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): "0.75" was replaced by "(75/100)". 4 more similar replacement(s)
Step 1 :
3
Simplify —
4
Equation at the end of step 1 :
5 2 16 3
((——+————)+—————)+—
10 1000 10000 4
Step 2 :
1
Simplify ———
625
Equation at the end of step 2 :
5 2 1 3
((—— + ————) + ———) + —
10 1000 625 4
Step 3 :
1
Simplify ———
500
Equation at the end of step 3 :
5 1 1 3
((—— + ———) + ———) + —
10 500 625 4
Step 4 :
1
Simplify —
2
Equation at the end of step 4 :
1 1 1 3
((— + ———) + ———) + —
2 500 625 4
Step 5 :
Calculating the Least Common Multiple :
5.1 Find the Least Common Multiple
The left denominator is : 2
The right denominator is : 500
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 1 | 2 | 2 |
| 5 | 0 | 3 | 3 |
| Product of all Prime Factors | 2 | 500 | 500 |
Least Common Multiple:
500
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 = 250
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. 250 —————————————————— = ——— L.C.M 500 R. Mult. • R. Num. 1 —————————————————— = ——— L.C.M 500
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:
250 + 1 251
——————— = ———
500 500
Equation at the end of step 5 :
251 1 3
(——— + ———) + —
500 625 4
Step 6 :
Calculating the Least Common Multiple :
6.1 Find the Least Common Multiple
The left denominator is : 500
The right denominator is : 625
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 2 | 0 | 2 |
| 5 | 3 | 4 | 4 |
| Product of all Prime Factors | 500 | 625 | 2500 |
Least Common Multiple:
2500
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 = 4
Making Equivalent Fractions :
6.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 251 • 5 —————————————————— = ——————— L.C.M 2500 R. Mult. • R. Num. 4 —————————————————— = ———— L.C.M 2500
Adding fractions that have a common denominator :
6.4 Adding up the two equivalent fractions
251 • 5 + 4 1259
——————————— = ————
2500 2500
Equation at the end of step 6 :
1259 3
———— + —
2500 4
Step 7 :
Calculating the Least Common Multiple :
7.1 Find the Least Common Multiple
The left denominator is : 2500
The right denominator is : 4
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 2 | 2 | 2 |
| 5 | 4 | 0 | 4 |
| Product of all Prime Factors | 2500 | 4 | 2500 |
Least Common Multiple:
2500
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 = 625
Making Equivalent Fractions :
7.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 1259 —————————————————— = ———— L.C.M 2500 R. Mult. • R. Num. 3 • 625 —————————————————— = ——————— L.C.M 2500
Adding fractions that have a common denominator :
7.4 Adding up the two equivalent fractions
1259 + 3 • 625 1567
—————————————— = ————
2500 1250
Final result :
1567
———— = 1.25360
1250
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