Changing improper fractions to mixed numbers | 4th grade, 5th ... - Free Printable

Problem Overview:

The task involves converting improper fractions to mixed numbers and vice versa. Let's solve each part step by step.

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#### Part 1: Changing Improper Fractions to Mixed Numbers

An improper fraction is a fraction where the numerator is greater than or equal to the denominator. To convert an improper fraction to a mixed number, follow these steps:

1. Divide the numerator by the denominator.
2. The quotient becomes the whole number part.
3. The remainder becomes the numerator of the fractional part.
4. The denominator remains the same.

Let’s solve each problem:

1. $\frac{25}{12}$
- Divide $25 \div 12$: Quotient = $2$, Remainder = $1$.
- Mixed number: $2 \frac{1}{12}$.

2. $\frac{17}{8}$
- Divide $17 \div 8$: Quotient = $2$, Remainder = $1$.
- Mixed number: $2 \frac{1}{8}$.

3. $\frac{31}{6}$
- Divide $31 \div 6$: Quotient = $5$, Remainder = $1$.
- Mixed number: $5 \frac{1}{6}$.

4. $\frac{29}{7}$
- Divide $29 \div 7$: Quotient = $4$, Remainder = $1$.
- Mixed number: $4 \frac{1}{7}$.

5. $\frac{43}{9}$
- Divide $43 \div 9$: Quotient = $4$, Remainder = $7$.
- Mixed number: $4 \frac{7}{9}$.

6. $\frac{50}{11}$
- Divide $50 \div 11$: Quotient = $4$, Remainder = $6$.
- Mixed number: $4 \frac{6}{11}$.

7. $\frac{67}{13}$
- Divide $67 \div 13$: Quotient = $5$, Remainder = $2$.
- Mixed number: $5 \frac{2}{13}$.

8. $\frac{82}{15}$
- Divide $82 \div 15$: Quotient = $5$, Remainder = $7$.
- Mixed number: $5 \frac{7}{15}$.

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#### Part 2: Changing Mixed Numbers to Improper Fractions

A mixed number consists of a whole number and a proper fraction. To convert a mixed number to an improper fraction, follow these steps:

1. Multiply the whole number by the denominator.
2. Add the result to the numerator.
3. The sum becomes the new numerator.
4. The denominator remains the same.

Let’s solve each problem:

1. $4 \frac{3}{5}$
- Multiply: $4 \times 5 = 20$.
- Add: $20 + 3 = 23$.
- Improper fraction: $\frac{23}{5}$.

2. $6 \frac{2}{7}$
- Multiply: $6 \times 7 = 42$.
- Add: $42 + 2 = 44$.
- Improper fraction: $\frac{44}{7}$.

3. $1 \frac{5}{8}$
- Multiply: $1 \times 8 = 8$.
- Add: $8 + 5 = 13$.
- Improper fraction: $\frac{13}{8}$.

4. $3 \frac{3}{4}$
- Multiply: $3 \times 4 = 12$.
- Add: $12 + 3 = 15$.
- Improper fraction: $\frac{15}{4}$.

5. $2 \frac{7}{9}$
- Multiply: $2 \times 9 = 18$.
- Add: $18 + 7 = 25$.
- Improper fraction: $\frac{25}{9}$.

6. $5 \frac{1}{6}$
- Multiply: $5 \times 6 = 30$.
- Add: $30 + 1 = 31$.
- Improper fraction: $\frac{31}{6}$.

7. $4 \frac{5}{12}$
- Multiply: $4 \times 12 = 48$.
- Add: $48 + 5 = 53$.
- Improper fraction: $\frac{53}{12}$.

8. $7 \frac{3}{10}$
- Multiply: $7 \times 10 = 70$.
- Add: $70 + 3 = 73$.
- Improper fraction: $\frac{73}{10}$.

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Final Answers:

#### Part 1: Improper Fractions to Mixed Numbers
1. $\frac{25}{12} = 2 \frac{1}{12}$
2. $\frac{17}{8} = 2 \frac{1}{8}$
3. $\frac{31}{6} = 5 \frac{1}{6}$
4. $\frac{29}{7} = 4 \frac{1}{7}$
5. $\frac{43}{9} = 4 \frac{7}{9}$
6. $\frac{50}{11} = 4 \frac{6}{11}$
7. $\frac{67}{13} = 5 \frac{2}{13}$
8. $\frac{82}{15} = 5 \frac{7}{15}$

#### Part 2: Mixed Numbers to Improper Fractions
1. $4 \frac{3}{5} = \frac{23}{5}$
2. $6 \frac{2}{7} = \frac{44}{7}$
3. $1 \frac{5}{8} = \frac{13}{8}$
4. $3 \frac{3}{4} = \frac{15}{4}$
5. $2 \frac{7}{9} = \frac{25}{9}$
6. $5 \frac{1}{6} = \frac{31}{6}$
7. $4 \frac{5}{12} = \frac{53}{12}$
8. $7 \frac{3}{10} = \frac{73}{10}$

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Boxed Final Answer:

\[
\boxed{
\begin{array}{ll}
\text{Part 1:} & 2 \frac{1}{12}, 2 \frac{1}{8}, 5 \frac{1}{6}, 4 \frac{1}{7}, 4 \frac{7}{9}, 4 \frac{6}{11}, 5 \frac{2}{13}, 5 \frac{7}{15} \\
\text{Part 2:} & \frac{23}{5}, \frac{44}{7}, \frac{13}{8}, \frac{15}{4}, \frac{25}{9}, \frac{31}{6}, \frac{53}{12}, \frac{73}{10}
\end{array}
}
\]