# Simplify 2* square root of 13/9+4/3-(3-(1+4/5)*2)÷2+1/3

2⋅139+43-(3-(1+45)⋅2)÷2+13
Simplify each term.
To write 43 as a fraction with a common denominator, multiply by 33.
2⋅139+43⋅33-(3-(1+45)⋅2)÷2+13
Write each expression with a common denominator of 9, by multiplying each by an appropriate factor of 1.
Multiply 43 and 33.
2⋅139+4⋅33⋅3-(3-(1+45)⋅2)÷2+13
Multiply 3 by 3.
2⋅139+4⋅39-(3-(1+45)⋅2)÷2+13
2⋅139+4⋅39-(3-(1+45)⋅2)÷2+13
Combine the numerators over the common denominator.
2⋅13+4⋅39-(3-(1+45)⋅2)÷2+13
Simplify the numerator.
Multiply 4 by 3.
2⋅13+129-(3-(1+45)⋅2)÷2+13
2⋅259-(3-(1+45)⋅2)÷2+13
2⋅259-(3-(1+45)⋅2)÷2+13
Rewrite 259 as 259.
2⋅259-(3-(1+45)⋅2)÷2+13
Simplify the numerator.
Rewrite 25 as 52.
2⋅529-(3-(1+45)⋅2)÷2+13
Pull terms out from under the radical, assuming positive real numbers.
2⋅59-(3-(1+45)⋅2)÷2+13
2⋅59-(3-(1+45)⋅2)÷2+13
Simplify the denominator.
Rewrite 9 as 32.
2⋅532-(3-(1+45)⋅2)÷2+13
Pull terms out from under the radical, assuming positive real numbers.
2⋅53-(3-(1+45)⋅2)÷2+13
2⋅53-(3-(1+45)⋅2)÷2+13
Multiply 2(53).
Combine 2 and 53.
2⋅53-(3-(1+45)⋅2)÷2+13
Multiply 2 by 5.
103-(3-(1+45)⋅2)÷2+13
103-(3-(1+45)⋅2)÷2+13
Rewrite the division as a fraction.
103-3-(1+45)⋅22+13
Simplify the numerator.
Write 1 as a fraction with a common denominator.
103-3-(55+45)⋅22+13
Combine the numerators over the common denominator.
103-3-5+45⋅22+13
103-3-95⋅22+13
Multiply -95⋅2.
Multiply 2 by -1.
103-3-2(95)2+13
Combine -2 and 95.
103-3+-2⋅952+13
Multiply -2 by 9.
103-3+-1852+13
103-3+-1852+13
Move the negative in front of the fraction.
103-3-1852+13
To write 3 as a fraction with a common denominator, multiply by 55.
103-3⋅55-1852+13
Combine 3 and 55.
103-3⋅55-1852+13
Combine the numerators over the common denominator.
103-3⋅5-1852+13
Simplify the numerator.
Multiply 3 by 5.
103-15-1852+13
Subtract 18 from 15.
103–352+13
103–352+13
Move the negative in front of the fraction.
103–352+13
103–352+13
Multiply the numerator by the reciprocal of the denominator.
103-(-35⋅12)+13
Multiply -35⋅12.
Multiply 12 and 35.
103–32⋅5+13
Multiply 2 by 5.
103–310+13
103–310+13
Multiply –310.
Multiply -1 by -1.
103+1(310)+13
Multiply 310 by 1.
103+310+13
103+310+13
103+310+13
Combine fractions.
Combine fractions with similar denominators.
10+13+310
113+310
113+310
To write 113 as a fraction with a common denominator, multiply by 1010.
113⋅1010+310
To write 310 as a fraction with a common denominator, multiply by 33.
113⋅1010+310⋅33
Write each expression with a common denominator of 30, by multiplying each by an appropriate factor of 1.
Multiply 113 and 1010.
11⋅103⋅10+310⋅33
Multiply 3 by 10.
11⋅1030+310⋅33
Multiply 310 and 33.
11⋅1030+3⋅310⋅3
Multiply 10 by 3.
11⋅1030+3⋅330
11⋅1030+3⋅330
Combine the numerators over the common denominator.
11⋅10+3⋅330
Simplify the numerator.
Multiply 11 by 10.
110+3⋅330
Multiply 3 by 3.
110+930
11930
11930
The result can be shown in multiple forms.
Exact Form:
11930
Decimal Form:
3.96‾
Mixed Number Form:
32930
Simplify 2* square root of 13/9+4/3-(3-(1+4/5)*2)÷2+1/3

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