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): "0.1" was replaced by "(1/10)". 4 more similar replacement(s)
Step 1 :
1
Simplify ——
10
Equation at the end of step 1 :
18965 1256 4563 1
((—————+————)+————)+——
1000 1000 100 10
Step 2 :
4563
Simplify ————
100
Equation at the end of step 2 :
18965 1256 4563 1
((————— + ————) + ————) + ——
1000 1000 100 10
Step 3 :
157
Simplify ———
125
Equation at the end of step 3 :
18965 157 4563 1
((————— + ———) + ————) + ——
1000 125 100 10
Step 4 :
3793
Simplify ————
200
Equation at the end of step 4 :
3793 157 4563 1
((———— + ———) + ————) + ——
200 125 100 10
Step 5 :
Calculating the Least Common Multiple :
5.1 Find the Least Common Multiple
The left denominator is : 200
The right denominator is : 125
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 3 | 0 | 3 |
| 5 | 2 | 3 | 3 |
| Product of all Prime Factors | 200 | 125 | 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 = 8
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. 3793 • 5 —————————————————— = ———————— L.C.M 1000 R. Mult. • R. Num. 157 • 8 —————————————————— = ——————— L.C.M 1000
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:
3793 • 5 + 157 • 8 20221
—————————————————— = —————
1000 1000
Equation at the end of step 5 :
20221 4563 1
(————— + ————) + ——
1000 100 10
Step 6 :
Calculating the Least Common Multiple :
6.1 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 :
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 = 1
Right_M = L.C.M / R_Deno = 10
Making Equivalent Fractions :
6.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 20221 —————————————————— = ————— L.C.M 1000 R. Mult. • R. Num. 4563 • 10 —————————————————— = ————————— L.C.M 1000
Adding fractions that have a common denominator :
6.4 Adding up the two equivalent fractions
20221 + 4563 • 10 65851
————————————————— = —————
1000 1000
Equation at the end of step 6 :
65851 1
————— + ——
1000 10
Step 7 :
Calculating the Least Common Multiple :
7.1 Find the Least Common Multiple
The left denominator is : 1000
The right denominator is : 10
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 3 | 1 | 3 |
| 5 | 3 | 1 | 3 |
| Product of all Prime Factors | 1000 | 10 | 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 = 100
Making Equivalent Fractions :
7.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 65851 —————————————————— = ————— L.C.M 1000 R. Mult. • R. Num. 100 —————————————————— = ———— L.C.M 1000
Adding fractions that have a common denominator :
7.4 Adding up the two equivalent fractions
65851 + 100 65951
——————————— = —————
1000 1000
Final result :
65951
————— = 65.95100
1000
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