# Solve for n 2 1/2+4 1/5+n=10 1/2

212+415+n=1012
Simplify 212+415+n.
Convert 212 to an improper fraction.
A mixed number is an addition of its whole and fractional parts.
2+12+415+n=1012
To write 2 as a fraction with a common denominator, multiply by 22.
2⋅22+12+415+n=1012
Combine 2 and 22.
2⋅22+12+415+n=1012
Combine the numerators over the common denominator.
2⋅2+12+415+n=1012
Simplify the numerator.
Multiply 2 by 2.
4+12+415+n=1012
52+415+n=1012
52+415+n=1012
52+415+n=1012
52+415+n=1012
Convert 415 to an improper fraction.
A mixed number is an addition of its whole and fractional parts.
52+4+15+n=1012
To write 4 as a fraction with a common denominator, multiply by 55.
52+4⋅55+15+n=1012
Combine 4 and 55.
52+4⋅55+15+n=1012
Combine the numerators over the common denominator.
52+4⋅5+15+n=1012
Simplify the numerator.
Multiply 4 by 5.
52+20+15+n=1012
52+215+n=1012
52+215+n=1012
52+215+n=1012
52+215+n=1012
To write 52 as a fraction with a common denominator, multiply by 55.
52⋅55+215+n=1012
To write 215 as a fraction with a common denominator, multiply by 22.
52⋅55+215⋅22+n=1012
Write each expression with a common denominator of 10, by multiplying each by an appropriate factor of 1.
Multiply 52 and 55.
5⋅52⋅5+215⋅22+n=1012
Multiply 2 by 5.
5⋅510+215⋅22+n=1012
Multiply 215 and 22.
5⋅510+21⋅25⋅2+n=1012
Multiply 5 by 2.
5⋅510+21⋅210+n=1012
5⋅510+21⋅210+n=1012
Combine the numerators over the common denominator.
5⋅5+21⋅210+n=1012
Simplify the numerator.
Multiply 5 by 5.
25+21⋅210+n=1012
Multiply 21 by 2.
25+4210+n=1012
6710+n=1012
6710+n=1012
6710+n=1012
Convert 1012 to an improper fraction.
A mixed number is an addition of its whole and fractional parts.
6710+n=10+12
To write 10 as a fraction with a common denominator, multiply by 22.
6710+n=10⋅22+12
Combine 10 and 22.
6710+n=10⋅22+12
Combine the numerators over the common denominator.
6710+n=10⋅2+12
Simplify the numerator.
Multiply 10 by 2.
6710+n=20+12
6710+n=212
6710+n=212
6710+n=212
6710+n=212
Move all terms not containing n to the right side of the equation.
Subtract 6710 from both sides of the equation.
n=212-6710
To write 212 as a fraction with a common denominator, multiply by 55.
n=212⋅55-6710
Write each expression with a common denominator of 10, by multiplying each by an appropriate factor of 1.
Multiply 212 and 55.
n=21⋅52⋅5-6710
Multiply 2 by 5.
n=21⋅510-6710
n=21⋅510-6710
Combine the numerators over the common denominator.
n=21⋅5-6710
Simplify the numerator.
Multiply 21 by 5.
n=105-6710
Subtract 67 from 105.
n=3810
n=3810
Cancel the common factor of 38 and 10.
Factor 2 out of 38.
n=2(19)10
Cancel the common factors.
Factor 2 out of 10.
n=2⋅192⋅5
Cancel the common factor.
n=2⋅192⋅5
Rewrite the expression.
n=195
n=195
n=195
n=195
The result can be shown in multiple forms.
Exact Form:
n=195
Decimal Form:
n=3.8
Mixed Number Form:
n=345
Solve for n 2 1/2+4 1/5+n=10 1/2

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