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): "16.42" was replaced by "(1642/100)". 4 more similar replacement(s)
Step 1 :
821
Simplify ———
50
Equation at the end of step 1 :
368 4975 13 821
((———+————)+——)+———
100 1000 10 50
Step 2 :
13
Simplify ——
10
Equation at the end of step 2 :
368 4975 13 821
((——— + ————) + ——) + ———
100 1000 10 50
Step 3 :
199
Simplify ———
40
Equation at the end of step 3 :
368 199 13 821
((——— + ———) + ——) + ———
100 40 10 50
Step 4 :
92
Simplify ——
25
Equation at the end of step 4 :
92 199 13 821
((—— + ———) + ——) + ———
25 40 10 50
Step 5 :
Calculating the Least Common Multiple :
5.1 Find the Least Common Multiple
The left denominator is : 25
The right denominator is : 40
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 5 | 2 | 1 | 2 |
| 2 | 0 | 3 | 3 |
| Product of all Prime Factors | 25 | 40 | 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 = 8
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. 92 • 8 —————————————————— = —————— L.C.M 200 R. Mult. • R. Num. 199 • 5 —————————————————— = ——————— 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:
92 • 8 + 199 • 5 1731
———————————————— = ————
200 200
Equation at the end of step 5 :
1731 13 821
(———— + ——) + ———
200 10 50
Step 6 :
Calculating the Least Common Multiple :
6.1 Find the Least Common Multiple
The left denominator is : 200
The right denominator is : 10
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 3 | 1 | 3 |
| 5 | 2 | 1 | 2 |
| Product of all Prime Factors | 200 | 10 | 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 = 20
Making Equivalent Fractions :
6.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 1731 —————————————————— = ———— L.C.M 200 R. Mult. • R. Num. 13 • 20 —————————————————— = ——————— L.C.M 200
Adding fractions that have a common denominator :
6.4 Adding up the two equivalent fractions
1731 + 13 • 20 1991
—————————————— = ————
200 200
Equation at the end of step 6 :
1991 821
———— + ———
200 50
Step 7 :
Calculating the Least Common Multiple :
7.1 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 :
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 = 4
Making Equivalent Fractions :
7.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 1991 —————————————————— = ———— L.C.M 200 R. Mult. • R. Num. 821 • 4 —————————————————— = ——————— L.C.M 200
Adding fractions that have a common denominator :
7.4 Adding up the two equivalent fractions
1991 + 821 • 4 211
—————————————— = ———
200 8
Final result :
211
——— = 26.37500
8
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