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): "2.9" was replaced by "(29/10)". 4 more similar replacement(s)
Step 1 :
29
Simplify ——
10
Equation at the end of step 1 :
8363 289 49 29
————-(———•(——-(——2)))
100 100 10 10
Step 2 :
2.1 10 = 2•5 (10)2 = (2•5)2 = 22 • 52
Equation at the end of step 2 :
8363 289 49 292
————-(———•(——-———————))
100 100 10 (22•52)
Step 3 :
49
Simplify ——
10
Equation at the end of step 3 :
8363 289 49 292
———— - (——— • (—— - ———————))
100 100 10 (22•52)
Step 4 :
Calculating the Least Common Multiple :
4.1 Find the Least Common Multiple
The left denominator is : 10
The right denominator is : 100
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 1 | 2 | 2 |
| 5 | 1 | 2 | 2 |
| Product of all Prime Factors | 10 | 100 | 100 |
Least Common Multiple:
100
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 = 10
Right_M = L.C.M / R_Deno = 1
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. 49 • 10 —————————————————— = ——————— L.C.M 100 R. Mult. • R. Num. 841 —————————————————— = ——— L.C.M 100
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:
49 • 10 - (841) -351
——————————————— = ————
100 100
Equation at the end of step 4 :
8363 289 -351
———— - (——— • ————)
100 100 100
Step 5 :
289
Simplify ———
100
Equation at the end of step 5 :
8363 289 -351
———— - (——— • ————)
100 100 100
Step 6 :
8363
Simplify ————
100
Equation at the end of step 6 :
8363 -101439
———— - ———————
100 10000
Step 7 :
Calculating the Least Common Multiple :
7.1 Find the Least Common Multiple
The left denominator is : 100
The right denominator is : 10000
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 2 | 4 | 4 |
| 5 | 2 | 4 | 4 |
| Product of all Prime Factors | 100 | 10000 | 10000 |
Least Common Multiple:
10000
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 = 100
Right_M = L.C.M / R_Deno = 1
Making Equivalent Fractions :
7.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 8363 • 100 —————————————————— = —————————— L.C.M 10000 R. Mult. • R. Num. -101439 —————————————————— = ——————— L.C.M 10000
Adding fractions that have a common denominator :
7.4 Adding up the two equivalent fractions
8363 • 100 - (-101439) 937739
—————————————————————— = ——————
10000 10000
Final result :
937739
—————— = 93.77390
10000
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