Step by step solution :Step 1 : 3
Simplify —
5
Equation at the end of step 1 : 7 9 3
(((—•m)+——)-2m)-—
8 10 5
Step 2 : 9
Simplify ——
10
Equation at the end of step 2 : 7 9 3
(((— • m) + ——) - 2m) - —
8 10 5
Step 3 : 7
Simplify —
8
Equation at the end of step 3 : 7 9 3
(((— • m) + ——) - 2m) - —
8 10 5
Step 4 :Calculating the Least Common Multiple :
4.1 Find the Least Common Multiple
The left denominator is : 8
The right denominator is : 10
Number of times each prime factor
appears in the factorization of: Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right} 23135011 Product of all
Prime Factors 81040
Least Common Multiple:
40
Calculating Multipliers :
4.2 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 = 5
Right_M = L.C.M / R_Deno = 4
Making Equivalent Fractions :
4.3 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. 7m • 5
—————————————————— = ——————
L.C.M 40
R. Mult. • R. Num. 9 • 4
—————————————————— = —————
L.C.M 40
Adding fractions that have a common denominator :
4.4 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:
7m • 5 + 9 • 4 35m + 36
—————————————— = ————————
40 40
Equation at the end of step 4 : (35m + 36) 3
(—————————— - 2m) - —
40 5
Step 5 :Rewriting the whole as an Equivalent Fraction :
5.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using 40 as the denominator :
2m 2m • 40
2m = —— = ———————
1 40
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 :
5.2 Adding up the two equivalent fractions
(35m+36) - (2m • 40) 36 - 45m
———————————————————— = ————————
40 40
Equation at the end of step 5 : (36 - 45m) 3
—————————— - —
40 5
Step 6 :Step 7 :Pulling out like terms :
7.1 Pull out like factors :
36 - 45m = -9 • (5m - 4)
Calculating the Least Common Multiple :
7.2 Find the Least Common Multiple
The left denominator is : 40
The right denominator is : 5
Number of times each prime factor
appears in the factorization of: Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right} 23035111 Product of all
Prime Factors 40540
Least Common Multiple:
40
Calculating Multipliers :
7.3 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 = 8
Making Equivalent Fractions :
7.4 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. -9 • (5m-4)
—————————————————— = ———————————
L.C.M 40
R. Mult. • R. Num. 3 • 8
—————————————————— = —————
L.C.M 40
Adding fractions that have a common denominator :
7.5 Adding up the two equivalent fractions
-9 • (5m-4) - (3 • 8) 12 - 45m
————————————————————— = ————————
40 40
Step 8 :Pulling out like terms :
8.1 Pull out like factors :
12 - 45m = -3 • (15m - 4)
Final result : -3 • (15m - 4)
——————————————
40
