Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
t/15-t/35-(1/15)=0
Step by step solution :Step 1 : 1
Simplify ——
15
Advertising SkipEquation at the end of step 1 : t t 1
(—— - ——) - —— = 0
15 35 15
Step 2 : t
Simplify ——
35
Equation at the end of step 2 : t t 1
(—— - ——) - —— = 0
15 35 15
Step 3 : t
Simplify ——
15
Equation at the end of step 3 : t t 1
(—— - ——) - —— = 0
15 35 15
Step 4 :Calculating the Least Common Multiple :
4.1 Find the Least Common Multiple
The left denominator is : 15
The right denominator is : 35
Number of times each prime factor
appears in the factorization of: Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right} 310151117011 Product of all
Prime Factors 1535105
Least Common Multiple:
105
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 = 7
Right_M = L.C.M / R_Deno = 3
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 respectiveMultiplier.
L. Mult. • L. Num. t • 7
—————————————————— = —————
L.C.M 105
R. Mult. • R. Num. t • 3
—————————————————— = —————
L.C.M 105
Adding fractions that have a common denominator :
4.4 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:
t • 7 - (t • 3) 4t
——————————————— = ———
105 105
Equation at the end of step 4 : 4t 1
——— - —— = 0
105 15
Step 5 :Calculating the Least Common Multiple :
5.1 Find the Least Common Multiple
The left denominator is : 105
The right denominator is : 15
Number of times each prime factor
appears in the factorization of: Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right} 311151117101 Product of all
Prime Factors 10515105
Least Common Multiple:
105
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 = 7
Making Equivalent Fractions :
5.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 4t
—————————————————— = ———
L.C.M 105
R. Mult. • R. Num. 7
—————————————————— = ———
L.C.M 105
Adding fractions that have a common denominator :
5.4 Adding up the two equivalent fractions
4t - (7) 4t - 7
———————— = ——————
105 105
Equation at the end of step 5 : 4t - 7
—————— = 0
105
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:
4t-7
———— • 105 = 0 • 105
105
Now, on the left hand side, the 105 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
4t-7 = 0
Solving a Single Variable Equation :
6.2 Solve : 4t-7 = 0
Add 7 to both sides of the equation :
4t = 7
Divide both sides of the equation by 4:
t = 7/4 = 1.750
