Solution - Adding, subtracting and finding the least common multiple
Step by Step Solution
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "0.8" was replaced by "(8/10)". 3 more similar replacement(s)
Step 1 :
4
Simplify —
5
Equation at the end of step 1 :
411 99 4
(———— + ——) + —
1000 10 5
Step 2 :
99
Simplify ——
10
Equation at the end of step 2 :
411 99 4
(———— + ——) + —
1000 10 5
Step 3 :
411
Simplify ————
1000
Equation at the end of step 3 :
411 99 4
(———— + ——) + —
1000 10 5
Step 4 :
Calculating the Least Common Multiple :
4.1 Find the Least Common Multiple
The left denominator is : 1000
The right denominator is : 10
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 3 | 1 | 3 |
| 5 | 3 | 1 | 3 |
| Product of all Prime Factors | 1000 | 10 | 1000 |
Least Common Multiple:
1000
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 = 1
Right_M = L.C.M / R_Deno = 100
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. 411 —————————————————— = ———— L.C.M 1000 R. Mult. • R. Num. 99 • 100 —————————————————— = ———————— L.C.M 1000
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:
411 + 99 • 100 10311
—————————————— = —————
1000 1000
Equation at the end of step 4 :
10311 4
————— + —
1000 5
Step 5 :
Calculating the Least Common Multiple :
5.1 Find the Least Common Multiple
The left denominator is : 1000
The right denominator is : 5
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 3 | 0 | 3 |
| 5 | 3 | 1 | 3 |
| Product of all Prime Factors | 1000 | 5 | 1000 |
Least Common Multiple:
1000
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 = 1
Right_M = L.C.M / R_Deno = 200
Making Equivalent Fractions :
5.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 10311 —————————————————— = ————— L.C.M 1000 R. Mult. • R. Num. 4 • 200 —————————————————— = ——————— L.C.M 1000
Adding fractions that have a common denominator :
5.4 Adding up the two equivalent fractions
10311 + 4 • 200 11111
——————————————— = —————
1000 1000
Final result :
11111
————— = 11.11100
1000
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