3/7+-5/22=6/11+-8/-21
Answers
3/7-6/11-8/21+5/22
Final result :
-125
———— = -0.27056
462
Step by step solution :
Step 1 :
5
Simplify ——
22
Equation at the end of step 1 :
3 6 8 5
((—-——)-——)+——
7 11 21 22
Step 2 :
8
Simplify ——
21
Equation at the end of step 2 :
3 6 8 5
((— - ——) - ——) + ——
7 11 21 22
Step 3 :
6
Simplify ——
11
Equation at the end of step 3 :
3 6 8 5
((— - ——) - ——) + ——
7 11 21 22
Step 4 :
3
Simplify —
7
Equation at the end of step 4 :
3 6 8 5
((— - ——) - ——) + ——
7 11 21 22
Step 5 :
Calculating the Least Common Multiple :
5.1 Find the Least Common Multiple
The left denominator is : 7
The right denominator is : 11
Number of times each prime factor
appears in the factorization of:
Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
7 1 0 1
11 0 1 1
Product of all
Prime Factors 7 11 77
Least Common Multiple:
77
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 = 11
Right_M = L.C.M / R_Deno = 7
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. 3 • 11
—————————————————— = ——————
L.C.M 77
R. Mult. • R. Num. 6 • 7
—————————————————— = —————
L.C.M 77
Adding fractions that have a common denominator :
5.4 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:
3 • 11 - (6 • 7) -9
———————————————— = ——
77 77
Equation at the end of step 5 :
-9 8 5
(—— - ——) + ——
77 21 22
Step 6 :
Calculating the Least Common Multiple :
6.1 Find the Least Common Multiple
The left denominator is : 77
The right denominator is : 21
Number of times each prime factor
appears in the factorization of:
Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
7 1 1 1
11 1 0 1
3 0 1 1
Product of all
Prime Factors 77 21 231
Least Common Multiple:
231
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 = 3
Right_M = L.C.M / R_Deno = 11
Making Equivalent Fractions :
6.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. -9 • 3
—————————————————— = ——————
L.C.M 231
R. Mult. • R. Num. 8 • 11
—————————————————— = ——————
L.C.M 231
Adding fractions that have a common denominator :
6.4 Adding up the two equivalent fractions
-9 • 3 - (8 • 11) -115
————————————————— = ————
231 231
Equation at the end of step 6 :
-115 5
———— + ——
231 22
Step 7 :
Calculating the Least Common Multiple :
7.1 Find the Least Common Multiple
The left denominator is : 231
The right denominator is : 22
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 0 1
7 1 0 1
11 1 1 1
2 0 1 1
Product of all
Prime Factors 231 22 462
Least Common Multiple:
462
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 = 2
Right_M = L.C.M / R_Deno = 21
Making Equivalent Fractions :
7.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. -115 • 2
—————————————————— = ————————
L.C.M 462
R. Mult. • R. Num. 5 • 21
—————————————————— = ——————
L.C.M 462
Adding fractions that have a common denominator :
7.4 Adding up the two equivalent fractions
-115 • 2 + 5 • 21 -125
————————————————— = ————
462 462
Final result :
-125
———— = -0.27056
462
