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): "0.832" was replaced by "(832/1000)". 4 more similar replacement(s)
Step 1 :
104
Simplify ———
125
Equation at the end of step 1 :
15 14673 19 104
((——+—————)+——)+———
10 100 10 125
Step 2 :
19
Simplify ——
10
Equation at the end of step 2 :
15 14673 19 104
((—— + —————) + ——) + ———
10 100 10 125
Step 3 :
14673
Simplify —————
100
Equation at the end of step 3 :
15 14673 19 104
((—— + —————) + ——) + ———
10 100 10 125
Step 4 :
3
Simplify —
2
Equation at the end of step 4 :
3 14673 19 104
((— + —————) + ——) + ———
2 100 10 125
Step 5 :
Calculating the Least Common Multiple :
5.1 Find the Least Common Multiple
The left denominator is : 2
The right denominator is : 100
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 1 | 2 | 2 |
| 5 | 0 | 2 | 2 |
| Product of all Prime Factors | 2 | 100 | 100 |
Least Common Multiple:
100
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 = 50
Right_M = L.C.M / R_Deno = 1
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. 3 • 50 —————————————————— = —————— L.C.M 100 R. Mult. • R. Num. 14673 —————————————————— = ————— L.C.M 100
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:
3 • 50 + 14673 14823
—————————————— = —————
100 100
Equation at the end of step 5 :
14823 19 104
(————— + ——) + ———
100 10 125
Step 6 :
Calculating the Least Common Multiple :
6.1 Find the Least Common Multiple
The left denominator is : 100
The right denominator is : 10
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 2 | 1 | 2 |
| 5 | 2 | 1 | 2 |
| Product of all Prime Factors | 100 | 10 | 100 |
Least Common Multiple:
100
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. 14823 —————————————————— = ————— L.C.M 100 R. Mult. • R. Num. 19 • 10 —————————————————— = ——————— L.C.M 100
Adding fractions that have a common denominator :
6.4 Adding up the two equivalent fractions
14823 + 19 • 10 15013
——————————————— = —————
100 100
Equation at the end of step 6 :
15013 104
————— + ———
100 125
Step 7 :
Calculating the Least Common Multiple :
7.1 Find the Least Common Multiple
The left denominator is : 100
The right denominator is : 125
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 2 | 0 | 2 |
| 5 | 2 | 3 | 3 |
| Product of all Prime Factors | 100 | 125 | 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 = 5
Right_M = L.C.M / R_Deno = 4
Making Equivalent Fractions :
7.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 15013 • 5 —————————————————— = ————————— L.C.M 500 R. Mult. • R. Num. 104 • 4 —————————————————— = ——————— L.C.M 500
Adding fractions that have a common denominator :
7.4 Adding up the two equivalent fractions
15013 • 5 + 104 • 4 75481
——————————————————— = —————
500 500
Final result :
75481
————— = 150.96200
500
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