4-2*6+189/2-37*5+102.3
Step-by-step explanation:
Step by step solution :
Step 1 :
1023
Simplify ————
10
Equation at the end of step 1 :
189 1023
((-8 + ———) - 185) + ————
2 10
Step 2 :
189
Simplify ———
2
Equation at the end of step 2 :
189 1023
((-8 + ———) - 185) + ————
2 10
Step 3 :
Rewriting the whole as an Equivalent Fraction :
3.1 Adding a fraction to a whole
Rewrite the whole as a fraction using 2 as the denominator :
-8 -8 • 2
-8 = —— = ——————
1 2
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 :
3.2 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:
-8 • 2 + 189 173
———————————— = ———
2 2
Equation at the end of step 3 :
173 1023
(——— - 185) + ————
2 10
Step 4 :
Rewriting the whole as an Equivalent Fraction :
4.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using 2 as the denominator :
185 185 • 2
185 = ——— = ———————
1 2
Adding fractions that have a common denominator :
4.2 Adding up the two equivalent fractions
173 - (185 • 2) -197
——————————————— = ————
2 2
Equation at the end of step 4 :
-197 1023
———— + ————
2 10
Step 5 :
Calculating the Least Common Multiple :
5.1 Find the Least Common Multiple
The left denominator is : 2
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}
2111
5011
Product of all
Prime Factors 21010
Least Common Multiple:
10
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 = 5
Right_M = L.C.M / R_Deno = 1
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. -197 • 5
—————————————————— = ————————
L.C.M 10
R. Mult. • R. Num. 1023
—————————————————— = ————
L.C.M 10
Adding fractions that have a common denominator :
5.4 Adding up the two equivalent fractions
-197 • 5 + 1023 19
——————————————— = ——
10 5
Final result :
19
—— = 3.80000
5
