Math worksheet for practicing conversion between improper fractions and mixed numbers.

Problem: Converting Improper Fractions to Mixed Numbers and Mixed Numbers to Improper Fractions

#### Part 1: Converting 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 step by step.

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Solutions for Converting Improper Fractions to Mixed Numbers

#### 1) $\frac{29}{4}$
- Divide $29 \div 4$:
$29 \div 4 = 7$ remainder $1$.
- The quotient is $7$, the remainder is $1$, and the denominator remains $4$.
- Mixed number: $7 \frac{1}{4}$.

#### 2) $\frac{13}{6}$
- Divide $13 \div 6$:
$13 \div 6 = 2$ remainder $1$.
- The quotient is $2$, the remainder is $1$, and the denominator remains $6$.
- Mixed number: $2 \frac{1}{6}$.

#### 3) $\frac{73}{9}$
- Divide $73 \div 9$:
$73 \div 9 = 8$ remainder $1$.
- The quotient is $8$, the remainder is $1$, and the denominator remains $9$.
- Mixed number: $8 \frac{1}{9}$.

#### 4) $\frac{65}{8}$
- Divide $65 \div 8$:
$65 \div 8 = 8$ remainder $1$.
- The quotient is $8$, the remainder is $1$, and the denominator remains $8$.
- Mixed number: $8 \frac{1}{8}$.

#### 5) $\frac{17}{2}$
- Divide $17 \div 2$:
$17 \div 2 = 8$ remainder $1$.
- The quotient is $8$, the remainder is $1$, and the denominator remains $2$.
- Mixed number: $8 \frac{1}{2}$.

#### 6) $\frac{5}{2}$
- Divide $5 \div 2$:
$5 \div 2 = 2$ remainder $1$.
- The quotient is $2$, the remainder is $1$, and the denominator remains $2$.
- Mixed number: $2 \frac{1}{2}$.

#### 7) $\frac{25}{4}$
- Divide $25 \div 4$:
$25 \div 4 = 6$ remainder $1$.
- The quotient is $6$, the remainder is $1$, and the denominator remains $4$.
- Mixed number: $6 \frac{1}{4}$.

#### 8) $\frac{43}{7}$
- Divide $43 \div 7$:
$43 \div 7 = 6$ remainder $1$.
- The quotient is $6$, the remainder is $1$, and the denominator remains $7$.
- Mixed number: $6 \frac{1}{7}$.

#### 9) $\frac{29}{4}$
- Divide $29 \div 4$:
$29 \div 4 = 7$ remainder $1$.
- The quotient is $7$, the remainder is $1$, and the denominator remains $4$.
- Mixed number: $7 \frac{1}{4}$.

#### 10) $\frac{73}{9}$
- Divide $73 \div 9$:
$73 \div 9 = 8$ remainder $1$.
- The quotient is $8$, the remainder is $1$, and the denominator remains $9$.
- Mixed number: $8 \frac{1}{9}$.

#### 11) $\frac{19}{3}$
- Divide $19 \div 3$:
$19 \div 3 = 6$ remainder $1$.
- The quotient is $6$, the remainder is $1$, and the denominator remains $3$.
- Mixed number: $6 \frac{1}{3}$.

#### 12) $\frac{43}{7}$
- Divide $43 \div 7$:
$43 \div 7 = 6$ remainder $1$.
- The quotient is $6$, the remainder is $1$, and the denominator remains $7$.
- Mixed number: $6 \frac{1}{7}$.

#### 13) $\frac{11}{5}$
- Divide $11 \div 5$:
$11 \div 5 = 2$ remainder $1$.
- The quotient is $2$, the remainder is $1$, and the denominator remains $5$.
- Mixed number: $2 \frac{1}{5}$.

#### 14) $\frac{91}{10}$
- Divide $91 \div 10$:
$91 \div 10 = 9$ remainder $1$.
- The quotient is $9$, the remainder is $1$, and the denominator remains $10$.
- Mixed number: $9 \frac{1}{10}$.

#### 15) $\frac{37}{6}$
- Divide $37 \div 6$:
$37 \div 6 = 6$ remainder $1$.
- The quotient is $6$, the remainder is $1$, and the denominator remains $6$.
- Mixed number: $6 \frac{1}{6}$.

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Final Answers for Part 1:

1) $7 \frac{1}{4}$
2) $2 \frac{1}{6}$
3) $8 \frac{1}{9}$
4) $8 \frac{1}{8}$
5) $8 \frac{1}{2}$
6) $2 \frac{1}{2}$
7) $6 \frac{1}{4}$
8) $6 \frac{1}{7}$
9) $7 \frac{1}{4}$
10) $8 \frac{1}{9}$
11) $6 \frac{1}{3}$
12) $6 \frac{1}{7}$
13) $2 \frac{1}{5}$
14) $9 \frac{1}{10}$
15) $6 \frac{1}{6}$

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Part 2: Converting 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. Write the sum as the new numerator, with the original denominator remaining the same.

Let's solve each problem step by step.

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Solutions for Converting Mixed Numbers to Improper Fractions

#### 1) $7 \frac{1}{3}$
- Multiply the whole number ($7$) by the denominator ($3$):
$7 \times 3 = 21$.
- Add the numerator ($1$) to this product:
$21 + 1 = 22$.
- The improper fraction is $\frac{22}{3}$.

#### 2) $7 \frac{9}{10}$
- Multiply the whole number ($7$) by the denominator ($10$):
$7 \times 10 = 70$.
- Add the numerator ($9$) to this product:
$70 + 9 = 79$.
- The improper fraction is $\frac{79}{10}$.

#### 3) $7 \frac{3}{4}$
- Multiply the whole number ($7$) by the denominator ($4$):
$7 \times 4 = 28$.
- Add the numerator ($3$) to this product:
$28 + 3 = 31$.
- The improper fraction is $\frac{31}{4}$.

#### 4) $2 \frac{1}{2}$
- Multiply the whole number ($2$) by the denominator ($2$):
$2 \times 2 = 4$.
- Add the numerator ($1$) to this product:
$4 + 1 = 5$.
- The improper fraction is $\frac{5}{2}$.

#### 5) $8 \frac{4}{7}$
- Multiply the whole number ($8$) by the denominator ($7$):
$8 \times 7 = 56$.
- Add the numerator ($4$) to this product:
$56 + 4 = 60$.
- The improper fraction is $\frac{60}{7}$.

#### 6) $2 \frac{3}{5}$
- Multiply the whole number ($2$) by the denominator ($5$):
$2 \times 5 = 10$.
- Add the numerator ($3$) to this product:
$10 + 3 = 13$.
- The improper fraction is $\frac{13}{5}$.

#### 7) $3 \frac{5}{8}$
- Multiply the whole number ($3$) by the denominator ($8$):
$3 \times 8 = 24$.
- Add the numerator ($5$) to this product:
$24 + 5 = 29$.
- The improper fraction is $\frac{29}{8}$.

#### 8) $6 \frac{7}{9}$
- Multiply the whole number ($6$) by the denominator ($9$):
$6 \times 9 = 54$.
- Add the numerator ($7$) to this product:
$54 + 7 = 61$.
- The improper fraction is $\frac{61}{9}$.

#### 9) $9 \frac{1}{8}$
- Multiply the whole number ($9$) by the denominator ($8$):
$9 \times 8 = 72$.
- Add the numerator ($1$) to this product:
$72 + 1 = 73$.
- The improper fraction is $\frac{73}{8}$.

#### 10) $6 \frac{2}{5}$
- Multiply the whole number ($6$) by the denominator ($5$):
$6 \times 5 = 30$.
- Add the numerator ($2$) to this product:
$30 + 2 = 32$.
- The improper fraction is $\frac{32}{5}$.

#### 11) $4 \frac{1}{3}$
- Multiply the whole number ($4$) by the denominator ($3$):
$4 \times 3 = 12$.
- Add the numerator ($1$) to this product:
$12 + 1 = 13$.
- The improper fraction is $\frac{13}{3}$.

#### 12) $2 \frac{2}{3}$
- Multiply the whole number ($2$) by the denominator ($3$):
$2 \times 3 = 6$.
- Add the numerator ($2$) to this product:
$6 + 2 = 8$.
- The improper fraction is $\frac{8}{3}$.

#### 13) $8 \frac{1}{2}$
- Multiply the whole number ($8$) by the denominator ($2$):
$8 \times 2 = 16$.
- Add the numerator ($1$) to this product:
$16 + 1 = 17$.
- The improper fraction is $\frac{17}{2}$.

#### 14) $4 \frac{3}{10}$
- Multiply the whole number ($4$) by the denominator ($10$):
$4 \times 10 = 40$.
- Add the numerator ($3$) to this product:
$40 + 3 = 43$.
- The improper fraction is $\frac{43}{10}$.

#### 15) $8 \frac{4}{5}$
- Multiply the whole number ($8$) by the denominator ($5$):
$8 \times 5 = 40$.
- Add the numerator ($4$) to this product:
$40 + 4 = 44$.
- The improper fraction is $\frac{44}{5}$.

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Final Answers for Part 2:

1) $\frac{22}{3}$
2) $\frac{79}{10}$
3) $\frac{31}{4}$
4) $\frac{5}{2}$
5) $\frac{60}{7}$
6) $\frac{13}{5}$
7) $\frac{29}{8}$
8) $\frac{61}{9}$
9) $\frac{73}{8}$
10) $\frac{32}{5}$
11) $\frac{13}{3}$
12) $\frac{8}{3}$
13) $\frac{17}{2}$
14) $\frac{43}{10}$
15) $\frac{44}{5}$

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Final Answer:

$$
\boxed{
\text{Part 1: } 7 \frac{1}{4}, 2 \frac{1}{6}, 8 \frac{1}{9}, 8 \frac{1}{8}, 8 \frac{1}{2}, 2 \frac{1}{2}, 6 \frac{1}{4}, 6 \frac{1}{7}, 7 \frac{1}{4}, 8 \frac{1}{9}, 6 \frac{1}{3}, 6 \frac{1}{7}, 2 \frac{1}{5}, 9 \frac{1}{10}, 6 \frac{1}{6}
}
$$
$$
\boxed{
\text{Part 2: } \frac{22}{3}, \frac{79}{10}, \frac{31}{4}, \frac{5}{2}, \frac{60}{7}, \frac{13}{5}, \frac{29}{8}, \frac{61}{9}, \frac{73}{8}, \frac{32}{5}, \frac{13}{3}, \frac{8}{3}, \frac{17}{2}, \frac{43}{10}, \frac{44}{5}
}
$$