Solution - Adding, subtracting and finding the least common multiple
Step by Step Solution
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "^-4" was replaced by "^(-4)". 1 more similar replacement(s)
(2): "6.53" was replaced by "(653/100)". 2 more similar replacement(s)
Step 1 :
1.1 10 = 2•5
(10)-4 = (2•5)(-4) = (2)(-4) • (5)(-4)
Equation at the end of step 1 :
274 653
(———•(10-1))-(———•((2)(-4)•(5)(-4)))
100 100
Step 2 :
653
Simplify ———
100
Equation at the end of step 2 :
274 653
(——— • (10-1)) - (——— • ((2)(-4)•(5)(-4)))
100 100
Step 3 :
Multiplying exponents :
3.1 22 multiplied by 24 = 2(2 + 4) = 26
Raising to a Power :
3.2 52 multiplied by 54 = 5(2 + 4) = 56
Equation at the end of step 3 :
274 653
(——— • (10-1)) - ———————
100 (26•56)
Step 4 :
4.1 10 = 2•5
(10)-1 = (2•5)(-1) = (2)(-1) • (5)(-1)
Equation at the end of step 4 :
274 653
(——— • ((2)(-1)•(5)(-1))) - ———————
100 (26•56)
Step 5 :
137
Simplify ———
50
Equation at the end of step 5 :
137 653
(——— • ((2)(-1)•(5)(-1))) - ———————
50 (26•56)
Step 6 :
Multiplying exponents :
6.1 21 multiplied by 21 = 2(1 + 1) = 22
Multiplying exponents :
6.2 52 multiplied by 51 = 5(2 + 1) = 53
Equation at the end of step 6 :
137 653
——— - ———————
500 (26•56)
Step 7 :
7.1 Finding a Common Denominator The left 500 The right 26 • 56 The product of any two denominators can be used as a common denominator. Said product is not necessarily the least common denominator. As a matter of fact, whenever the two denominators have a common factor, their product will be bigger than the least common denominator. Anyway, the product is a fine common denominator and can perfectly be used for calculating multipliers, as well as for generating equivalent fractions. 500 • 26 • 56 will be used as a common denominator.
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 = 26 • 56
Right_M = L.C.M / R_Deno = 500
Making Equivalent Fractions :
7.3 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. 137 • (26•56) —————————————————— = ————————————— Common denominator 500 • (26•56) R. Mult. • R. Num. 653 • 500 —————————————————— = ————————————— Common denominator 500 • (26•56)
Adding fractions that have a common denominator :
7.4 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:
137 • (26•56) - (653 • 500) 137•26•56 - 326500
——————————————————————————— = ——————————————————
500 • (26•56) 500 • (26•56)
Final result :
137 - 326500
—————————————
500 • (26•56)
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