Mixed and Improper Fractions worksheet - Free Printable

To solve the problem of converting between improper fractions and mixed numbers based on the given images, we need to carefully analyze each picture and determine the corresponding improper fraction and mixed number. Let's go through each row step by step.

Row 1:

- Picture: Two circles divided into 8 equal parts. One circle is completely shaded, and the other has 3 parts shaded.
- Improper Fraction: There are a total of \(8 + 3 = 11\) parts shaded out of 8 parts in each whole. So, the improper fraction is \(\frac{11}{8}\).
- Mixed Number: This can be written as \(1 \frac{3}{8}\) because 11 divided by 8 is 1 with a remainder of 3.

Answer:
- Improper Fraction: \(\frac{11}{8}\)
- Mixed Number: \(1 \frac{3}{8}\)

Row 2:

- Picture: Four pentagons. Three are completely shaded, and the fourth has 2 parts shaded out of 5.
- Improper Fraction: There are a total of \(3 \times 5 + 2 = 15 + 2 = 17\) parts shaded out of 5 parts in each whole. So, the improper fraction is \(\frac{17}{5}\).
- Mixed Number: This can be written as \(3 \frac{2}{5}\) because 17 divided by 5 is 3 with a remainder of 2.

Answer:
- Improper Fraction: \(\frac{17}{5}\)
- Mixed Number: \(3 \frac{2}{5}\)

Row 3:

- Picture: Three squares divided into 4 equal parts. Two squares are completely shaded, and the third has 1 part shaded.
- Improper Fraction: There are a total of \(2 \times 4 + 1 = 8 + 1 = 9\) parts shaded out of 4 parts in each whole. So, the improper fraction is \(\frac{9}{4}\).
- Mixed Number: This can be written as \(2 \frac{1}{4}\) because 9 divided by 4 is 2 with a remainder of 1.

Answer:
- Improper Fraction: \(\frac{9}{4}\)
- Mixed Number: \(2 \frac{1}{4}\)

Row 4:

- Picture: Five triangles. Four are completely shaded, and the fifth has 1 part shaded out of 2.
- Improper Fraction: There are a total of \(4 \times 2 + 1 = 8 + 1 = 9\) parts shaded out of 2 parts in each whole. So, the improper fraction is \(\frac{9}{2}\).
- Mixed Number: This can be written as \(4 \frac{1}{2}\) because 9 divided by 2 is 4 with a remainder of 1.

Answer:
- Improper Fraction: \(\frac{9}{2}\)
- Mixed Number: \(4 \frac{1}{2}\)

Row 5:

- Picture: Four pentagons. Three are completely shaded, and the fourth has 4 parts shaded out of 5.
- Improper Fraction: There are a total of \(3 \times 5 + 4 = 15 + 4 = 19\) parts shaded out of 5 parts in each whole. So, the improper fraction is \(\frac{19}{5}\).
- Mixed Number: This can be written as \(3 \frac{4}{5}\) because 19 divided by 5 is 3 with a remainder of 4.

Answer:
- Improper Fraction: \(\frac{19}{5}\)
- Mixed Number: \(3 \frac{4}{5}\)

Row 6:

- Picture: Four grids divided into 9 equal parts. Three grids are completely shaded, and the fourth has 4 parts shaded.
- Improper Fraction: There are a total of \(3 \times 9 + 4 = 27 + 4 = 31\) parts shaded out of 9 parts in each whole. So, the improper fraction is \(\frac{31}{9}\).
- Mixed Number: This can be written as \(3 \frac{4}{9}\) because 31 divided by 9 is 3 with a remainder of 4.

Answer:
- Improper Fraction: \(\frac{31}{9}\)
- Mixed Number: \(3 \frac{4}{9}\)

Row 7:

- Picture: Two sets of 10 rectangles. The first set is completely shaded, and the second set has 7 rectangles shaded.
- Improper Fraction: There are a total of \(10 + 7 = 17\) parts shaded out of 10 parts in each whole. So, the improper fraction is \(\frac{17}{10}\).
- Mixed Number: This can be written as \(1 \frac{7}{10}\) because 17 divided by 10 is 1 with a remainder of 7.

Answer:
- Improper Fraction: \(\frac{17}{10}\)
- Mixed Number: \(1 \frac{7}{10}\)

Final Answer:

\[
\boxed{
\begin{array}{|c|c|c|}
\hline
\text{Picture} & \text{Improper Fractions} & \text{Mixed Numbers} \\
\hline
\text{(Row 1)} & \frac{11}{8} & 1 \frac{3}{8} \\
\hline
\text{(Row 2)} & \frac{17}{5} & 3 \frac{2}{5} \\
\hline
\text{(Row 3)} & \frac{9}{4} & 2 \frac{1}{4} \\
\hline
\text{(Row 4)} & \frac{9}{2} & 4 \frac{1}{2} \\
\hline
\text{(Row 5)} & \frac{19}{5} & 3 \frac{4}{5} \\
\hline
\text{(Row 6)} & \frac{31}{9} & 3 \frac{4}{9} \\
\hline
\text{(Row 7)} & \frac{17}{10} & 1 \frac{7}{10} \\
\hline
\end{array}
}
\]