Long division practice worksheet with decimal numbers and whole number divisors.

Problem Overview:

The task involves solving division problems where the divisor is a whole number, and the dividend includes decimals. The goal is to perform long division while handling the decimal points correctly.

Steps to Solve Each Problem:

1. Ignore the Decimal Point Initially: Perform the division as if both numbers were whole numbers.
2. Place the Decimal Point: Once the division is complete, place the decimal point in the quotient directly above the decimal point in the dividend.
3. Continue Dividing: If there are remaining digits after the decimal point, continue dividing until you reach the desired precision or the remainder is zero.

Solutions:

#### Problem 1: \( 6 \div 14.37 \)
- Treat it as \( 6 \div 1437 \) (ignoring the decimal).
- Perform long division:
- \( 6 \) goes into \( 14 \) twice (\( 2 \times 6 = 12 \)).
- Subtract \( 12 \) from \( 14 \) to get \( 2 \).
- Bring down the next digit (\( 3 \)) to make it \( 23 \).
- \( 6 \) goes into \( 23 \) three times (\( 3 \times 6 = 18 \)).
- Subtract \( 18 \) from \( 23 \) to get \( 5 \).
- Bring down the next digit (\( 7 \)) to make it \( 57 \).
- \( 6 \) goes into \( 57 \) nine times (\( 9 \times 6 = 54 \)).
- Subtract \( 54 \) from \( 57 \) to get \( 3 \).

- Quotient: \( 2.39 \) (rounded to two decimal places).

Answer: \( 2.39 \)

#### Problem 2: \( 9 \div 62.91 \)
- Treat it as \( 9 \div 6291 \).
- Perform long division:
- \( 9 \) goes into \( 62 \) six times (\( 6 \times 9 = 54 \)).
- Subtract \( 54 \) from \( 62 \) to get \( 8 \).
- Bring down the next digit (\( 9 \)) to make it \( 89 \).
- \( 9 \) goes into \( 89 \) nine times (\( 9 \times 9 = 81 \)).
- Subtract \( 81 \) from \( 89 \) to get \( 8 \).
- Bring down the next digit (\( 1 \)) to make it \( 81 \).
- \( 9 \) goes into \( 81 \) nine times (\( 9 \times 9 = 81 \)).
- Subtract \( 81 \) from \( 81 \) to get \( 0 \).

- Quotient: \( 6.99 \).

Answer: \( 6.99 \)

#### Problem 3: \( 7 \div 34.51 \)
- Treat it as \( 7 \div 3451 \).
- Perform long division:
- \( 7 \) goes into \( 34 \) four times (\( 4 \times 7 = 28 \)).
- Subtract \( 28 \) from \( 34 \) to get \( 6 \).
- Bring down the next digit (\( 5 \)) to make it \( 65 \).
- \( 7 \) goes into \( 65 \) nine times (\( 9 \times 7 = 63 \)).
- Subtract \( 63 \) from \( 65 \) to get \( 2 \).
- Bring down the next digit (\( 1 \)) to make it \( 21 \).
- \( 7 \) goes into \( 21 \) three times (\( 3 \times 7 = 21 \)).
- Subtract \( 21 \) from \( 21 \) to get \( 0 \).

- Quotient: \( 4.93 \).

Answer: \( 4.93 \)

#### Problem 4: \( 3 \div 76.98 \)
- Treat it as \( 3 \div 7698 \).
- Perform long division:
- \( 3 \) goes into \( 76 \) twenty-five times (\( 25 \times 3 = 75 \)).
- Subtract \( 75 \) from \( 76 \) to get \( 1 \).
- Bring down the next digit (\( 9 \)) to make it \( 19 \).
- \( 3 \) goes into \( 19 \) six times (\( 6 \times 3 = 18 \)).
- Subtract \( 18 \) from \( 19 \) to get \( 1 \).
- Bring down the next digit (\( 8 \)) to make it \( 18 \).
- \( 3 \) goes into \( 18 \) six times (\( 6 \times 3 = 18 \)).
- Subtract \( 18 \) from \( 18 \) to get \( 0 \).

- Quotient: \( 25.66 \).

Answer: \( 25.66 \)

#### Problem 5: \( 5 \div 23.82 \)
- Treat it as \( 5 \div 2382 \).
- Perform long division:
- \( 5 \) goes into \( 23 \) four times (\( 4 \times 5 = 20 \)).
- Subtract \( 20 \) from \( 23 \) to get \( 3 \).
- Bring down the next digit (\( 8 \)) to make it \( 38 \).
- \( 5 \) goes into \( 38 \) seven times (\( 7 \times 5 = 35 \)).
- Subtract \( 35 \) from \( 38 \) to get \( 3 \).
- Bring down the next digit (\( 2 \)) to make it \( 32 \).
- \( 5 \) goes into \( 32 \) six times (\( 6 \times 5 = 30 \)).
- Subtract \( 30 \) from \( 32 \) to get \( 2 \).

- Quotient: \( 4.76 \).

Answer: \( 4.76 \)

#### Problem 6: \( 4 \div 23.82 \)
- Treat it as \( 4 \div 2382 \).
- Perform long division:
- \( 4 \) goes into \( 23 \) five times (\( 5 \times 4 = 20 \)).
- Subtract \( 20 \) from \( 23 \) to get \( 3 \).
- Bring down the next digit (\( 8 \)) to make it \( 38 \).
- \( 4 \) goes into \( 38 \) nine times (\( 9 \times 4 = 36 \)).
- Subtract \( 36 \) from \( 38 \) to get \( 2 \).
- Bring down the next digit (\( 2 \)) to make it \( 22 \).
- \( 4 \) goes into \( 22 \) five times (\( 5 \times 4 = 20 \)).
- Subtract \( 20 \) from \( 22 \) to get \( 2 \).

- Quotient: \( 5.95 \).

Answer: \( 5.95 \)

#### Problem 7: \( 2 \div 32.67 \)
- Treat it as \( 2 \div 3267 \).
- Perform long division:
- \( 2 \) goes into \( 32 \) sixteen times (\( 16 \times 2 = 32 \)).
- Subtract \( 32 \) from \( 32 \) to get \( 0 \).
- Bring down the next digit (\( 6 \)) to make it \( 6 \).
- \( 2 \) goes into \( 6 \) three times (\( 3 \times 2 = 6 \)).
- Subtract \( 6 \) from \( 6 \) to get \( 0 \).
- Bring down the next digit (\( 7 \)) to make it \( 7 \).
- \( 2 \) goes into \( 7 \) three times (\( 3 \times 2 = 6 \)).
- Subtract \( 6 \) from \( 7 \) to get \( 1 \).

- Quotient: \( 16.33 \).

Answer: \( 16.33 \)

#### Problem 8: \( 6 \div 54.96 \)
- Treat it as \( 6 \div 5496 \).
- Perform long division:
- \( 6 \) goes into \( 54 \) nine times (\( 9 \times 6 = 54 \)).
- Subtract \( 54 \) from \( 54 \) to get \( 0 \).
- Bring down the next digit (\( 9 \)) to make it \( 9 \).
- \( 6 \) goes into \( 9 \) one time (\( 1 \times 6 = 6 \)).
- Subtract \( 6 \) from \( 9 \) to get \( 3 \).
- Bring down the next digit (\( 6 \)) to make it \( 36 \).
- \( 6 \) goes into \( 36 \) six times (\( 6 \times 6 = 36 \)).
- Subtract \( 36 \) from \( 36 \) to get \( 0 \).

- Quotient: \( 9.16 \).

Answer: \( 9.16 \)

#### Problem 9: \( 5 \div 56.34 \)
- Treat it as \( 5 \div 5634 \).
- Perform long division:
- \( 5 \) goes into \( 56 \) eleven times (\( 11 \times 5 = 55 \)).
- Subtract \( 55 \) from \( 56 \) to get \( 1 \).
- Bring down the next digit (\( 3 \)) to make it \( 13 \).
- \( 5 \) goes into \( 13 \) two times (\( 2 \times 5 = 10 \)).
- Subtract \( 10 \) from \( 13 \) to get \( 3 \).
- Bring down the next digit (\( 4 \)) to make it \( 34 \).
- \( 5 \) goes into \( 34 \) six times (\( 6 \times 5 = 30 \)).
- Subtract \( 30 \) from \( 34 \) to get \( 4 \).

- Quotient: \( 11.26 \).

Answer: \( 11.26 \)

#### Problem 10: \( 8 \div 79.56 \)
- Treat it as \( 8 \div 7956 \).
- Perform long division:
- \( 8 \) goes into \( 79 \) nine times (\( 9 \times 8 = 72 \)).
- Subtract \( 72 \) from \( 79 \) to get \( 7 \).
- Bring down the next digit (\( 5 \)) to make it \( 75 \).
- \( 8 \) goes into \( 75 \) nine times (\( 9 \times 8 = 72 \)).
- Subtract \( 72 \) from \( 75 \) to get \( 3 \).
- Bring down the next digit (\( 6 \)) to make it \( 36 \).
- \( 8 \) goes into \( 36 \) four times (\( 4 \times 8 = 32 \)).
- Subtract \( 32 \) from \( 36 \) to get \( 4 \).

- Quotient: \( 9.94 \).

Answer: \( 9.94 \)

#### Problem 11: \( 7 \div 45.29 \)
- Treat it as \( 7 \div 4529 \).
- Perform long division:
- \( 7 \) goes into \( 45 \) six times (\( 6 \times 7 = 42 \)).
- Subtract \( 42 \) from \( 45 \) to get \( 3 \).
- Bring down the next digit (\( 2 \)) to make it \( 32 \).
- \( 7 \) goes into \( 32 \) four times (\( 4 \times 7 = 28 \)).
- Subtract \( 28 \) from \( 32 \) to get \( 4 \).
- Bring down the next digit (\( 9 \)) to make it \( 49 \).
- \( 7 \) goes into \( 49 \) seven times (\( 7 \times 7 = 49 \)).
- Subtract \( 49 \) from \( 49 \) to get \( 0 \).

- Quotient: \( 6.47 \).

Answer: \( 6.47 \)

#### Problem 12: \( 3 \div 52.89 \)
- Treat it as \( 3 \div 5289 \).
- Perform long division:
- \( 3 \) goes into \( 52 \) seventeen times (\( 17 \times 3 = 51 \)).
- Subtract \( 51 \) from \( 52 \) to get \( 1 \).
- Bring down the next digit (\( 8 \)) to make it \( 18 \).
- \( 3 \) goes into \( 18 \) six times (\( 6 \times 3 = 18 \)).
- Subtract \( 18 \) from \( 18 \) to get \( 0 \).
- Bring down the next digit (\( 9 \)) to make it \( 9 \).
- \( 3 \) goes into \( 9 \) three times (\( 3 \times 3 = 9 \)).
- Subtract \( 9 \) from \( 9 \) to get \( 0 \).

- Quotient: \( 17.63 \).

Answer: \( 17.63 \)

Final Answers:

\[
\boxed{
\begin{array}{cccc}
1. & 2.39 & 2. & 6.99 \\
3. & 4.93 & 4. & 25.66 \\
5. & 4.76 & 6. & 5.95 \\
7. & 16.33 & 8. & 9.16 \\
9. & 11.26 & 10. & 9.94 \\
11. & 6.47 & 12. & 17.63 \\
\end{array}
}
\]