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): "^-5" was replaced by "^(-5)". 1 more similar replacement(s)
(2): "1.7" was replaced by "(17/10)". 2 more similar replacement(s)
Step 1 :
1.1 10 = 2•5
(10)-5 = (2•5)(-5) = (2)(-5) • (5)(-5)
Equation at the end of step 1 :
543 17
(———•(10-2))-(——•((2)(-5)•(5)(-5)))
10 10
Step 2 :
17
Simplify ——
10
Equation at the end of step 2 :
543 17
(——— • (10-2)) - (—— • ((2)(-5)•(5)(-5)))
10 10
Step 3 :
Multiplying exponents :
3.1 21 multiplied by 25 = 2(1 + 5) = 26
Raising to a Power :
3.2 51 multiplied by 55 = 5(1 + 5) = 56
Equation at the end of step 3 :
543 17
(——— • (10-2)) - ———————
10 (26•56)
Step 4 :
4.1 10 = 2•5
(10)-2 = (2•5)(-2) = (2)(-2) • (5)(-2)
Equation at the end of step 4 :
543 17
(——— • ((2)(-2)•(5)(-2))) - ———————
10 (26•56)
Step 5 :
543
Simplify ———
10
Equation at the end of step 5 :
543 17
(——— • ((2)(-2)•(5)(-2))) - ———————
10 (26•56)
Step 6 :
Multiplying exponents :
6.1 21 multiplied by 22 = 2(1 + 2) = 23
Multiplying exponents :
6.2 51 multiplied by 52 = 5(1 + 2) = 53
Equation at the end of step 6 :
543 17
———— - ———————
1000 (26•56)
Step 7 :
7.1 Finding a Common Denominator The left 1000 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. 1000 • 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 = 1000
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. 543 • (26•56) —————————————————— = —————————————— Common denominator 1000 • (26•56) R. Mult. • R. Num. 17 • 1000 —————————————————— = —————————————— Common denominator 1000 • (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:
543 • (26•56) - (17 • 1000) 3•181•26•56 - 17000
——————————————————————————— = ———————————————————
1000 • (26•56) 1000 • (26•56)
Final result :
543 - 17000
——————————————
1000 • (26•56)
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