# Solve for a 1/8+1/11=1/a 18+111=1a
Rewrite the equation as 1a=18+111.
1a=18+111
Factor each term.
To write 18 as a fraction with a common denominator, multiply by 1111.
1a=18⋅1111+111
To write 111 as a fraction with a common denominator, multiply by 88.
1a=18⋅1111+111⋅88
Write each expression with a common denominator of 88, by multiplying each by an appropriate factor of 1.
Multiply 18 and 1111.
1a=118⋅11+111⋅88
Multiply 8 by 11.
1a=1188+111⋅88
Multiply 111 and 88.
1a=1188+811⋅8
Multiply 11 by 8.
1a=1188+888
1a=1188+888
Combine the numerators over the common denominator.
1a=11+888
1a=1988
1a=1988
Set up the rational expression with the same denominator over the entire equation.
Multiply each term by a factor of 1 that will equate all the denominators. In this case, all terms need a denominator of 88a. The 1a expression needs to be multiplied by 8888 to make the denominator 88a. The 1988 expression needs to be multiplied by aa to make the denominator 88a.
1a⋅8888=1988⋅aa
Multiply the expression by a factor of 1 to create the least common denominator (LCD) of 88a.
1(88)
Multiply 88 by 1.
8888a=1988⋅aa
Multiply the expression by a factor of 1 to create the least common denominator (LCD) of 88a.
19(a)
Multiply 19 by a.
8888a=19a88a
8888a=19a88a
Since the expression on each side of the equation has the same denominator, the numerators must be equal.
88=19a
Rewrite the equation as 19a=88.
19a=88
Divide each term by 19 and simplify.
Divide each term in 19a=88 by 19.
19a19=8819
Cancel the common factor of 19.
Cancel the common factor.
19a19=8819
Divide a by 1.
a=8819
a=8819
a=8819
The result can be shown in multiple forms.
Exact Form:
a=8819
Decimal Form:
a=4.63157894…
Mixed Number Form:
a=41219
Solve for a 1/8+1/11=1/a

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