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): "26.4" was replaced by "(264/10)". 4 more similar replacement(s)
Step 1 :
132
Simplify ———
5
Equation at the end of step 1 :
103 232 64 132
(((———+8)+———)+——)+———
10 10 10 5
Step 2 :
32
Simplify ——
5
Equation at the end of step 2 :
103 232 32 132
(((———+8)+———)+——)+———
10 10 5 5
Step 3 :
116
Simplify ———
5
Equation at the end of step 3 :
103 116 32 132
(((——— + 8) + ———) + ——) + ———
10 5 5 5
Step 4 :
103
Simplify ———
10
Equation at the end of step 4 :
103 116 32 132
(((——— + 8) + ———) + ——) + ———
10 5 5 5
Step 5 :
Rewriting the whole as an Equivalent Fraction :
5.1 Adding a whole to a fraction
Rewrite the whole as a fraction using 10 as the denominator :
8 8 • 10
8 = — = ——————
1 10
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 :
5.2 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:
103 + 8 • 10 183
———————————— = ———
10 10
Equation at the end of step 5 :
183 116 32 132
((——— + ———) + ——) + ———
10 5 5 5
Step 6 :
Calculating the Least Common Multiple :
6.1 Find the Least Common Multiple
The left denominator is : 10
The right denominator is : 5
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 1 | 0 | 1 |
| 5 | 1 | 1 | 1 |
| Product of all Prime Factors | 10 | 5 | 10 |
Least Common Multiple:
10
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 = 1
Right_M = L.C.M / R_Deno = 2
Making Equivalent Fractions :
6.3 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. 183 —————————————————— = ——— L.C.M 10 R. Mult. • R. Num. 116 • 2 —————————————————— = ——————— L.C.M 10
Adding fractions that have a common denominator :
6.4 Adding up the two equivalent fractions
183 + 116 • 2 83
————————————— = ——
10 2
Equation at the end of step 6 :
83 32 132
(—— + ——) + ———
2 5 5
Step 7 :
Calculating the Least Common Multiple :
7.1 Find the Least Common Multiple
The left denominator is : 2
The right denominator is : 5
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 1 | 0 | 1 |
| 5 | 0 | 1 | 1 |
| Product of all Prime Factors | 2 | 5 | 10 |
Least Common Multiple:
10
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 = 5
Right_M = L.C.M / R_Deno = 2
Making Equivalent Fractions :
7.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 83 • 5 —————————————————— = —————— L.C.M 10 R. Mult. • R. Num. 32 • 2 —————————————————— = —————— L.C.M 10
Adding fractions that have a common denominator :
7.4 Adding up the two equivalent fractions
83 • 5 + 32 • 2 479
——————————————— = ———
10 10
Equation at the end of step 7 :
479 132
——— + ———
10 5
Step 8 :
Calculating the Least Common Multiple :
8.1 Find the Least Common Multiple
The left denominator is : 10
The right denominator is : 5
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 1 | 0 | 1 |
| 5 | 1 | 1 | 1 |
| Product of all Prime Factors | 10 | 5 | 10 |
Least Common Multiple:
10
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 = 2
Making Equivalent Fractions :
8.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 479 —————————————————— = ——— L.C.M 10 R. Mult. • R. Num. 132 • 2 —————————————————— = ——————— L.C.M 10
Adding fractions that have a common denominator :
8.4 Adding up the two equivalent fractions
479 + 132 • 2 743
————————————— = ———
10 10
Final result :
743
——— = 74.30000
10
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