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): "7.95" was replaced by "(795/100)". 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 :
y-(433/100)-((167/100)*(x+(795/100)))=0
Step 1 :
159
Simplify ———
20
Equation at the end of step 1 :
433 167 159
(y-———)-(———•(x+———)) = 0
100 100 20
Step 2 :
Rewriting the whole as an Equivalent Fraction :
2.1 Adding a fraction to a whole
Rewrite the whole as a fraction using 20 as the denominator :
x x • 20
x = — = ——————
1 20
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 :
2.2 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:
x • 20 + 159 20x + 159
———————————— = —————————
20 20
Equation at the end of step 2 :
433 167 (20x + 159)
(y - ———) - (——— • ———————————) = 0
100 100 20
Step 3 :
167
Simplify ———
100
Equation at the end of step 3 :
433 167 (20x + 159)
(y - ———) - (——— • ———————————) = 0
100 100 20
Step 4 :
Equation at the end of step 4 :
433 167 • (20x + 159)
(y - ———) - ————————————————— = 0
100 2000
Step 5 :
433
Simplify ———
100
Equation at the end of step 5 :
433 167 • (20x + 159)
(y - ———) - ————————————————— = 0
100 2000
Step 6 :
Rewriting the whole as an Equivalent Fraction :
6.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using 100 as the denominator :
y y • 100
y = — = ———————
1 100
Adding fractions that have a common denominator :
6.2 Adding up the two equivalent fractions
y • 100 - (433) 100y - 433
——————————————— = ——————————
100 100
Equation at the end of step 6 :
(100y - 433) 167 • (20x + 159)
———————————— - ————————————————— = 0
100 2000
Step 7 :
Calculating the Least Common Multiple :
7.1 Find the Least Common Multiple
The left denominator is : 100
The right denominator is : 2000
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 2 | 4 | 4 |
| 5 | 2 | 3 | 3 |
| Product of all Prime Factors | 100 | 2000 | 2000 |
Least Common Multiple:
2000
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 = 20
Right_M = L.C.M / R_Deno = 1
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. (100y-433) • 20 —————————————————— = ——————————————— L.C.M 2000 R. Mult. • R. Num. 167 • (20x+159) —————————————————— = ——————————————— L.C.M 2000
Adding fractions that have a common denominator :
7.4 Adding up the two equivalent fractions
(100y-433) • 20 - (167 • (20x+159)) 2000y - 3340x - 35213
——————————————————————————————————— = —————————————————————
2000 2000
Equation at the end of step 7 :
2000y - 3340x - 35213
————————————————————— = 0
2000
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:
2000y-3340x-35213
————————————————— • 2000 = 0 • 2000
2000
Now, on the left hand side, the 2000 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
2000y-3340x-35213 = 0
Equation of a Straight Line
8.2 Solve 2000y-3340x-35213 = 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 2000y-3340x-35213 = 0 and calculate its properties
Graph of a Straight Line :
Calculate the Y-Intercept :
Notice that when x = 0 the value of y is 35213/2000 so this line "cuts" the y axis at y=17.60650
y-intercept = 35213/2000 = 17.60650 Calculate the X-Intercept :
When y = 0 the value of x is 35213/-3340 Our line therefore "cuts" the x axis at x=-10.54281
x-intercept = 35213/-3340 = -10.54281 Calculate the Slope :
Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 17.607 and for x=2.000, the value of y is 20.947. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 20.947 - 17.607 = 3.340 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
Slope = 3.340/2.000 = 1.670 Geometric figure: Straight Line
- Slope = 3.340/2.000 = 1.670
- x-intercept = 35213/-3340 = -10.54281
- y-intercept = 35213/2000 = 17.60650
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