5463
Simplify ββββ
20
Equation at the end of step 1 :
5 5463
k - ((β β’ (f - 32)) + ββββ) = 0
9 20
Step 2 :
5
Simplify β
9
Equation at the end of step 2 :
5 5463
k - ((β β’ (f - 32)) + ββββ) = 0
9 20
Step 3 :
Equation at the end of step 3 :
5 β’ (f - 32) 5463
k - (ββββββββββββ + ββββ) = 0
9 20
Step 4 :
Calculating the Least Common Multiple :
4.1 Find the Least Common Multiple
The left denominator is : 9
The right denominator is : 20
Number of times each prime factor
appears in the factorization of:
Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
3202
2022
5011
Product of all
Prime Factors 920180
Least Common Multiple:
180
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 = 20
Right_M = L.C.M / R_Deno = 9
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. β’ L. Num. 5 β’ (f-32) β’ 20
ββββββββββββββββββ = βββββββββββββββ
L.C.M 180
R. Mult. β’ R. Num. 5463 β’ 9
ββββββββββββββββββ = ββββββββ
L.C.M 180
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:
5 β’ (f-32) β’ 20 + 5463 β’ 9 100f + 45967
ββββββββββββββββββββββββββ = ββββββββββββ
180 180
Equation at the end of step 4 :
(100f + 45967)
k - ββββββββββββββ = 0
180
Step 5 :
Rewriting the whole as an Equivalent Fraction :
5.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using 180 as the denominator :
k k β’ 180
k = β = βββββββ
1 180
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 :
5.2 Adding up the two equivalent fractions
k β’ 180 - ((100f+45967)) 180k - 100f - 45967
ββββββββββββββββββββββββ = βββββββββββββββββββ
180 180
Equation at the end of step 5 :
180k - 100f - 45967
βββββββββββββββββββ = 0
180
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:
180k-100f-45967
βββββββββββββββ β’ 180 = 0 β’ 180
180
Now, on the left hand side, the 180 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
180k-100f-45967 = 0
Equation of a Straight Line
6.2 Solve 180k-100f-45967 = 0
Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).
"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.
In this formula :
y tells us how far up the line goes
x tells us how far along
m is the Slope or Gradient i.e. how steep the line is
b is the Y-intercept i.e. where the line crosses the Y axis
The X and Y intercepts and the Slope are called the line properties. We shall now graph the line 180k-100f-45967 = 0 and calculate its properties
Graph of a Straight Line :
Calculate the Y-Intercept :
Notice that when k = 0 the value of f is 45967/-100 so this line "cuts" the f axis at f=-459.67000
f-intercept = 45967/-100 = -459.67000
Calculate the X-Intercept :
When f = 0 the value of k is 45967/180 Our line therefore "cuts" the k axis at k=255.37222
k-intercept = 45967/180 = 255.37222
Calculate the Slope :
Slope is defined as the change in f divided by the change in k. We note that for k=0, the value of f is -459.670 and for k=2.000, the value of f is -456.070. So, for a change of 2.000 in k (The change in k is sometimes referred to as "RUN") we get a change of -456.070 - (-459.670) = 3.600 in f. (The change in f is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
Slope = 3.600/2.000 = 1.800
Geometric figure: Straight Line
Slope = 3.600/2.000 = 1.800
k-intercept = 45967/180 = 255.37222
f-intercept = 45967/-100 = -459.67000
