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): "4.004" was replaced by "(4004/1000)". 3 more similar replacement(s)
Step 1 :
1001
Simplify ————
250
Equation at the end of step 1 :
214 1717 1001
((——— + 15) + ————) + ————
10 100 250
Step 2 :
1717
Simplify ————
100
Equation at the end of step 2 :
214 1717 1001
((——— + 15) + ————) + ————
10 100 250
Step 3 :
107
Simplify ———
5
Equation at the end of step 3 :
107 1717 1001
((——— + 15) + ————) + ————
5 100 250
Step 4 :
Rewriting the whole as an Equivalent Fraction :
4.1 Adding a whole to a fraction
Rewrite the whole as a fraction using 5 as the denominator :
15 15 • 5
15 = —— = ——————
1 5
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:
107 + 15 • 5 182
———————————— = ———
5 5
Equation at the end of step 4 :
182 1717 1001
(——— + ————) + ————
5 100 250
Step 5 :
Calculating the Least Common Multiple :
5.1 Find the Least Common Multiple
The left denominator is : 5
The right denominator is : 100
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 5 | 1 | 2 | 2 |
| 2 | 0 | 2 | 2 |
| Product of all Prime Factors | 5 | 100 | 100 |
Least Common Multiple:
100
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 = 20
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. 182 • 20 —————————————————— = ———————— L.C.M 100 R. Mult. • R. Num. 1717 —————————————————— = ———— L.C.M 100
Adding fractions that have a common denominator :
5.4 Adding up the two equivalent fractions
182 • 20 + 1717 5357
——————————————— = ————
100 100
Equation at the end of step 5 :
5357 1001
———— + ————
100 250
Step 6 :
Calculating the Least Common Multiple :
6.1 Find the Least Common Multiple
The left denominator is : 100
The right denominator is : 250
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 2 | 1 | 2 |
| 5 | 2 | 3 | 3 |
| Product of all Prime Factors | 100 | 250 | 500 |
Least Common Multiple:
500
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 = 5
Right_M = L.C.M / R_Deno = 2
Making Equivalent Fractions :
6.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 5357 • 5 —————————————————— = ———————— L.C.M 500 R. Mult. • R. Num. 1001 • 2 —————————————————— = ———————— L.C.M 500
Adding fractions that have a common denominator :
6.4 Adding up the two equivalent fractions
5357 • 5 + 1001 • 2 28787
——————————————————— = —————
500 500
Final result :
28787
————— = 57.57400
500
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