Solve: 2/5+3/10+4/15
step by step
Answers
Answer:
29/30
Step-by-step explanation:
Step by Step Solution:
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STEP
1
:
4
Simplify ——
15
Equation at the end of step
1
:
2 3 4
(— + ——) + ——
5 10 15
STEP
2
:
3
Simplify ——
10
Equation at the end of step
2
:
2 3 4
(— + ——) + ——
5 10 15
STEP
3
:
2
Simplify —
5
Equation at the end of step
3
:
2 3 4
(— + ——) + ——
5 10 15
STEP
4
:
Calculating the Least Common Multiple
4.1 Find the Least Common Multiple
The left denominator is : 5
The right denominator is : 10
Number of times each prime factor
appears in the factorization of:
Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
5 1 1 1
2 0 1 1
Product of all
Prime Factors 5 10 10
Least Common Multiple:
10
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 = 2
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. 2 • 2
—————————————————— = —————
L.C.M 10
R. Mult. • R. Num. 3
—————————————————— = ——
L.C.M 10
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:
2 • 2 + 3 7
————————— = ——
10 10
Equation at the end of step
4
:
7 4
—— + ——
10 15
STEP
5
:
Calculating the Least Common Multiple
5.1 Find the Least Common Multiple
The left denominator is : 10
The right denominator is : 15
Number of times each prime factor
appears in the factorization of:
Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
2 1 0 1
5 1 1 1
3 0 1 1
Product of all
Prime Factors 10 15 30
Least Common Multiple:
30
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 = 3
Right_M = L.C.M / R_Deno = 2
Making Equivalent Fractions :
5.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 7 • 3
—————————————————— = —————
L.C.M 30
R. Mult. • R. Num. 4 • 2
—————————————————— = —————
L.C.M 30
Adding fractions that have a common denominator :
5.4 Adding up the two equivalent fractions
7 • 3 + 4 • 2 29
————————————— = ——
30 30
Final result :
29
—— = 0.96667
30