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): "4.4" was replaced by "(44/10)". 4 more similar replacement(s)
Step 1 :
22
Simplify ——
5
Equation at the end of step 1 :
121 57 83 22
(((———+6)+——)+——)+——
10 10 10 5
Step 2 :
83
Simplify ——
10
Equation at the end of step 2 :
121 57 83 22
(((———+6)+——)+——)+——
10 10 10 5
Step 3 :
57
Simplify ——
10
Equation at the end of step 3 :
121 57 83 22
(((——— + 6) + ——) + ——) + ——
10 10 10 5
Step 4 :
121
Simplify ———
10
Equation at the end of step 4 :
121 57 83 22
(((——— + 6) + ——) + ——) + ——
10 10 10 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 :
6 6 • 10
6 = — = ——————
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:
121 + 6 • 10 181
———————————— = ———
10 10
Equation at the end of step 5 :
181 57 83 22
((——— + ——) + ——) + ——
10 10 10 5
Step 6 :
Adding fractions which have a common denominator :
6.1 Adding fractions which have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
181 + 57 119
———————— = ———
10 5
Equation at the end of step 6 :
119 83 22
(——— + ——) + ——
5 10 5
Step 7 :
Calculating the Least Common Multiple :
7.1 Find the Least Common Multiple
The left denominator is : 5
The right denominator is : 10
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 5 | 1 | 1 | 1 |
| 2 | 0 | 1 | 1 |
| Product of all Prime Factors | 5 | 10 | 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 = 2
Right_M = L.C.M / R_Deno = 1
Making Equivalent Fractions :
7.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 119 • 2 —————————————————— = ——————— L.C.M 10 R. Mult. • R. Num. 83 —————————————————— = —— L.C.M 10
Adding fractions that have a common denominator :
7.4 Adding up the two equivalent fractions
119 • 2 + 83 321
———————————— = ———
10 10
Equation at the end of step 7 :
321 22
——— + ——
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. 321 —————————————————— = ——— L.C.M 10 R. Mult. • R. Num. 22 • 2 —————————————————— = —————— L.C.M 10
Adding fractions that have a common denominator :
8.4 Adding up the two equivalent fractions
321 + 22 • 2 73
———————————— = ——
10 2
Final result :
73
—— = 36.50000
2
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