Answer:
(19a-279)/18
Step-by-step explanation:
STEP
1
:
17
Simplify ——
2
Equation at the end of step
1
:
2 7 17
(((—•a)-7)+(——•a))-——
3 18 2
STEP
2
:
7
Simplify ——
18
Equation at the end of step
2
:
2 7 17
(((—•a)-7)+(——•a))-——
3 18 2
STEP
3
:
2
Simplify —
3
Equation at the end of step
3
:
2 7a 17
(((— • a) - 7) + ——) - ——
3 18 2
STEP
4
:
Rewriting the whole as an Equivalent Fraction
4.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using 3 as the denominator :
7 7 • 3
7 = — = —————
1 3
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 :
4.2 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:
2a - (7 • 3) 2a - 21
———————————— = ———————
3 3
Equation at the end of step
4
:
(2a - 21) 7a 17
(————————— + ——) - ——
3 18 2
STEP
5
:
Calculating the Least Common Multiple :
5.1 Find the Least Common Multiple
The left denominator is : 3
The right denominator is : 18
Number of times each prime factor
appears in the factorization of:
Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
3 1 2 2
2 0 1 1
Product of all
Prime Factors 3 18 18
Least Common Multiple:
18
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 = 6
Right_M = L.C.M / R_Deno = 1
Making Equivalent Fractions :
5.3 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. (2a-21) • 6
—————————————————— = ———————————
L.C.M 18
R. Mult. • R. Num. 7a
—————————————————— = ——
L.C.M 18
Adding fractions that have a common denominator :
5.4 Adding up the two equivalent fractions
(2a-21) • 6 + 7a 19a - 126
———————————————— = —————————
18 18
Equation at the end of step
5
:
(19a - 126) 17
——————————— - ——
18 2
STEP
6
:
Calculating the Least Common Multiple :
6.1 Find the Least Common Multiple
The left denominator is : 18
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}
2 1 1 1
3 2 0 2
Product of all
Prime Factors 18 2 18
Least Common Multiple:
18
Calculating Multipliers :
6.2 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 = 9
Making Equivalent Fractions :
6.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. (19a-126)
—————————————————— = —————————
L.C.M 18
R. Mult. • R. Num. 17 • 9
—————————————————— = ——————
L.C.M 18
Adding fractions that have a common denominator :
6.4 Adding up the two equivalent fractions
(19a-126) - (17 • 9) 19a - 279
———————————————————— = —————————
18 18
Final result :
19a - 279
—————————
18
