Multi-Digit Division for 5th Grade: Long Division with 2-Digit Divisors

Multi-digit division is used when splitting quantities into equal groups—packing books into boxes, dividing students into teams, or sharing items among people. In Grade 5, students divide whole numbers with two or more digits using long division (the standard algorithm). Long division breaks the division into repeated steps: estimate how many times the divisor fits into a part of the dividend, multiply, subtract, and bring down the next digit. This skill helps students solve real-world problems involving fair sharing, grouping, and finding how many groups of a given size fit into a total.

The long division algorithm uses four steps repeated: Divide, Multiply, Subtract, Bring down (DMSB, sometimes remembered as “Does McDonald’s Sell Burgers”). We start with the leftmost digits of the dividend that form a number at least as large as the divisor, find how many times the divisor fits, multiply and subtract, then bring down the next digit and repeat until we have processed all digits. The quotient may have a remainder if the division does not come out evenly.

DETAILED EXPLANATION

Steps for long division (e.g., 648 ÷ 24):

1. Set up: Write the dividend inside the division bracket, the divisor outside.

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2. Divide: Look at the first digit(s) of the dividend. How many times does the divisor fit? (If the divisor doesn’t fit into the first digit, use the first two digits.)

3. Multiply: Multiply the divisor by the quotient digit and write the product below the part of the dividend you used.

4. Subtract: Subtract the product from that part of the dividend.

5. Bring down: Bring down the next digit of the dividend.

6. Repeat: Go back to step 2 until all digits have been brought down. The final subtraction may leave a remainder.

Example: 648 ÷ 24. 24 goes into 64 twice (24 × 2 = 48). Subtract: 64 − 48 = 16. Bring down 8: 168. 24 goes into 168 seven times (24 × 7 = 168). Subtract: 0. Quotient: 27.

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WORKED EXAMPLES WITH STEP BY STEP SOLUTIONS

Example 1

648 books are packed into boxes of 24. How many boxes are needed?

Solutions:

Step 1: Divide 648 ÷ 24. Set up: 24 ) 648

Step 2: 24 does not go into 6, so use 64. How many times does 24 go into 64? 24 × 2 = 48, 24 × 3 = 72 (too big). So 2 times. Write 2 above the 4.

Step 3: Multiply: 24 × 2 = 48. Write 48 below 64. Subtract: 64 − 48 = 16.

Step 4: Bring down the next digit: 8. So we have 168.

Step 5: How many times does 24 go into 168? 24 × 7 = 168. Write 7 above the 8. Subtract: 168 − 168 = 0.

Step 6: Quotient: 27. We need 27 boxes.

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Answer: 27 boxes

Example 2

Divide 1,536 ÷ 32

Solutions:

Step 1: Set up: 32 ) 1536

Step 2: 32 does not go into 1. Use 15: still no. Use 153. 32 × 4 = 128, 32 × 5 = 160 (too big). Write 4 above the 3.

Step 3: Multiply: 32 × 4 = 128. Subtract: 153 − 128 = 25.

Step 4: Bring down 6: 256. 32 × 8 = 256. Write 8 above the 6. Subtract: 256 − 256 = 0.

Step 5: Quotient: 48.

Answer: 48

Example 3

1,248 ÷ 52

Solutions:

Step 1: Set up: 52 ) 1248

Step 2: 52 goes into 124 twice (52 × 2 = 104). Write 2 above the 4. Subtract: 124 − 104 = 20.

Step 3: Bring down 8: 208. 52 × 4 = 208. Write 4 above the 8. Subtract: 208 − 208 = 0.

Step 4: Quotient: 24, remainder 0.

Answer: 24

Example 4

Divide 892 ÷ 17 (with remainder)

Solutions:

Step 1: 17 ) 892. 17 goes into 89 five times (17 × 5 = 85). Write 5. Subtract: 89 − 85 = 4.

Step 2: Bring down 2: 42. 17 × 2 = 34. Write 2. Subtract: 42 − 34 = 8.

Step 3: No more digits to bring down. Quotient: 52, remainder: 8.

Answer: 52 R 8