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): "72.45" was replaced by "(7245/100)". 2 more similar replacement(s)
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
(x*(4099/10000))+x-((7245/100))=0
Step by step solution :
Step 1 :
1449
Simplify ————
20
Equation at the end of step 1 :
4099 1449
((x • —————) + x) - ———— = 0
10000 20
Step 2 :
4099
Simplify —————
10000
Equation at the end of step 2 :
4099 1449
((x • —————) + x) - ———— = 0
10000 20
Step 3 :
Rewriting the whole as an Equivalent Fraction :
3.1 Adding a whole to a fraction
Rewrite the whole as a fraction using 10000 as the denominator :
x x • 10000
x = — = —————————
1 10000
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
3.2 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:
4099x + x • 10000 14099x
————————————————— = ——————
10000 10000
Equation at the end of step 3 :
14099x 1449
—————— - ———— = 0
10000 20
Step 4 :
Calculating the Least Common Multiple :
4.1 Find the Least Common Multiple
The left denominator is : 10000
The right denominator is : 20
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 4 | 2 | 4 |
| 5 | 4 | 1 | 4 |
| Product of all Prime Factors | 10000 | 20 | 10000 |
Least Common Multiple:
10000
Calculating Multipliers :
4.2 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 = 500
Making Equivalent Fractions :
4.3 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. 14099x —————————————————— = —————— L.C.M 10000 R. Mult. • R. Num. 1449 • 500 —————————————————— = —————————— L.C.M 10000
Adding fractions that have a common denominator :
4.4 Adding up the two equivalent fractions
14099x - (1449 • 500) 14099x - 724500
————————————————————— = ———————————————
10000 10000
Step 5 :
Pulling out like terms :
5.1 Pull out like factors :
14099x - 724500 = 23 • (613x - 31500)
Equation at the end of step 5 :
23 • (613x - 31500)
——————————————————— = 0
10000
Step 6 :
When a fraction equals zero :
6.1 When a fraction equals zero ...Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.
Here's how:
23•(613x-31500)
——————————————— • 10000 = 0 • 10000
10000
Now, on the left hand side, the 10000 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
23 • (613x-31500) = 0
Equations which are never true :
6.2 Solve : 23 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Solving a Single Variable Equation :
6.3 Solve : 613x-31500 = 0
Add 31500 to both sides of the equation :
613x = 31500
Divide both sides of the equation by 613:
x = 31500/613 = 51.387
One solution was found :
x = 31500/613 = 51.387How did we do?
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