Solution - Adding, subtracting and finding the least common multiple
Step by Step Solution
Step 1 :
119
Simplify ———
80
Equation at the end of step 1 :
7 7 119
(—— + ———) + ———
40 100 80
Step 2 :
7
Simplify ———
100
Equation at the end of step 2 :
7 7 119
(—— + ———) + ———
40 100 80
Step 3 :
7
Simplify ——
40
Equation at the end of step 3 :
7 7 119
(—— + ———) + ———
40 100 80
Step 4 :
Calculating the Least Common Multiple :
4.1 Find the Least Common Multiple
The left denominator is : 40
The right denominator is : 100
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 3 | 2 | 3 |
| 5 | 1 | 2 | 2 |
| Product of all Prime Factors | 40 | 100 | 200 |
Least Common Multiple:
200
Calculating Multipliers :
4.2 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 = 5
Right_M = L.C.M / R_Deno = 2
Making Equivalent Fractions :
4.3 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 • 5 —————————————————— = ————— L.C.M 200 R. Mult. • R. Num. 7 • 2 —————————————————— = ————— L.C.M 200
Adding fractions that have a common denominator :
4.4 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:
7 • 5 + 7 • 2 49
————————————— = ———
200 200
Equation at the end of step 4 :
49 119
——— + ———
200 80
Step 5 :
Calculating the Least Common Multiple :
5.1 Find the Least Common Multiple
The left denominator is : 200
The right denominator is : 80
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 3 | 4 | 4 |
| 5 | 2 | 1 | 2 |
| Product of all Prime Factors | 200 | 80 | 400 |
Least Common Multiple:
400
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 = 2
Right_M = L.C.M / R_Deno = 5
Making Equivalent Fractions :
5.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 49 • 2 —————————————————— = —————— L.C.M 400 R. Mult. • R. Num. 119 • 5 —————————————————— = ——————— L.C.M 400
Adding fractions that have a common denominator :
5.4 Adding up the two equivalent fractions
49 • 2 + 119 • 5 693
———————————————— = ———
400 400
Final result :
693
——— = 1.73250
400
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