Solution - Adding, subtracting and finding the least common multiple
Step by Step Solution
Step 1 :
12
Simplify ——
7
Equation at the end of step 1 :
6 7 19 12
(((—+1)-—)+——)-——
7 9 21 7
Step 2 :
19
Simplify ——
21
Equation at the end of step 2 :
6 7 19 12
(((—+1)-—)+——)-——
7 9 21 7
Step 3 :
7
Simplify —
9
Equation at the end of step 3 :
6 7 19 12
(((— + 1) - —) + ——) - ——
7 9 21 7
Step 4 :
6
Simplify —
7
Equation at the end of step 4 :
6 7 19 12
(((— + 1) - —) + ——) - ——
7 9 21 7
Step 5 :
Rewriting the whole as an Equivalent Fraction :
5.1 Adding a whole to a fraction
Rewrite the whole as a fraction using 7 as the denominator :
1 1 • 7
1 = — = —————
1 7
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:
6 + 7 13
————— = ——
7 7
Equation at the end of step 5 :
13 7 19 12
((—— - —) + ——) - ——
7 9 21 7
Step 6 :
Calculating the Least Common Multiple :
6.1 Find the Least Common Multiple
The left denominator is : 7
The right denominator is : 9
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 7 | 1 | 0 | 1 |
| 3 | 0 | 2 | 2 |
| Product of all Prime Factors | 7 | 9 | 63 |
Least Common Multiple:
63
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 = 9
Right_M = L.C.M / R_Deno = 7
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. 13 • 9 —————————————————— = —————— L.C.M 63 R. Mult. • R. Num. 7 • 7 —————————————————— = ————— L.C.M 63
Adding fractions that have a common denominator :
6.4 Adding up the two equivalent fractions
13 • 9 - (7 • 7) 68
———————————————— = ——
63 63
Equation at the end of step 6 :
68 19 12
(—— + ——) - ——
63 21 7
Step 7 :
Calculating the Least Common Multiple :
7.1 Find the Least Common Multiple
The left denominator is : 63
The right denominator is : 21
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 3 | 2 | 1 | 2 |
| 7 | 1 | 1 | 1 |
| Product of all Prime Factors | 63 | 21 | 63 |
Least Common Multiple:
63
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 = 1
Right_M = L.C.M / R_Deno = 3
Making Equivalent Fractions :
7.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 68 —————————————————— = —— L.C.M 63 R. Mult. • R. Num. 19 • 3 —————————————————— = —————— L.C.M 63
Adding fractions that have a common denominator :
7.4 Adding up the two equivalent fractions
68 + 19 • 3 125
——————————— = ———
63 63
Equation at the end of step 7 :
125 12
——— - ——
63 7
Step 8 :
Calculating the Least Common Multiple :
8.1 Find the Least Common Multiple
The left denominator is : 63
The right denominator is : 7
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 3 | 2 | 0 | 2 |
| 7 | 1 | 1 | 1 |
| Product of all Prime Factors | 63 | 7 | 63 |
Least Common Multiple:
63
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 = 9
Making Equivalent Fractions :
8.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 125 —————————————————— = ——— L.C.M 63 R. Mult. • R. Num. 12 • 9 —————————————————— = —————— L.C.M 63
Adding fractions that have a common denominator :
8.4 Adding up the two equivalent fractions
125 - (12 • 9) 17
—————————————— = ——
63 63
Final result :
17
—— = 0.26984
63
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