Solution - Adding, subtracting and finding the least common multiple
Step by Step Solution
Step 1 :
2
Simplify —
7
Equation at the end of step 1 :
17 3 2
—— - (— + —)
21 7 7
Step 2 :
3
Simplify —
7
Equation at the end of step 2 :
17 3 2
—— - (— + —)
21 7 7
Step 3 :
Adding fractions which have a common denominator :
3.1 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:
3 + 2 5
————— = —
7 7
Equation at the end of step 3 :
17 5
—— - —
21 7
Step 4 :
17
Simplify ——
21
Equation at the end of step 4 :
17 5
—— - —
21 7
Step 5 :
Calculating the Least Common Multiple :
5.1 Find the Least Common Multiple
The left denominator is : 21
The right denominator is : 7
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 3 | 1 | 0 | 1 |
| 7 | 1 | 1 | 1 |
| Product of all Prime Factors | 21 | 7 | 21 |
Least Common Multiple:
21
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 = 3
Making Equivalent Fractions :
5.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 17 —————————————————— = —— L.C.M 21 R. Mult. • R. Num. 5 • 3 —————————————————— = ————— L.C.M 21
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:
17 - (5 • 3) 2
———————————— = ——
21 21
Final result :
2
—— = 0.09524
21
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