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): "4.55" was replaced by "(455/100)". 4 more similar replacement(s)
Step 1 :
91
Simplify ——
20
Equation at the end of step 1 :
1235 242 336 91
((————+———)+———)+——
1000 100 100 20
Step 2 :
84
Simplify ——
25
Equation at the end of step 2 :
1235 242 84 91
((———— + ———) + ——) + ——
1000 100 25 20
Step 3 :
121
Simplify ———
50
Equation at the end of step 3 :
1235 121 84 91
((———— + ———) + ——) + ——
1000 50 25 20
Step 4 :
247
Simplify ———
200
Equation at the end of step 4 :
247 121 84 91
((——— + ———) + ——) + ——
200 50 25 20
Step 5 :
Calculating the Least Common Multiple :
5.1 Find the Least Common Multiple
The left denominator is : 200
The right denominator is : 50
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 3 | 1 | 3 |
| 5 | 2 | 2 | 2 |
| Product of all Prime Factors | 200 | 50 | 200 |
Least Common Multiple:
200
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 = 4
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. 247 —————————————————— = ——— L.C.M 200 R. Mult. • R. Num. 121 • 4 —————————————————— = ——————— L.C.M 200
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:
247 + 121 • 4 731
————————————— = ———
200 200
Equation at the end of step 5 :
731 84 91
(——— + ——) + ——
200 25 20
Step 6 :
Calculating the Least Common Multiple :
6.1 Find the Least Common Multiple
The left denominator is : 200
The right denominator is : 25
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 3 | 0 | 3 |
| 5 | 2 | 2 | 2 |
| Product of all Prime Factors | 200 | 25 | 200 |
Least Common Multiple:
200
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 = 8
Making Equivalent Fractions :
6.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 731 —————————————————— = ——— L.C.M 200 R. Mult. • R. Num. 84 • 8 —————————————————— = —————— L.C.M 200
Adding fractions that have a common denominator :
6.4 Adding up the two equivalent fractions
731 + 84 • 8 1403
———————————— = ————
200 200
Equation at the end of step 6 :
1403 91
———— + ——
200 20
Step 7 :
Calculating the Least Common Multiple :
7.1 Find the Least Common Multiple
The left denominator is : 200
The right denominator is : 20
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 3 | 2 | 3 |
| 5 | 2 | 1 | 2 |
| Product of all Prime Factors | 200 | 20 | 200 |
Least Common Multiple:
200
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. 1403 —————————————————— = ———— L.C.M 200 R. Mult. • R. Num. 91 • 10 —————————————————— = ——————— L.C.M 200
Adding fractions that have a common denominator :
7.4 Adding up the two equivalent fractions
1403 + 91 • 10 2313
—————————————— = ————
200 200
Final result :
2313
———— = 11.56500
200
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