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): "8.95" was replaced by "(895/100)". 4 more similar replacement(s)
Step 1 :
179
Simplify ———
20
Equation at the end of step 1 :
8954 752 3 179
(((————+———)+20)+——)+———
1000 100 10 20
Step 2 :
3
Simplify ——
10
Equation at the end of step 2 :
8954 752 3 179
(((————+———)+20)+——)+———
1000 100 10 20
Step 3 :
188
Simplify ———
25
Equation at the end of step 3 :
8954 188 3 179
(((———— + ———) + 20) + ——) + ———
1000 25 10 20
Step 4 :
4477
Simplify ————
500
Equation at the end of step 4 :
4477 188 3 179
(((———— + ———) + 20) + ——) + ———
500 25 10 20
Step 5 :
Calculating the Least Common Multiple :
5.1 Find the Least Common Multiple
The left denominator is : 500
The right denominator is : 25
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 2 | 0 | 2 |
| 5 | 3 | 2 | 3 |
| Product of all Prime Factors | 500 | 25 | 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 = 1
Right_M = L.C.M / R_Deno = 20
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. 4477 —————————————————— = ———— L.C.M 500 R. Mult. • R. Num. 188 • 20 —————————————————— = ———————— 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:
4477 + 188 • 20 8237
——————————————— = ————
500 500
Equation at the end of step 5 :
8237 3 179
((———— + 20) + ——) + ———
500 10 20
Step 6 :
Rewriting the whole as an Equivalent Fraction :
6.1 Adding a whole to a fraction
Rewrite the whole as a fraction using 500 as the denominator :
20 20 • 500
20 = —— = ————————
1 500
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 :
6.2 Adding up the two equivalent fractions
8237 + 20 • 500 18237
——————————————— = —————
500 500
Equation at the end of step 6 :
18237 3 179
(————— + ——) + ———
500 10 20
Step 7 :
Calculating the Least Common Multiple :
7.1 Find the Least Common Multiple
The left denominator is : 500
The right denominator is : 10
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 2 | 1 | 2 |
| 5 | 3 | 1 | 3 |
| Product of all Prime Factors | 500 | 10 | 500 |
Least Common Multiple:
500
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 = 50
Making Equivalent Fractions :
7.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 18237 —————————————————— = ————— L.C.M 500 R. Mult. • R. Num. 3 • 50 —————————————————— = —————— L.C.M 500
Adding fractions that have a common denominator :
7.4 Adding up the two equivalent fractions
18237 + 3 • 50 18387
—————————————— = —————
500 500
Equation at the end of step 7 :
18387 179
————— + ———
500 20
Step 8 :
Calculating the Least Common Multiple :
8.1 Find the Least Common Multiple
The left denominator is : 500
The right denominator is : 20
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 2 | 2 | 2 |
| 5 | 3 | 1 | 3 |
| Product of all Prime Factors | 500 | 20 | 500 |
Least Common Multiple:
500
Calculating Multipliers :
8.2 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 = 25
Making Equivalent Fractions :
8.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 18387 —————————————————— = ————— L.C.M 500 R. Mult. • R. Num. 179 • 25 —————————————————— = ———————— L.C.M 500
Adding fractions that have a common denominator :
8.4 Adding up the two equivalent fractions
18387 + 179 • 25 11431
———————————————— = —————
500 250
Final result :
11431
————— = 45.72400
250
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