Solution - Adding, subtracting and finding the least common multiple
Step by Step Solution
Step 1 :
1
Simplify —
3
Equation at the end of step 1 :
2 8 2 1
(((0-—)-—)+—)-—
5 9 9 3
Step 2 :
2
Simplify —
9
Equation at the end of step 2 :
2 8 2 1
(((0-—)-—)+—)-—
5 9 9 3
Step 3 :
8
Simplify —
9
Equation at the end of step 3 :
2 8 2 1
(((0 - —) - —) + —) - —
5 9 9 3
Step 4 :
2
Simplify —
5
Equation at the end of step 4 :
2 8 2 1
(((0 - —) - —) + —) - —
5 9 9 3
Step 5 :
Calculating the Least Common Multiple :
5.1 Find the Least Common Multiple
The left denominator is : 5
The right denominator is : 9
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 5 | 1 | 0 | 1 |
| 3 | 0 | 2 | 2 |
| Product of all Prime Factors | 5 | 9 | 45 |
Least Common Multiple:
45
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 = 9
Right_M = L.C.M / R_Deno = 5
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. -2 • 9 —————————————————— = —————— L.C.M 45 R. Mult. • R. Num. 8 • 5 —————————————————— = ————— L.C.M 45
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:
-2 • 9 - (8 • 5) -58
———————————————— = ———
45 45
Equation at the end of step 5 :
-58 2 1
(——— + —) - —
45 9 3
Step 6 :
Calculating the Least Common Multiple :
6.1 Find the Least Common Multiple
The left denominator is : 45
The right denominator is : 9
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 3 | 2 | 2 | 2 |
| 5 | 1 | 0 | 1 |
| Product of all Prime Factors | 45 | 9 | 45 |
Least Common Multiple:
45
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 = 5
Making Equivalent Fractions :
6.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. -58 —————————————————— = ——— L.C.M 45 R. Mult. • R. Num. 2 • 5 —————————————————— = ————— L.C.M 45
Adding fractions that have a common denominator :
6.4 Adding up the two equivalent fractions
-58 + 2 • 5 -16
——————————— = ———
45 15
Equation at the end of step 6 :
-16 1
——— - —
15 3
Step 7 :
Calculating the Least Common Multiple :
7.1 Find the Least Common Multiple
The left denominator is : 15
The right denominator is : 3
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 3 | 1 | 1 | 1 |
| 5 | 1 | 0 | 1 |
| Product of all Prime Factors | 15 | 3 | 15 |
Least Common Multiple:
15
Calculating Multipliers :
7.2 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 = 5
Making Equivalent Fractions :
7.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. -16 —————————————————— = ——— L.C.M 15 R. Mult. • R. Num. 5 —————————————————— = —— L.C.M 15
Adding fractions that have a common denominator :
7.4 Adding up the two equivalent fractions
-16 - (5) -7
————————— = ——
15 5
Final result :
-7
—— = -1.40000
5
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