60
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Step by Step Solution:
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(1): "2.7" was replaced by "(27/10)". 8 more similar replacement(s)
STEP
1
:
27
Simplify ——
10
Equation at the end of step
1
:
27 62 93 12 62 93 12 27
(((——•——)-(——•——))+(——•——))-(——•——)
10 10 10 10 10 10 10 10
STEP
2
:
6
Simplify —
5
Equation at the end of step
2
:
27 62 93 12 62 93 6 27
(((——•——)-(——•——))+(——•——))-(—•——)
10 10 10 10 10 10 5 10
STEP
3
:
93
Simplify ——
10
Equation at the end of step
3
:
27 62 93 12 62 93 81
(((——•——)-(——•——))+(——•——))-——
10 10 10 10 10 10 25
STEP
4
:
31
Simplify ——
5
Equation at the end of step
4
:
27 62 93 12 31 93 81
(((——•——)-(——•——))+(——•——))-——
10 10 10 10 5 10 25
STEP
5
:
6
Simplify —
5
Equation at the end of step
5
:
27 62 93 6 2883 81
(((——•——)-(——•—))+————)-——
10 10 10 5 50 25
STEP
6
:
93
Simplify ——
10
Equation at the end of step
6
:
27 62 93 6 2883 81
(((——•——)-(——•—))+————)-——
10 10 10 5 50 25
STEP
7
:
31
Simplify ——
5
Equation at the end of step
7
:
27 31 279 2883 81
(((—— • ——) - ———) + ————) - ——
10 5 25 50 25
STEP
8
:
27
Simplify ——
10
Equation at the end of step
8
:
27 31 279 2883 81
(((—— • ——) - ———) + ————) - ——
10 5 25 50 25
STEP
9
:
Calculating the Least Common Multiple
9.1 Find the Least Common Multiple
The left denominator is : 50
The right denominator is : 25
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
5 2 2 2
Product of all
Prime Factors 50 25 50
Least Common Multiple:
50
Calculating Multipliers :
9.2 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 :
9.3 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. 837
—————————————————— = ———
L.C.M 50
R. Mult. • R. Num. 279 • 2
—————————————————— = ———————
L.C.M 50
Adding fractions that have a common denominator :
9.4 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:
837 - (279 • 2) 279
——————————————— = ———
50 50
Equation at the end of step
9
:
279 2883 81
(——— + ————) - ——
50 50 25
STEP
10
:
Adding fractions which have a common denominator
10.1 Adding fractions which have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
279 + 2883 1581
—————————— = ————
50 25
Equation at the end of step
10
:
1581 81
———— - ——
25 25
STEP
11
:
Adding fractions which have a common denominator
11.1 Adding fractions which have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
1581 - (81) 60
——————————— = ——
25 1
Final result :
60