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): "7.8" was replaced by "(78/10)". 3 more similar replacement(s)
Step 1 :
39
Simplify ——
5
Equation at the end of step 1 :
151 101 39
((——— + ———) + ——) + 16
10 100 5
Step 2 :
101
Simplify ———
100
Equation at the end of step 2 :
151 101 39
((——— + ———) + ——) + 16
10 100 5
Step 3 :
151
Simplify ———
10
Equation at the end of step 3 :
151 101 39
((——— + ———) + ——) + 16
10 100 5
Step 4 :
Calculating the Least Common Multiple :
4.1 Find the Least Common Multiple
The left denominator is : 10
The right denominator is : 100
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 1 | 2 | 2 |
| 5 | 1 | 2 | 2 |
| Product of all Prime Factors | 10 | 100 | 100 |
Least Common Multiple:
100
Calculating Multipliers :
4.2 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 = 10
Right_M = L.C.M / R_Deno = 1
Making Equivalent Fractions :
4.3 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. 151 • 10 —————————————————— = ———————— L.C.M 100 R. Mult. • R. Num. 101 —————————————————— = ——— L.C.M 100
Adding fractions that have a common denominator :
4.4 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:
151 • 10 + 101 1611
—————————————— = ————
100 100
Equation at the end of step 4 :
1611 39
(———— + ——) + 16
100 5
Step 5 :
Calculating the Least Common Multiple :
5.1 Find the Least Common Multiple
The left denominator is : 100
The right denominator is : 5
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 2 | 0 | 2 |
| 5 | 2 | 1 | 2 |
| Product of all Prime Factors | 100 | 5 | 100 |
Least Common Multiple:
100
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 = 20
Making Equivalent Fractions :
5.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 1611 —————————————————— = ———— L.C.M 100 R. Mult. • R. Num. 39 • 20 —————————————————— = ——————— L.C.M 100
Adding fractions that have a common denominator :
5.4 Adding up the two equivalent fractions
1611 + 39 • 20 2391
—————————————— = ————
100 100
Equation at the end of step 5 :
2391
———— + 16
100
Step 6 :
Rewriting the whole as an Equivalent Fraction :
6.1 Adding a whole to a fraction
Rewrite the whole as a fraction using 100 as the denominator :
16 16 • 100
16 = —— = ————————
1 100
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 :
6.2 Adding up the two equivalent fractions
2391 + 16 • 100 3991
——————————————— = ————
100 100
Final result :
3991
———— = 39.91000
100
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