Find the product of 9a 4ab and -2a
Answers
5a + 7b
Simplify ———————
6a
Equation at the end of step
1
:
(4a - b) (5a + 7b)
(———————— - —————————) + 1
9a 6a
STEP
2
:
4a - b
Simplify ——————
9a
Equation at the end of step
2
:
(4a - b) (5a + 7b)
(———————— - —————————) + 1
9a 6a
STEP
3
:
Calculating the Least Common Multiple :
3.1 Find the Least Common Multiple
The left denominator is : 9a
The right denominator is : 6a
Number of times each prime factor
appears in the factorization of:
Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
3 2 1 2
2 0 1 1
Product of all
Prime Factors 9 6 18
Number of times each Algebraic Factor
appears in the factorization of:
Algebraic
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
a 1 1 1
Least Common Multiple:
18a
Calculating Multipliers :
3.2 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 :
3.3 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. (4a-b) • 2
—————————————————— = ——————————
L.C.M 18a
R. Mult. • R. Num. (5a+7b) • 3
—————————————————— = ———————————
L.C.M 18a
Adding fractions that have a common denominator :
3.4 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:
(4a-b) • 2 - ((5a+7b) • 3) -7a - 23b
—————————————————————————— = —————————
18a 18a
Equation at the end of step
3
:
(-7a - 23b)
——————————— + 1
18a
STEP
4
:
Rewriting the whole as an Equivalent Fraction :
4.1 Adding a whole to a fraction
Rewrite the whole as a fraction using 18a as the denominator :
1 1 • 18a
1 = — = ———————
1 18a
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
STEP
5
:
Pulling out like terms :
5.1 Pull out like factors :
-7a - 23b = -1 • (7a + 23b)
Adding fractions that have a common denominator :
5.2 Adding up the two equivalent fractions
(-7a-23b) + 18a 11a - 23b
——————————————— = —————————
18a 18a
Final result :
11a - 23b
—————————
18a