 1 | 2 | 2 |
| 2 | 0 | 3 | 3 |
| Product of all Prime Factors | 5 | 200 | 200 |
Least Common Multiple:
200
Calculating Multipliers :
4.2 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 = 40
Right_M = L.C.M / R_Deno = 1
Making Equivalent Fractions :
4.3 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. 537 • 40 —————————————————— = ———————— L.C.M 200 R. Mult. • R. Num. 2099 —————————————————— = ———— L.C.M 200
Adding fractions that have a common denominator :
4.4 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:
537 • 40 + 2099 23579
——————————————— = —————
200 200
Equation at the end of step 4 :
23579 13458537
————— + ————————
200 1000
Step 5 :
Calculating the Least Common Multiple :
5.1 Find the Least Common Multiple
The left denominator is : 200
The right denominator is : 1000
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 3 | 3 | 3 |
| 5 | 2 | 3 | 3 |
| Product of all Prime Factors | 200 | 1000 | 1000 |
Least Common Multiple:
1000
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 = 5
Right_M = L.C.M / R_Deno = 1
Making Equivalent Fractions :
5.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 23579 • 5 —————————————————— = ————————— L.C.M 1000 R. Mult. • R. Num. 13458537 —————————————————— = ———————— L.C.M 1000
Adding fractions that have a common denominator :
5.4 Adding up the two equivalent fractions
23579 • 5 + 13458537 1697054
———————————————————— = ———————
1000 125
Final result :
1697054
——————— = 13576.43200
125
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