Solution - Adding, subtracting and finding the least common multiple
Step by Step Solution
Step 1 :
1
Simplify ——
45
Equation at the end of step 1 :
1 1 5 1
((—+——)+——)+——
5 15 54 45
Step 2 :
5
Simplify ——
54
Equation at the end of step 2 :
1 1 5 1
((— + ——) + ——) + ——
5 15 54 45
Step 3 :
1
Simplify ——
15
Equation at the end of step 3 :
1 1 5 1
((— + ——) + ——) + ——
5 15 54 45
Step 4 :
1
Simplify —
5
Equation at the end of step 4 :
1 1 5 1
((— + ——) + ——) + ——
5 15 54 45
Step 5 :
Calculating the Least Common Multiple :
5.1 Find the Least Common Multiple
The left denominator is : 5
The right denominator is : 15
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 5 | 1 | 1 | 1 |
| 3 | 0 | 1 | 1 |
| Product of all Prime Factors | 5 | 15 | 15 |
Least Common Multiple:
15
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. 3 —————————————————— = —— L.C.M 15 R. Mult. • R. Num. 1 —————————————————— = —— L.C.M 15
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:
3 + 1 4
————— = ——
15 15
Equation at the end of step 5 :
4 5 1
(—— + ——) + ——
15 54 45
Step 6 :
Calculating the Least Common Multiple :
6.1 Find the Least Common Multiple
The left denominator is : 15
The right denominator is : 54
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 3 | 1 | 3 | 3 |
| 5 | 1 | 0 | 1 |
| 2 | 0 | 1 | 1 |
| Product of all Prime Factors | 15 | 54 | 270 |
Least Common Multiple:
270
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 = 18
Right_M = L.C.M / R_Deno = 5
Making Equivalent Fractions :
6.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 4 • 18 —————————————————— = —————— L.C.M 270 R. Mult. • R. Num. 5 • 5 —————————————————— = ————— L.C.M 270
Adding fractions that have a common denominator :
6.4 Adding up the two equivalent fractions
4 • 18 + 5 • 5 97
—————————————— = ———
270 270
Equation at the end of step 6 :
97 1
——— + ——
270 45
Step 7 :
Calculating the Least Common Multiple :
7.1 Find the Least Common Multiple
The left denominator is : 270
The right denominator is : 45
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 1 | 0 | 1 |
| 3 | 3 | 2 | 3 |
| 5 | 1 | 1 | 1 |
| Product of all Prime Factors | 270 | 45 | 270 |
Least Common Multiple:
270
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 = 6
Making Equivalent Fractions :
7.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 97 —————————————————— = ——— L.C.M 270 R. Mult. • R. Num. 6 —————————————————— = ——— L.C.M 270
Adding fractions that have a common denominator :
7.4 Adding up the two equivalent fractions
97 + 6 103
—————— = ———
270 270
Final result :
103
——— = 0.38148
270
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