Solution - Adding, subtracting and finding the least common multiple
Other Ways to Solve:
Step by Step Solution
Step 1 :
25
Simplify ——
42
Equation at the end of step 1 :
13 25
(0 - ——) + ——
30 42
Step 2 :
13
Simplify ——
30
Equation at the end of step 2 :
13 25
(0 - ——) + ——
30 42
Step 3 :
Calculating the Least Common Multiple :
3.1 Find the Least Common Multiple
The left denominator is : 30
The right denominator is : 42
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 1 | 1 | 1 |
| 3 | 1 | 1 | 1 |
| 5 | 1 | 0 | 1 |
| 7 | 0 | 1 | 1 |
| Product of all Prime Factors | 30 | 42 | 210 |
Least Common Multiple:
210
Calculating Multipliers :
3.2 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 = 7
Right_M = L.C.M / R_Deno = 5
Making Equivalent Fractions :
3.3 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. -13 • 7 —————————————————— = ——————— L.C.M 210 R. Mult. • R. Num. 25 • 5 —————————————————— = —————— L.C.M 210
Adding fractions that have a common denominator :
3.4 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:
-13 • 7 + 25 • 5 17
———————————————— = ———
210 105
Final result :
17
——— = 0.16190
105
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