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): "56.198" was replaced by "(56198/1000)". 4 more similar replacement(s)
Step 1 :
28099
Simplify —————
500
Equation at the end of step 1 :
506 3 314 28099
((————+———)+———)+—————
1000 100 100 500
Step 2 :
157
Simplify ———
50
Equation at the end of step 2 :
506 3 157 28099
((———— + ———) + ———) + —————
1000 100 50 500
Step 3 :
3
Simplify ———
100
Equation at the end of step 3 :
506 3 157 28099
((———— + ———) + ———) + —————
1000 100 50 500
Step 4 :
253
Simplify ———
500
Equation at the end of step 4 :
253 3 157 28099
((——— + ———) + ———) + —————
500 100 50 500
Step 5 :
Calculating the Least Common Multiple :
5.1 Find the Least Common Multiple
The left denominator is : 500
The right denominator is : 100
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 2 | 2 | 2 |
| 5 | 3 | 2 | 3 |
| Product of all Prime Factors | 500 | 100 | 500 |
Least Common Multiple:
500
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 = 1
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. 253 —————————————————— = ——— L.C.M 500 R. Mult. • R. Num. 3 • 5 —————————————————— = ————— L.C.M 500
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:
253 + 3 • 5 67
——————————— = ———
500 125
Equation at the end of step 5 :
67 157 28099
(——— + ———) + —————
125 50 500
Step 6 :
Calculating the Least Common Multiple :
6.1 Find the Least Common Multiple
The left denominator is : 125
The right denominator is : 50
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 5 | 3 | 2 | 3 |
| 2 | 0 | 1 | 1 |
| Product of all Prime Factors | 125 | 50 | 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 = 2
Right_M = L.C.M / R_Deno = 5
Making Equivalent Fractions :
6.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 67 • 2 —————————————————— = —————— L.C.M 250 R. Mult. • R. Num. 157 • 5 —————————————————— = ——————— L.C.M 250
Adding fractions that have a common denominator :
6.4 Adding up the two equivalent fractions
67 • 2 + 157 • 5 919
———————————————— = ———
250 250
Equation at the end of step 6 :
919 28099
——— + —————
250 500
Step 7 :
Calculating the Least Common Multiple :
7.1 Find the Least Common Multiple
The left denominator is : 250
The right denominator is : 500
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 1 | 2 | 2 |
| 5 | 3 | 3 | 3 |
| Product of all Prime Factors | 250 | 500 | 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 = 1
Making Equivalent Fractions :
7.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 919 • 2 —————————————————— = ——————— L.C.M 500 R. Mult. • R. Num. 28099 —————————————————— = ————— L.C.M 500
Adding fractions that have a common denominator :
7.4 Adding up the two equivalent fractions
919 • 2 + 28099 29937
——————————————— = —————
500 500
Final result :
29937
————— = 59.87400
500
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