Question

Select the fraction(s) which is/are in its simplest form.

• A. $\frac{5}{11}$
• B. $\frac{5}{10}$
• C. $\frac{3}{10}$
• D. $\frac{3}{9}$

Answer 1

Answer: (A), (C)

$\frac{3}{10}$

$\frac{5}{11}:$
Let's rewrite the numerator and the denominator into its factors
Factors of $5:\underset{–}{1},5$
Factors of $11:\underset{–}{1},11$
$\frac{5}{11}$ is in the simplest form, because 5 and 11 have no common factors other than 1.

$\frac{5}{10}:$
Let's rewrite the numerator and the denominator into its factors
Factors of $5:\underset{–}{1},\underset{–}{5}$
Factors of $10:\underset{–}{1},2,\underset{–}{5},10$
$\frac{5}{11}$ is not in the simplest form, because 5 and 10 share common factors of 1 and 5.

$\frac{3}{10}:$
Let's rewrite the numerator and the denominator into its factors
Factors of $3:\underset{–}{1},3$
Factors of $10:\underset{–}{1},2,5,10$
$\frac{3}{10}$ is in the simplest form, because 3 and 10 have no common factors other than 1.

$\frac{3}{9}:$
Let's rewrite the numerator and the denominator into its factors
Factors of $3:1,3$
Factors of $9:1,3,9$
$\frac{3}{9}$ is not in the simplest form, because 3 and 9 share common factors of 1 and 3.