Simplify
y:1÷{1/2+1/3+1/6÷(3/4-1/3)
Answers
Answer:
10
Step-by-step explanation:
Step 1 :
1
Simplify —
6
Equation at the end of step 1 :
1 1 1 1
(—+—) ÷ (—-—)
2 3 4 6
Step 2 :
1
Simplify —
4
Equation at the end of step 2 :
1 1 1 1
(— + —) ÷ (— - —)
2 3 4 6
Step 3 :
The left denominator is : 4
The right denominator is : 6
Product of all
Prime Factors 4 6 12
Least Common Multiple:
12
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 = 3
Right_M = L.C.M / R_Deno = 2
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. 3
—————————————————— = ——
L.C.M 12
R. Mult. • R. Num. 2
—————————————————— = ——
L.C.M 12
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:
3 - (2) 1
——————— = ——
12 12
Equation at the end of step 3 :
1 1 1
(— + —) ÷ ——
2 3 12
Step 4 :
1
Simplify —
3
Equation at the end of step 4 :
1 1 1
(— + —) ÷ ——
2 3 12
Step 5 :
1
Simplify —
2
Equation at the end of step 5 :
1 1 1
(— + —) ÷ ——
2 3 12
Step 6 :
The left denominator is : 2
The right denominator is : 3
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
3 0 1 1
Product of all
Prime Factors 2 3 6
Least Common Multiple:
6
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 = 3
Right_M = L.C.M / R_Deno = 2
Making Equivalent Fractions :
6.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 3
—————————————————— = —
L.C.M 6
R. Mult. • R. Num. 2
—————————————————— = —
L.C.M 6
Adding fractions that have a common denominator :
6.4 Adding up the two equivalent fractions
3 + 2 5
————— = —
6 6
Equation at the end of step 6 :
5 1
— ÷ ——
6 12
Step 7 :
5 1
Divide — by ——
6 12
To divide fractions, write the divison as multiplication by the reciprocal of the divisor :
5 1 5 12
— ÷ —— = — • ——
6 12 6 1
Final result :
10
HOPE THIS HELPS U