Convert improper fractions to mixed numbers with this math worksheet.

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

Steps to Convert an Improper Fraction to a Mixed Number:

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

Let's solve each problem step by step.

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1. $\frac{16}{3}$

- Divide $16 \div 3$:
- Quotient = $5$ (whole number part)
- Remainder = $1$ (numerator of the fractional part)
- Denominator remains $3$.
- Mixed number: $5 \frac{1}{3}$

2. $\frac{45}{4}$

- Divide $45 \div 4$:
- Quotient = $11$ (whole number part)
- Remainder = $1$ (numerator of the fractional part)
- Denominator remains $4$.
- Mixed number: $11 \frac{1}{4}$

3. $\frac{21}{2}$

- Divide $21 \div 2$:
- Quotient = $10$ (whole number part)
- Remainder = $1$ (numerator of the fractional part)
- Denominator remains $2$.
- Mixed number: $10 \frac{1}{2}$

4. $\frac{32}{6}$

- Simplify the fraction first:
- Both $32$ and $6$ are divisible by $2$:
$\frac{32 \div 2}{6 \div 2} = \frac{16}{3}$
- Now divide $16 \div 3$:
- Quotient = $5$ (whole number part)
- Remainder = $1$ (numerator of the fractional part)
- Denominator remains $3$.
- Mixed number: $5 \frac{1}{3}$

5. $\frac{30}{9}$

- Simplify the fraction first:
- Both $30$ and $9$ are divisible by $3$:
$\frac{30 \div 3}{9 \div 3} = \frac{10}{3}$
- Now divide $10 \div 3$:
- Quotient = $3$ (whole number part)
- Remainder = $1$ (numerator of the fractional part)
- Denominator remains $3$.
- Mixed number: $3 \frac{1}{3}$

6. $\frac{43}{5}$

- Divide $43 \div 5$:
- Quotient = $8$ (whole number part)
- Remainder = $3$ (numerator of the fractional part)
- Denominator remains $5$.
- Mixed number: $8 \frac{3}{5}$

7. $\frac{68}{7}$

- Divide $68 \div 7$:
- Quotient = $9$ (whole number part)
- Remainder = $5$ (numerator of the fractional part)
- Denominator remains $7$.
- Mixed number: $9 \frac{5}{7}$

8. $\frac{85}{10}$

- Simplify the fraction first:
- Both $85$ and $10$ are divisible by $5$:
$\frac{85 \div 5}{10 \div 5} = \frac{17}{2}$
- Now divide $17 \div 2$:
- Quotient = $8$ (whole number part)
- Remainder = $1$ (numerator of the fractional part)
- Denominator remains $2$.
- Mixed number: $8 \frac{1}{2}$

9. $\frac{59}{9}$

- Divide $59 \div 9$:
- Quotient = $6$ (whole number part)
- Remainder = $5$ (numerator of the fractional part)
- Denominator remains $9$.
- Mixed number: $6 \frac{5}{9}$

10. $\frac{88}{12}$

- Simplify the fraction first:
- Both $88$ and $12$ are divisible by $4$:
$\frac{88 \div 4}{12 \div 4} = \frac{22}{3}$
- Now divide $22 \div 3$:
- Quotient = $7$ (whole number part)
- Remainder = $1$ (numerator of the fractional part)
- Denominator remains $3$.
- Mixed number: $7 \frac{1}{3}$

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Final Answers:

1. $\frac{16}{3} = 5 \frac{1}{3}$
2. $\frac{45}{4} = 11 \frac{1}{4}$
3. $\frac{21}{2} = 10 \frac{1}{2}$
4. $\frac{32}{6} = 5 \frac{1}{3}$
5. $\frac{30}{9} = 3 \frac{1}{3}$
6. $\frac{43}{5} = 8 \frac{3}{5}$
7. $\frac{68}{7} = 9 \frac{5}{7}$
8. $\frac{85}{10} = 8 \frac{1}{2}$
9. $\frac{59}{9} = 6 \frac{5}{9}$
10. $\frac{88}{12} = 7 \frac{1}{3}$

Boxed Final Answer:

$$
\boxed{
\begin{aligned}
1. & \ 5 \frac{1}{3} \\
2. & \ 11 \frac{1}{4} \\
3. & \ 10 \frac{1}{2} \\
4. & \ 5 \frac{1}{3} \\
5. & \ 3 \frac{1}{3} \\
6. & \ 8 \frac{3}{5} \\
7. & \ 9 \frac{5}{7} \\
8. & \ 8 \frac{1}{2} \\
9. & \ 6 \frac{5}{9} \\
10. & \ 7 \frac{1}{3}
\end{aligned}
}
$$