Solution - Adding, subtracting and finding the least common multiple
Step by Step Solution
Step 1 :
2
Simplify —
5
Equation at the end of step 1 :
11 8 2
(—— - ——— ÷ 6) - —
30 157 5
Step 2 :
8
Simplify ———
157
Equation at the end of step 2 :
11 8 2
(—— - ——— ÷ 6) - —
30 157 5
Step 3 :
8
Divide ——— by 6
157
Equation at the end of step 3 :
11 4 2
(—— - ———) - —
30 471 5
Step 4 :
11
Simplify ——
30
Equation at the end of step 4 :
11 4 2
(—— - ———) - —
30 471 5
Step 5 :
Calculating the Least Common Multiple :
5.1 Find the Least Common Multiple
The left denominator is : 30
The right denominator is : 471
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 1 | 0 | 1 |
| 3 | 1 | 1 | 1 |
| 5 | 1 | 0 | 1 |
| 157 | 0 | 1 | 1 |
| Product of all Prime Factors | 30 | 471 | 4710 |
Least Common Multiple:
4710
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 = 157
Right_M = L.C.M / R_Deno = 10
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. 11 • 157 —————————————————— = ———————— L.C.M 4710 R. Mult. • R. Num. 4 • 10 —————————————————— = —————— L.C.M 4710
Adding fractions that have a common denominator :
5.4 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:
11 • 157 - (4 • 10) 1687
——————————————————— = ————
4710 4710
Equation at the end of step 5 :
1687 2
———— - —
4710 5
Step 6 :
Calculating the Least Common Multiple :
6.1 Find the Least Common Multiple
The left denominator is : 4710
The right denominator is : 5
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 1 | 0 | 1 |
| 3 | 1 | 0 | 1 |
| 5 | 1 | 1 | 1 |
| 157 | 1 | 0 | 1 |
| Product of all Prime Factors | 4710 | 5 | 4710 |
Least Common Multiple:
4710
Calculating Multipliers :
6.2 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 = 1
Right_M = L.C.M / R_Deno = 942
Making Equivalent Fractions :
6.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 1687 —————————————————— = ———— L.C.M 4710 R. Mult. • R. Num. 2 • 942 —————————————————— = ——————— L.C.M 4710
Adding fractions that have a common denominator :
6.4 Adding up the two equivalent fractions
1687 - (2 • 942) -197
———————————————— = ————
4710 4710
Final result :
-197
———— = -0.04183
4710
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