16/3(6/8b+9/2) Final result : 4 • (b + 6)
Step by step solution :
Step 1 : 9
Simplify —
2
Equation at the end of step 1 : 16 6 9
—— • ((— • b) + —)
3 8 2
Step 2 : 3
Simplify —
4
Equation at the end of step 2 : 16 3 9
—— • ((— • b) + —)
3 4 2
Step 3 :Calculating the Least Common Multiple :
3.1 Find the Least Common Multiple
The left denominator is : 4
The right denominator is : 2
Number of times each prime factor
appears in the factorization of: Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right} 2212 Product of all
Prime Factors 424
Least Common Multiple:
4
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 = 1
Right_M = L.C.M / R_Deno = 2
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 respectiveMultiplier.
L. Mult. • L. Num. 3b
—————————————————— = ——
L.C.M 4
R. Mult. • R. Num. 9 • 2
—————————————————— = —————
L.C.M 4
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:
3b + 9 • 2 3b + 18
—————————— = ———————
4 4
Equation at the end of step 3 : 16 (3b + 18)
—— • —————————
3 4
Step 4 : 16
Simplify ——
3
Equation at the end of step 4 : 16 (3b + 18)
—— • —————————
3 4
Step 5 :Step 6 :Pulling out like terms :
6.1 Pull out like factors :
3b + 18 = 3 • (b + 6)
Final result :
4 • (b + 6)
