Answer:
[tex]\dfrac{37}{12}, \dfrac{19}{6}, \dfrac{13}{4}, \dfrac{10}{3}, \dfrac{41}{12}, \dfrac{7}{2}[/tex]
Step-by-step explanation:
Write 3 and 4 as rational numbers with a common denominator.
Common denominator = common multiple = 12
[tex]\implies 3=\dfrac{3 \times 12}{12}=\dfrac{36}{12}[/tex]
[tex]\implies 4=\dfrac{4 \times 12}{12}=\dfrac{48}{12}[/tex]
Therefore, the rational numbers between them with a denominator of 12 are:
[tex]\dfrac{37}{12}, \dfrac{38}{12}, \dfrac{39}{12}, \dfrac{40}{12}, \dfrac{41}{12}, \dfrac{42}{12}, \dfrac{43}{12}, \dfrac{44}{12}, \dfrac{45}{12}, \dfrac{46}{12}, \dfrac{47}{12}[/tex]
Reduced to their simplest form:
[tex]\dfrac{37}{12}, \dfrac{19}{6}, \dfrac{13}{4}, \dfrac{10}{3}, \dfrac{41}{12}, \dfrac{7}{2}, \dfrac{43}{12}, \dfrac{11}{3}\dfrac{15}{4}, \dfrac{23}{6}, \dfrac{47}{12}[/tex]
**There are many, many more rational numbers between 3 and 4 that we could find by changing the denominator**
