Multi-Digit Division

Grade 5 · mathematics · 71 practice problems · read aloud

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Multi-Digit Division: Conquering Big Numbers! 🧮

Division is all about fair sharing or splitting a large number into equal smaller groups. Multi-digit division helps us solve real-world problems, like figuring out how many teams of 4 you can make from 28 students, or how many weeks are in 365 days.

How to Solve: The Standard Algorithm (Long Division)

We use the steps DMSB: Divide, Multiply, Subtract, Bring Down. Remember it as: "Does McDonald's Sell Burgers?"

Example 1: 84 ÷ 4

  1. Divide: How many times does 4 go into 8? 2 times. Write the 2 above the 8.
  2. Multiply: 2 x 4 = 8. Write this below the first 8.
  3. Subtract: 8 - 8 = 0.
  4. Bring Down: Bring down the 4.
  5. Repeat: Now, 4 goes into 4 1 time. Write the 1 above the 4. Multiply (1x4=4), subtract (4-4=0).

Answer: 21

Example 2: 136 ÷ 4 (With a Remainder)

  1. Divide: 4 doesn't go into 1, so look at 13. 4 goes into 13 3 times. Write 3 above the 3.
  2. Multiply & Subtract: 3 x 4 = 12. 13 - 12 = 1.
  3. Bring Down: Bring down the 6 to make 16.
  4. Repeat: 4 goes into 16 4 times. Write 4 above the 6. Multiply (4x4=16), subtract (16-16=0).

Answer: 34

Common Mistakes to Avoid 🚫

  • Forgetting to Bring Down: After subtracting, don't forget the next digit! This is the most common error.
  • Incorrect Multiplication: Double-check your multiplication step before you subtract.
  • Misplacing the Quotient Digit: Write each new number in the correct place value spot above the dividend.

Tips & Tricks

  • Estimate First: Before you start, round the numbers. For 84 ÷ 4, you know 80 ÷ 4 = 20, so your answer should be close to 20.
  • Use Multiplication Facts: Strong multiplication skills make division much easier. Practice your times tables!
  • Check Your Work: Multiply your quotient by the divisor. You should get the original dividend back. (e.g., 21 x 4 = 84).

How to Practice

Mastery comes with practice! Try these:

  • Start with simple 2-digit by 1-digit problems (e.g., 96 ÷ 3).
  • Move on to 3-digit by 1-digit problems (e.g., 225 ÷ 5).
  • Create your own word problems. "If I have 145 stickers and 5 friends, how many does each get?"
  • Use online math games or flashcards for quick, fun practice.

Practice problems

6 of the 71, worked through step by step — try them before opening the answer.

1 756 ÷ 12 = ?

Hint: Think about how many times the divisor fits into the dividend, starting with the largest place value.

Show the answer

Answer: 63

  1. Set up the division problem. We want to divide 756 by 12. Think of it as: how many times does 12 go into 756?
  2. Start with the first digit(s). The first digit is 7, but 12 is bigger than 7, so we take the first two digits: 75.
  3. Divide 75 by 12. 12 × 6 = 72, which is less than 75. 12 × 7 = 84, which is too big. So, 12 goes into 75 six times. Write 6 above the 5 (tens place of the quotient).
  4. Multiply and subtract. 6 × 12 = 72. 75 − 72 = 3.
  5. Bring down the next digit. Bring down the 6 from 756, making the new number 36.
  6. Divide 36 by 12. 12 × 3 = 36 exactly. So, write 3 above the 6 (units place of the quotient).
  7. Multiply and subtract again. 3 × 12 = 36. 36 − 36 = 0. There is no remainder.
  8. Conclusion. The quotient is 63. So, 756 ÷ 12 = 63.

Let's solve 756 ÷ 12 step by step.

2 1,248 ÷ 26 = ?

Hint: Break down the division into manageable steps, starting with the largest place value.

Show the answer

Answer: 48

  1. Check how many times 26 goes into the first two digits of 1,248. The first two digits are 12. 26 is bigger than 12, so we take the first three digits: 124.
  2. How many times does 26 go into 124? Estimate: 26 × 4 = 104 (less than 124) 26 × 5 = 130 (too big, more than 124) So we use 4. Write 4 above the third digit of 1,248 (above the 4 in 1248).
  3. Multiply 26 × 4 = 104. Subtract 104 from 124: 124 − 104 = 20.
  4. Bring down the next digit (8) from 1,248. Now we have 208.
  5. How many times does 26 go into 208? Estimate: 26 × 8 = 208 exactly. So we use 8. Write 8 above the last digit of 1,248 (above the 8 in 1248).
  6. Multiply 26 × 8 = 208. Subtract: 208 − 208 = 0. No remainder. So the quotient is 48. Final check: 26 × 48 = 26 × 50 − 26 × 2 = 1,300 − 52 = 1,248. Correct. ANSWER: 48

Let's solve 1,248 ÷ 26 step by step. We are dividing 1,248 by 26 using long division.

3 1,365 ÷ 15 = ?

Hint: Break down the division into manageable parts by considering place values.

Show the answer

Answer: 91

  1. Set up the division: 15 into 1,365
  2. 15 goes into 13 zero times, so consider 136
  3. 15 × 9 = 135, which fits into 136
  4. Subtract: 136 - 135 = 1
  5. Bring down the 5 to make 15
  6. 15 × 1 = 15, which fits exactly
  7. Subtract: 15 - 15 = 0
  8. The quotient is 91

The answer is 91.

4 1,728 ÷ 24 = ?

Hint: Think about how many times the divisor fits into the dividend. You can break down the division into smaller steps.

Show the answer

Answer: 72

  1. Set up the long division: 24 into 1,728.
  2. 24 does not go into 1. 24 goes into 17 zero times. Consider 172.
  3. 24 × 7 = 168. 172 - 168 = 4.
  4. Bring down the next digit (8) to make 48.
  5. 24 × 2 = 48. 48 - 48 = 0.
  6. The final result is 72.

The answer is 72.

5 1,275 ÷ 15 = ?

Hint: Break down the division into smaller steps using estimation or place value

Show the answer

Answer: 85

  1. Set up the division: 15 into 1,275
  2. 15 goes into 127 how many times? 15 × 8 = 120, so 8 times
  3. Subtract: 127 - 120 = 7
  4. Bring down the 5 to make 75
  5. 15 goes into 75 how many times? 15 × 5 = 75, so 5 times
  6. Subtract: 75 - 75 = 0
  7. The quotient is 85
  8. Check: 85 × 15 = 1,275

The answer is 85.

6 1,728 ÷ 36 = ?

Hint: Think about how many times the divisor fits into the dividend. You can break down the division into smaller steps.

Show the answer

Answer: 48

  1. Set up the division problem: 36 into 1,728.
  2. 36 does not go into 1 or 17, so consider 172. 36 × 4 = 144, which is less than 172.
  3. Subtract: 172 - 144 = 28. Bring down the next digit (8) to make 288.
  4. Now, 36 into 288. 36 × 8 = 288 exactly.
  5. Subtract: 288 - 288 = 0. There is no remainder.
  6. The quotient is 48.

The answer is 48.

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