Question

5/6 - 2/7 common demoninator

Answer 1

The answer is 23/42. CD is 42

Answer 2

5/6-2/7

Final result :

23
—— = 0.54762
42
Step by step solution :

Step 1 :

2
Simplify —
7
Equation at the end of step 1 :

5 2
— - —
6 7
Step 2 :

5
Simplify —
6
Equation at the end of step 2 :

5 2
— - —
6 7
Step 3 :

Calculating the Least Common Multiple :

3.1 Find the Least Common Multiple

The left denominator is : 6

The right denominator is : 7

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 1 0 1
7 0 1 1
Product of all
Prime Factors 6 7 42

Least Common Multiple:
42

Calculating Multipliers :

3.2 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 = 7

Right_M = L.C.M / R_Deno = 6


Making Equivalent Fractions :

3.3 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. 5 • 7
—————————————————— = —————
L.C.M 42

R. Mult. • R. Num. 2 • 6
—————————————————— = —————
L.C.M 42
Adding fractions that have a common denominator :

3.4 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:

5 • 7 - (2 • 6) 23
——————————————— = ——
42 42
Final result :

23
—— = 0.54762
42