Solution - Adding, subtracting and finding the least common multiple
Other Ways to Solve
Adding, subtracting and finding the least common multipleStep by Step Solution
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "0.41" was replaced by "(41/100)". 3 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 :
((252731/1000)*x)/((252731/1000)*x^60*12)-((41/100))=0
Step by step solution :
Step 1 :
41
Simplify ———
100
Equation at the end of step 1 :
252731 252731 41 ——————•x)——————•(x60))•12)-——— = 0 1000 (( 1000 100Step 2 :
252731 Simplify —————— 1000
Equation at the end of step 2 :
252731 252731 41
——————•x)——————•x60)•12)-——— = 0
1000 (( 1000 100
Step 3 :
Equation at the end of step 3 :
252731 252731x60 41
—————— • x) ÷ (————————— • 12) - ——— = 0
1000 1000 100
Step 4 :
Dividing exponents :
4.1 22 divided by 23 = 2(2 - 3) = 2(-1) = 1/21 = 1/2
Equation at the end of step 4 :
252731 (252731•3x60) 41
—————— • x) ÷ ————————————— - ——— = 0
1000 250 100
Step 5 :
252731
Simplify ——————
1000
Equation at the end of step 5 :
252731 (252731•3x60) 41
—————— • x) ÷ ————————————— - ——— = 0
1000 250 100
Step 6 :
252731x (252731•3x60)
Divide ——————— by —————————————
1000 250
6.1 Dividing fractions
To divide fractions, write the divison as multiplication by the reciprocal of the divisor :
252731x (252731•3x60) 252731x 250 ——————— ÷ ————————————— = ——————— • ————————————— 1000 250 1000 (252731•3x60)
Dividing exponential expressions :
6.2 x1 divided by x60 = x(1 - 60) = x(-59) = 1/x59
Dividing exponents :
6.3 21 divided by 23 = 2(1 - 3) = 2(-2) = 1/22
Canceling Out :
6.4 Canceling out 53 as it appears on both sides of the fraction line
Canceling Out :
6.5 Canceling out 252731 as it appears on both sides of the fraction line
Equation at the end of step 6 :
1 41
————— - ——— = 0
12x59 100
Step 7 :
Calculating the Least Common Multiple :
7.1 Find the Least Common Multiple
The left denominator is : 12x59
The right denominator is : 100
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 2 | 2 | 2 |
| 3 | 1 | 0 | 1 |
| 5 | 0 | 2 | 2 |
| Product of all Prime Factors | 12 | 100 | 300 |
| Algebraic Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| x | 59 | 0 | 59 |
Least Common Multiple:
300x59
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 = 25
Right_M = L.C.M / R_Deno = 3x59
Making Equivalent Fractions :
7.3 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. 25 —————————————————— = —————— L.C.M 300x59 R. Mult. • R. Num. 41 • 3x59 —————————————————— = ————————— L.C.M 300x59
Adding fractions that have a common denominator :
7.4 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:
25 - (41 • 3x59) 25 - 123x59
———————————————— = ———————————
300x59 300x59
Equation at the end of step 7 :
25 - 123x59
——————————— = 0
300x59
Step 8 :
When a fraction equals zero :
8.1 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:
25-123x59
————————— • 300x59 = 0 • 300x59
300x59
Now, on the left hand side, the 300x59 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
25-123x59 = 0
Solving a Single Variable Equation :
8.2 Solve : -123x59+25 = 0
Subtract 25 from both sides of the equation :
-123x59 = -25
Multiply both sides of the equation by (-1) : 123x59 = 25
Divide both sides of the equation by 123:
x59 = 25/123 = 0.203
x = 59th root of (25/123)
The equation has one real solution
This solution is x = 59th root of ( 0.203) = 0.97336
One solution was found :
x = 59th root of ( 0.203) = 0.97336How did we do?
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