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): "991.2" was replaced by "(9912/10)". 3 more similar replacement(s)
Step 1 :
4956
Simplify ————
5
Equation at the end of step 1 :
5293 43421 4956
((———— + 380) + —————) + ————
100 1000 5
Step 2 :
43421
Simplify —————
1000
Equation at the end of step 2 :
5293 43421 4956
((———— + 380) + —————) + ————
100 1000 5
Step 3 :
5293
Simplify ————
100
Equation at the end of step 3 :
5293 43421 4956
((———— + 380) + —————) + ————
100 1000 5
Step 4 :
Rewriting the whole as an Equivalent Fraction :
4.1 Adding a whole to a fraction
Rewrite the whole as a fraction using 100 as the denominator :
380 380 • 100
380 = ——— = —————————
1 100
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
4.2 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:
5293 + 380 • 100 43293
———————————————— = —————
100 100
Equation at the end of step 4 :
43293 43421 4956
(————— + —————) + ————
100 1000 5
Step 5 :
Calculating the Least Common Multiple :
5.1 Find the Least Common Multiple
The left denominator is : 100
The right denominator is : 1000
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 2 | 3 | 3 |
| 5 | 2 | 3 | 3 |
| Product of all Prime Factors | 100 | 1000 | 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 = 10
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. 43293 • 10 —————————————————— = —————————— L.C.M 1000 R. Mult. • R. Num. 43421 —————————————————— = ————— L.C.M 1000
Adding fractions that have a common denominator :
5.4 Adding up the two equivalent fractions
43293 • 10 + 43421 476351
—————————————————— = ——————
1000 1000
Equation at the end of step 5 :
476351 4956
—————— + ————
1000 5
Step 6 :
Calculating the Least Common Multiple :
6.1 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 :
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 = 200
Making Equivalent Fractions :
6.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 476351 —————————————————— = —————— L.C.M 1000 R. Mult. • R. Num. 4956 • 200 —————————————————— = —————————— L.C.M 1000
Adding fractions that have a common denominator :
6.4 Adding up the two equivalent fractions
476351 + 4956 • 200 1467551
——————————————————— = ———————
1000 1000
Final result :
1467551
——————— = 1467.55100
1000
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