Option a: multiply [tex]\frac{2}{5}[/tex] by 4.
Explanation:
The expression is [tex]\frac{2}{5} \div \frac{1}{4}[/tex]
Dividing the two fractions which is the same as multiplying the first fraction by the reciprocal value of the second fraction.
Hence, it can be written as
[tex]\frac{2}{5} \times \frac{4}{1}=\frac{8}{5}[/tex]
Hence, [tex]\frac{8}{5}[/tex] is the quotient.
Option a: multiply [tex]\frac{2}{5}[/tex] by 4.
To determine the quotient, let us multiply the term [tex]\frac{2}{5}[/tex] by 4, we get,
[tex]\frac{2}{5} \times 4=\frac{8}{5}[/tex]
Hence, [tex]\frac{8}{5}[/tex] is the quotient.
Thus, Option a is the correct answer.
Option b: multiply [tex]\frac{2}{5}[/tex] by [tex]\frac{1}{4}[/tex]
To determine the quotient, let us multiply the term [tex]\frac{2}{5}[/tex] by 4, we get,
[tex]\frac{2}{5} \times \frac{1}{4}=\frac{1}{10}[/tex]
[tex]\frac{1}{10}[/tex] is not the quotient. Since, the quotient is [tex]\frac{1}{10}[/tex] which is not equivalent to [tex]\frac{8}{5}[/tex] and hence we cannot multiply [tex]\frac{2}{5}[/tex] by [tex]\frac{1}{4}[/tex]
Hence, Option b is not the correct answer.
Option c: multiply [tex]\frac{5}{2}[/tex] by [tex]\frac{1}{4}[/tex]
To determine the quotient, let us multiply the term [tex]\frac{5}{2}[/tex] by [tex]\frac{1}{4}[/tex], we get,
[tex]\frac{5}{2} \times\frac{1}{4}=\frac{5}{8}[/tex]
[tex]\frac{5}{8}[/tex] is not the quotient. Since, the quotient is [tex]\frac{5}{8}[/tex] which is not equivalent to [tex]\frac{8}{5}[/tex] and hence we cannot multiply [tex]\frac{5}{2}[/tex] by [tex]\frac{1}{4}[/tex]
Hence, Option c is not the correct answer.
Option d: multiply [tex]\frac{5}{2}[/tex] by 4
To determine the quotient, let us multiply the term [tex]\frac{5}{2}[/tex] by 4, we get,
[tex]\frac{5}{2} \times4=10[/tex]
10 is not the quotient. Since, the quotient 10 which is not equivalent to [tex]\frac{8}{5}[/tex] and hence we cannot multiply [tex]\frac{5}{2}[/tex] by 4.
Hence, Option d is not the correct answer.
