Converting Mixed Numbers to Improper Fractions Worksheets ... - Free Printable

To solve the problem of converting mixed numbers to improper fractions, we follow these steps:

Step-by-Step Process:

1. Identify the parts of the mixed number: A mixed number consists of a whole number and a fraction. For example, in \( 6 \frac{2}{5} \), the whole number is 6, and the fraction is \( \frac{2}{5} \).
2. Multiply the whole number by the denominator of the fraction: This gives us the total number of parts represented by the whole number.
3. Add the numerator of the fraction to the result from step 2: This gives us the new numerator of the improper fraction.
4. Keep the denominator the same: The denominator of the improper fraction remains the same as the denominator of the original fraction.

Formula:

If the mixed number is \( a \frac{b}{c} \), the improper fraction is:
\[
\text{Improper Fraction} = \frac{(a \times c) + b}{c}
\]

Solving Each Problem:

#### 1. \( 6 \frac{2}{5} \)
\[
\text{Whole number} = 6, \quad \text{Numerator} = 2, \quad \text{Denominator} = 5
\]
\[
\text{Improper Fraction} = \frac{(6 \times 5) + 2}{5} = \frac{30 + 2}{5} = \frac{32}{5}
\]

#### 2. \( 5 \frac{3}{4} \)
\[
\text{Whole number} = 5, \quad \text{Numerator} = 3, \quad \text{Denominator} = 4
\]
\[
\text{Improper Fraction} = \frac{(5 \times 4) + 3}{4} = \frac{20 + 3}{4} = \frac{23}{4}
\]

#### 3. \( 7 \frac{3}{5} \)
\[
\text{Whole number} = 7, \quad \text{Numerator} = 3, \quad \text{Denominator} = 5
\]
\[
\text{Improper Fraction} = \frac{(7 \times 5) + 3}{5} = \frac{35 + 3}{5} = \frac{38}{5}
\]

#### 4. \( 2 \frac{5}{9} \)
\[
\text{Whole number} = 2, \quad \text{Numerator} = 5, \quad \text{Denominator} = 9
\]
\[
\text{Improper Fraction} = \frac{(2 \times 9) + 5}{9} = \frac{18 + 5}{9} = \frac{23}{9}
\]

#### 5. \( 6 \frac{4}{7} \)
\[
\text{Whole number} = 6, \quad \text{Numerator} = 4, \quad \text{Denominator} = 7
\]
\[
\text{Improper Fraction} = \frac{(6 \times 7) + 4}{7} = \frac{42 + 4}{7} = \frac{46}{7}
\]

#### 6. \( 8 \frac{3}{7} \)
\[
\text{Whole number} = 8, \quad \text{Numerator} = 3, \quad \text{Denominator} = 7
\]
\[
\text{Improper Fraction} = \frac{(8 \times 7) + 3}{7} = \frac{56 + 3}{7} = \frac{59}{7}
\]

#### 7. \( 5 \frac{3}{5} \)
\[
\text{Whole number} = 5, \quad \text{Numerator} = 3, \quad \text{Denominator} = 5
\]
\[
\text{Improper Fraction} = \frac{(5 \times 5) + 3}{5} = \frac{25 + 3}{5} = \frac{28}{5}
\]

#### 8. \( 6 \frac{4}{5} \)
\[
\text{Whole number} = 6, \quad \text{Numerator} = 4, \quad \text{Denominator} = 5
\]
\[
\text{Improper Fraction} = \frac{(6 \times 5) + 4}{5} = \frac{30 + 4}{5} = \frac{34}{5}
\]

#### 9. \( 9 \frac{1}{5} \)
\[
\text{Whole number} = 9, \quad \text{Numerator} = 1, \quad \text{Denominator} = 5
\]
\[
\text{Improper Fraction} = \frac{(9 \times 5) + 1}{5} = \frac{45 + 1}{5} = \frac{46}{5}
\]

#### 10. \( 7 \frac{3}{5} \)
\[
\text{Whole number} = 7, \quad \text{Numerator} = 3, \quad \text{Denominator} = 5
\]
\[
\text{Improper Fraction} = \frac{(7 \times 5) + 3}{5} = \frac{35 + 3}{5} = \frac{38}{5}
\]

Final Answers:

\[
\boxed{
\begin{array}{ll}
6 \frac{2}{5} = \frac{32}{5} & 5 \frac{3}{4} = \frac{23}{4} \\
7 \frac{3}{5} = \frac{38}{5} & 2 \frac{5}{9} = \frac{23}{9} \\
6 \frac{4}{7} = \frac{46}{7} & 8 \frac{3}{7} = \frac{59}{7} \\
5 \frac{3}{5} = \frac{28}{5} & 6 \frac{4}{5} = \frac{34}{5} \\
9 \frac{1}{5} = \frac{46}{5} & 7 \frac{3}{5} = \frac{38}{5}
\end{array}
}
\]