expand (x/2+2y/3-3z/4)
Answers
Answer:
6x + 8y - 9z
————————————
12
Step-by-step explanation:
Step 1 :
z
Simplify —
4
Equation at the end of step 1 :
x y z
(—+(2•—))-(3•—)
2 3 4
Step 2 :
y
Simplify —
3
Equation at the end of step 2 :
x y 3z
(— + (2 • —)) - ——
2 3 4
Step 3 :
x
Simplify —
2
Equation at the end of step 3 :
x 2y 3z
(— + ——) - ——
2 3 4
Step 4 :
Calculating the Least Common Multiple :
4.1 Find the Least Common Multiple
The left denominator is : 2
The right denominator is : 3
Number of times each prime factor
appears in the factorization of:
Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
2 1 0 1
3 0 1 1
Product of all
Prime Factors 2 3 6
Least Common Multiple:
6
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 = 3
Right_M = L.C.M / R_Deno = 2
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. x • 3
—————————————————— = —————
L.C.M 6
R. Mult. • R. Num. 2y • 2
—————————————————— = ——————
L.C.M 6
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:
x • 3 + 2y • 2 3x + 4y
—————————————— = ———————
6 6
Equation at the end of step 4 :
(3x + 4y) 3z
————————— - ——
6 4
Step 5 :
Calculating the Least Common Multiple :
5.1 Find the Least Common Multiple
The left denominator is : 6
The right denominator is : 4
Number of times each prime factor
appears in the factorization of:
Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
2 1 2 2
3 1 0 1
Product of all
Prime Factors 6 4 12
Least Common Multiple:
12
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 = 2
Right_M = L.C.M / R_Deno = 3
Making Equivalent Fractions :
5.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. (3x+4y) • 2
—————————————————— = ———————————
L.C.M 12
R. Mult. • R. Num. 3z • 3
—————————————————— = ——————
L.C.M 12
Adding fractions that have a common denominator :
5.4 Adding up the two equivalent fractions
(3x+4y) • 2 - (3z • 3) 6x + 8y - 9z
—————————————————————— = ————————————
12 12
Final result :
6x + 8y - 9z
————————————
12