Solution - Adding, subtracting and finding the least common multiple
Step by Step Solution
Step 1 :
6
Simplify —
1
Equation at the end of step 1 :
3 4 5
((————+——)+———)+6
1000 10 100
Step 2 :
1
Simplify ——
20
Equation at the end of step 2 :
3 4 1
((———— + ——) + ——) + 6
1000 10 20
Step 3 :
2
Simplify —
5
Equation at the end of step 3 :
3 2 1
((———— + —) + ——) + 6
1000 5 20
Step 4 :
3
Simplify ————
1000
Equation at the end of step 4 :
3 2 1
((———— + —) + ——) + 6
1000 5 20
Step 5 :
Calculating the Least Common Multiple :
5.1 Find the Least Common Multiple
The left denominator is : 1000
The right denominator is : 5
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 3 | 0 | 3 |
| 5 | 3 | 1 | 3 |
| Product of all Prime Factors | 1000 | 5 | 1000 |
Least Common Multiple:
1000
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 = 200
Making Equivalent Fractions :
5.3 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. 3 —————————————————— = ———— L.C.M 1000 R. Mult. • R. Num. 2 • 200 —————————————————— = ——————— L.C.M 1000
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:
3 + 2 • 200 403
——————————— = ————
1000 1000
Equation at the end of step 5 :
403 1
(———— + ——) + 6
1000 20
Step 6 :
Calculating the Least Common Multiple :
6.1 Find the Least Common Multiple
The left denominator is : 1000
The right denominator is : 20
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 3 | 2 | 3 |
| 5 | 3 | 1 | 3 |
| Product of all Prime Factors | 1000 | 20 | 1000 |
Least Common Multiple:
1000
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 = 50
Making Equivalent Fractions :
6.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 403 —————————————————— = ———— L.C.M 1000 R. Mult. • R. Num. 50 —————————————————— = ———— L.C.M 1000
Adding fractions that have a common denominator :
6.4 Adding up the two equivalent fractions
403 + 50 453
———————— = ————
1000 1000
Equation at the end of step 6 :
453
———— + 6
1000
Step 7 :
Rewriting the whole as an Equivalent Fraction :
7.1 Adding a whole to a fraction
Rewrite the whole as a fraction using 1000 as the denominator :
6 6 • 1000
6 = — = ————————
1 1000
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 :
7.2 Adding up the two equivalent fractions
453 + 6 • 1000 6453
—————————————— = ————
1000 1000
Final result :
6453
———— = 6.45300
1000
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