Question
Mathematics
(4) $11\frac{3}{7}+3\frac{4}{5}=11$11(3)/(7)+3(4)/(5)=11
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To solve the equation $11\frac{3}{7}+3\frac{4}{5}=11$11(3)/(7)+3(4)/(5)=11, we can begin by converting the mixed numbers to improper fractions.
$11\frac{3}{7}$11(3)/(7) can be written as $\frac{11×7+3}{7}=\frac{80}{7}$(11 xx7+3)/(7)=(80)/(7).
$3\frac{4}{5}$3(4)/(5) can be written as $\frac{3×5+4}{5}=\frac{19}{5}$(3xx5+4)/(5)=(19)/(5).
Substituting these values, the equation becomes:
$\frac{80}{7}+\frac{19}{5}=11$(80)/(7)+(19)/(5)=11
To add fractions with different denominators, we need to find a common denominator. In this case, we can use the least common multiple (LCM) of 7 and 5, which is 35.
$\frac{80}{7}\cdot \frac{5}{5}=\frac{400}{35}$(80)/(7)*(5)/(5)=(400)/(35)
$\frac{19}{5}\cdot \frac{7}{7}=\frac{133}{35}$(19)/(5)*(7)/(7)=(133)/(35)
Substituting these values, the equation becomes:
$\frac{400}{35}+\frac{133}{35}=11$(400)/(35)+(133)/(35)=11
Now we can add the fractions:
$\frac{533}{35}=11$(533)/(35)=11
To isolate the variable, we can multiply both sides by the reciprocal of the coefficient of the variable:
$35\cdot \frac{533}{35}=11\cdot 35$35*(533)/(35)=11*35
$533=385$533=385
As $533\ne 385$533!=385 , we get a contradiction.
Therefore, the given equation has no solution.
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