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): "18.01" was replaced by "(1801/100)". 4 more similar replacement(s)
Step 1 :
1801
Simplify ————
100
Equation at the end of step 1 :
5536 623 2369 1801
((————+———)+————)+————
100 10 1000 100
Step 2 :
2369
Simplify ————
1000
Equation at the end of step 2 :
5536 623 2369 1801
((———— + ———) + ————) + ————
100 10 1000 100
Step 3 :
623
Simplify ———
10
Equation at the end of step 3 :
5536 623 2369 1801
((———— + ———) + ————) + ————
100 10 1000 100
Step 4 :
1384
Simplify ————
25
Equation at the end of step 4 :
1384 623 2369 1801
((———— + ———) + ————) + ————
25 10 1000 100
Step 5 :
Calculating the Least Common Multiple :
5.1 Find the Least Common Multiple
The left denominator is : 25
The right denominator is : 10
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 5 | 2 | 1 | 2 |
| 2 | 0 | 1 | 1 |
| Product of all Prime Factors | 25 | 10 | 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 = 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. 1384 • 2 —————————————————— = ———————— L.C.M 50 R. Mult. • R. Num. 623 • 5 —————————————————— = ——————— 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:
1384 • 2 + 623 • 5 5883
—————————————————— = ————
50 50
Equation at the end of step 5 :
5883 2369 1801
(———— + ————) + ————
50 1000 100
Step 6 :
Calculating the Least Common Multiple :
6.1 Find the Least Common Multiple
The left denominator is : 50
The right denominator is : 1000
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 1 | 3 | 3 |
| 5 | 2 | 3 | 3 |
| Product of all Prime Factors | 50 | 1000 | 1000 |
Least Common Multiple:
1000
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 = 20
Right_M = L.C.M / R_Deno = 1
Making Equivalent Fractions :
6.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 5883 • 20 —————————————————— = ————————— L.C.M 1000 R. Mult. • R. Num. 2369 —————————————————— = ———— L.C.M 1000
Adding fractions that have a common denominator :
6.4 Adding up the two equivalent fractions
5883 • 20 + 2369 120029
———————————————— = ——————
1000 1000
Equation at the end of step 6 :
120029 1801
—————— + ————
1000 100
Step 7 :
Calculating the Least Common Multiple :
7.1 Find the Least Common Multiple
The left denominator is : 1000
The right denominator is : 100
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 3 | 2 | 3 |
| 5 | 3 | 2 | 3 |
| Product of all Prime Factors | 1000 | 100 | 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 = 1
Right_M = L.C.M / R_Deno = 10
Making Equivalent Fractions :
7.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 120029 —————————————————— = —————— L.C.M 1000 R. Mult. • R. Num. 1801 • 10 —————————————————— = ————————— L.C.M 1000
Adding fractions that have a common denominator :
7.4 Adding up the two equivalent fractions
120029 + 1801 • 10 138039
—————————————————— = ——————
1000 1000
Final result :
138039
—————— = 138.03900
1000
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