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): "2.7" was replaced by "(27/10)". 6 more similar replacement(s)
Step 1 :
27
Simplify ——
10
Equation at the end of step 1 :
73 73 27 27 73 27
((——•——)-(——•—— ÷ ——))-——
10 10 10 10 10 10
Step 2 :
73
Simplify ——
10
Equation at the end of step 2 :
73 73 27 27 73 27
((——•——)-(——•—— ÷ ——))-——
10 10 10 10 10 10
Step 3 :
27
Simplify ——
10
Equation at the end of step 3 :
73 73 27 27 73 27
((——•——)-(——•—— ÷ ——))-——
10 10 10 10 10 10
Step 4 :
27 73
Divide —— by ——
10 10
4.1 Dividing fractions
To divide fractions, write the divison as multiplication by the reciprocal of the divisor :
27 73 27 10 —— ÷ —— = —— • —— 10 10 10 73
Equation at the end of step 4 :
73 73 27 27 27
((——•——)-(——•——))-——
10 10 10 73 10
Step 5 :
27
Simplify ——
10
Equation at the end of step 5 :
73 73 27 27 27
((——•——)-(——•——))-——
10 10 10 73 10
Step 6 :
73
Simplify ——
10
Equation at the end of step 6 :
73 73 729 27
((—— • ——) - ———) - ——
10 10 730 10
Step 7 :
73
Simplify ——
10
Equation at the end of step 7 :
73 73 729 27
((—— • ——) - ———) - ——
10 10 730 10
Step 8 :
Calculating the Least Common Multiple :
8.1 Find the Least Common Multiple
The left denominator is : 100
The right denominator is : 730
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 2 | 1 | 2 |
| 5 | 2 | 1 | 2 |
| 73 | 0 | 1 | 1 |
| Product of all Prime Factors | 100 | 730 | 7300 |
Least Common Multiple:
7300
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 = 73
Right_M = L.C.M / R_Deno = 10
Making Equivalent Fractions :
8.3 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. 5329 • 73 —————————————————— = ————————— L.C.M 7300 R. Mult. • R. Num. 729 • 10 —————————————————— = ———————— L.C.M 7300
Adding fractions that have a common denominator :
8.4 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:
5329 • 73 - (729 • 10) 381727
—————————————————————— = ——————
7300 7300
Equation at the end of step 8 :
381727 27
—————— - ——
7300 10
Step 9 :
Calculating the Least Common Multiple :
9.1 Find the Least Common Multiple
The left denominator is : 7300
The right denominator is : 10
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 2 | 1 | 2 |
| 5 | 2 | 1 | 2 |
| 73 | 1 | 0 | 1 |
| Product of all Prime Factors | 7300 | 10 | 7300 |
Least Common Multiple:
7300
Calculating Multipliers :
9.2 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 = 730
Making Equivalent Fractions :
9.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 381727 —————————————————— = —————— L.C.M 7300 R. Mult. • R. Num. 27 • 730 —————————————————— = ———————— L.C.M 7300
Adding fractions that have a common denominator :
9.4 Adding up the two equivalent fractions
381727 - (27 • 730) 362017
——————————————————— = ——————
7300 7300
Final result :
362017
—————— = 49.59137
7300
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