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): "246.9" was replaced by "(2469/10)". 4 more similar replacement(s)
Step 1 :
2469
Simplify ————
10
Equation at the end of step 1 :
75006 23 15863 2469
((—————+——)+—————)+————
1000 10 1000 10
Step 2 :
15863
Simplify —————
1000
Equation at the end of step 2 :
75006 23 15863 2469
((————— + ——) + —————) + ————
1000 10 1000 10
Step 3 :
23
Simplify ——
10
Equation at the end of step 3 :
75006 23 15863 2469
((————— + ——) + —————) + ————
1000 10 1000 10
Step 4 :
37503
Simplify —————
500
Equation at the end of step 4 :
37503 23 15863 2469
((————— + ——) + —————) + ————
500 10 1000 10
Step 5 :
Calculating the Least Common Multiple :
5.1 Find the Least Common Multiple
The left denominator is : 500
The right denominator is : 10
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 2 | 1 | 2 |
| 5 | 3 | 1 | 3 |
| Product of all Prime Factors | 500 | 10 | 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 = 50
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. 37503 —————————————————— = ————— L.C.M 500 R. Mult. • R. Num. 23 • 50 —————————————————— = ——————— 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:
37503 + 23 • 50 38653
——————————————— = —————
500 500
Equation at the end of step 5 :
38653 15863 2469
(————— + —————) + ————
500 1000 10
Step 6 :
Calculating the Least Common Multiple :
6.1 Find the Least Common Multiple
The left denominator is : 500
The right denominator is : 1000
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 2 | 3 | 3 |
| 5 | 3 | 3 | 3 |
| Product of all Prime Factors | 500 | 1000 | 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 = 2
Right_M = L.C.M / R_Deno = 1
Making Equivalent Fractions :
6.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 38653 • 2 —————————————————— = ————————— L.C.M 1000 R. Mult. • R. Num. 15863 —————————————————— = ————— L.C.M 1000
Adding fractions that have a common denominator :
6.4 Adding up the two equivalent fractions
38653 • 2 + 15863 93169
————————————————— = —————
1000 1000
Equation at the end of step 6 :
93169 2469
————— + ————
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. 93169 —————————————————— = ————— L.C.M 1000 R. Mult. • R. Num. 2469 • 100 —————————————————— = —————————— L.C.M 1000
Adding fractions that have a common denominator :
7.4 Adding up the two equivalent fractions
93169 + 2469 • 100 340069
—————————————————— = ——————
1000 1000
Final result :
340069
—————— = 340.06900
1000
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