Converting between improper fractions and mixed numbers

Changing a mixed number into an improper fraction.

Consider the mixed number $1\frac{3}{5}$. Here is how you can imagine $1\frac{3}{5}$ on a number line.

$1\frac{3}{5}$ means each whole number is cut into five pieces and there are three additional fractional pieces. Therefore there are eight fractional pieces in $1\frac{3}{5}$.

1. Change each improper fraction into a mixed number. (Use the applet above to check your answer.)

a) $\frac{11}{3} =$

b) $\frac{21}{8} = $

c) $\frac{7}{4} = $

d) $\frac{20}{5} = $

2. Change each mixed number into an improper fraction. (Use the applet above to check your answer.)

a) $2\frac{2}{3} = $

b) $5\frac{1}{4} = $

c) $8\frac{1}{2} = $

d) $2\frac{6}{7} = $

3. Use words to describe what the picture would look like for the improper fraction $\frac{16}{3}$. Draw a sketch of the number line for $\frac{16}{3}$. Confirm your thoughts by setting the sliders to $\frac{16}{3}$.

Self-Check

Q1: Change $4\frac{1}{3}$ into an improper fraction. [show answer]

$\frac{13}{3}$

Q2: Change $3\frac{4}{5}$ into an improper fraction. [show answer]

$\frac{19}{5}$

Q3: Change $\frac{16}{5}$ into a mixed number. [show answer]

$3\frac{1}{5}$

Q4: Change $\frac{14}{4}$ into a mixed number. [show answer]