2
Step-by-step explanation:
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "2.8" was replaced by "(28/10)". 2 more similar replacement(s)
Step by step solution :
Step 1 :
14
Simplify ——
5
Equation at the end of step 1 :
5 1 1 7 14
(——+——) ÷ —)-——) ÷ ——
10 18 6 18 5
Step 2 :
7
Simplify ——
18
Equation at the end of step 2 :
5 1 1 7 14
(——+——) ÷ —)-——) ÷ ——
10 18 6 18 5
Step 3 :
1
Simplify —
6
Equation at the end of step 3 :
5 1 1 7 14
(——+——) ÷ —)-——) ÷ ——
10 18 6 18 5
Step 4 :
Rewriting the whole as an Equivalent Fraction :
4.1 Adding a fraction to a whole
Rewrite the whole as a fraction using 6 as the denominator :
1 1 • 6
1 = — = —————
1 6
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 :
4.2 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:
6 + 1 7
————— = —
6 6
Equation at the end of step 4 :
5 1 7 7 14
(——+——) ÷ —-——) ÷ ——
10 18 6 18 5
Step 5 :
Calculating the Least Common Multiple :
5.1 Find the Least Common Multiple
The left denominator is : 6
The right denominator is : 18
Number of times each prime factor
appears in the factorization of:
Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
2111
3122
Product of all
Prime Factors 61818
Least Common Multiple:
18
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 = 3
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. 7 • 3
—————————————————— = —————
L.C.M 18
R. Mult. • R. Num. 7
—————————————————— = ——
L.C.M 18
Adding fractions that have a common denominator :
5.4 Adding up the two equivalent fractions
7 • 3 - (7) 7
——————————— = —
18 9
Equation at the end of step 5 :
5 1 7 14
(—— + ——) ÷ — ÷ ——
10 18 9 5
Step 6 :
7 14
Divide — by ——
9 5
6.1 Dividing fractions
To divide fractions, write the divison as multiplication by the reciprocal of the divisor :
7 14 7 5
— ÷ —— = — • ——
9 5 9 14
Equation at the end of step 6 :
5 1 5
(—— + ——) ÷ ——
10 18 18
Step 7 :
1
Simplify ——
18
Equation at the end of step 7 :
5 1 5
(—— + ——) ÷ ——
10 18 18
Step 8 :
1
Simplify —
2
Equation at the end of step 8 :
1 1 5
(— + ——) ÷ ——
2 18 18
Step 9 :
Calculating the Least Common Multiple :
9.1 Find the Least Common Multiple
The left denominator is : 2
The right denominator is : 18
Number of times each prime factor
appears in the factorization of:
Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
2111
3022
Product of all
Prime Factors 21818
Least Common Multiple:
18
Calculating Multipliers :
9.2 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 = 9
Right_M = L.C.M / R_Deno = 1
Making Equivalent Fractions :
9.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 9
—————————————————— = ——
L.C.M 18
R. Mult. • R. Num. 1
—————————————————— = ——
L.C.M 18
Adding fractions that have a common denominator :
9.4 Adding up the two equivalent fractions
9 + 1 5
————— = —
18 9
Equation at the end of step 9 :
5 5
— ÷ ——
9 18
Step 10 :
5 5
Divide — by ——
9 18
10.1 Dividing fractions
To divide fractions, write the divison as multiplication by the reciprocal of the divisor :
5 5 5 18
— ÷ —— = — • ——
9 18 9 5
Final result :
2
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