Double Digits, Double Fun: How to Solve Word Problems with Two-digit Divisors

Dividing Two-digit and Three-digit Numbers by Two-digit Numbers in Word Problems

Example 1:

A school ordered \(240\) pencils and wants to distribute them equally among \(20\) classrooms. How many pencils will each classroom receive?

Solution Process:

Divide \(240\) by \(20\).

Answer:

Each classroom will receive \(12\) pencils.

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Example 2:

There are \(154\) students in a school who want to play soccer. If each team requires \(22\) players, how many full teams can the school form?

Solution Process:

Divide \(154\) by \(22\).

Answer:

The school can form \(7\) full teams with \(0\) students left over.

Dividing two-digit and three-digit numbers by two-digit numbers in word problems requires careful reading and understanding of the problem’s context. By identifying the numbers involved and performing the division, you can find the solution and apply this knowledge to various real-world scenarios. Whether it’s distributing resources, forming groups, or calculating averages, division plays an important part. Practice regularly with different word problems to become adept at using division in practical situations!

Practice Questions:

1. A bakery baked \(360\) muffins and wants to pack them in boxes of \(24\). How many full boxes will they have?

2. A library has \(528\) books and wants to distribute them equally among \(33\) tables. How many books will each table get?

3. There are \(275\) students going on a field trip. If each bus can carry \(25\) students, how many buses are needed?

4. A factory produces \(462\) toys and wants to pack them in boxes of \(21\). How many boxes will they prepare?

5. A marathon event has \(540\) water bottles to be distributed equally among \(45\) hydration stations. How many bottles will each station get?

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Answers:

1. \(15\) full boxes

2. \(16\) books per table with a remainder of \(0\)

3. \(11\) buses

4. \(22\) boxes

5. \(12\) bottles per station

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A Reliable 4-Step Method for Two-Digit Word Problems

Word problems built around two-digit numbers (10 to 99) trip up many students because the words pile up faster than the math. The fix is the same every time: slow the reading down, capture what you know, decide on the operation, and check the answer makes sense. Here’s the method that works for almost every two-digit word problem in elementary and middle-school math.

1. Read the problem twice. The first read is for the story. The second read is for the numbers and the question being asked.
2. Underline the question. What exactly is the problem asking you to find? “How many in all?” “How many more?” “How many are left?”
3. Pick the operation. “In all” / “altogether” → addition. “How many more” / “difference” → subtraction. “Each” / “groups of” → multiplication or division.
4. Solve and double-check. Estimate first (“about 80 + 20 ≈ 100”), then compute carefully. If your exact answer is far from your estimate, recheck the setup.

Worked Examples

Example 1: Addition

“Mia read 47 pages on Monday and 38 pages on Tuesday. How many pages did she read in all?” The phrase “in all” tells you to add. \(47 + 38 = 85\) pages. Estimate check: \(50 + 40 = 90\). Close to 85, answer is reasonable.

Example 2: Subtraction

“A bookstore had 92 books on the shelf. After a busy weekend, only 56 were left. How many books were sold?” “How many were sold” = the difference. \(92 – 56 = 36\) books. Estimate: \(90 – 60 = 30\). Reasonable.

Example 3: Multiplication

“A school orders 24 boxes of pencils. Each box has 12 pencils. How many pencils total?” “Each” + total → multiply. \(24 \times 12 = 288\) pencils. Estimate: \(25 \times 12 = 300\). Within range.

Common Mistakes to Avoid

• Picking the wrong operation. Don’t grab the first number you see and add it to the second. Read for what’s being asked.
• Forgetting to regroup. When subtracting and the top digit is smaller, you have to borrow, practice this until it’s automatic.
• Skipping the estimate. A quick estimate catches huge errors before you turn in the answer.
• Mixing up the order. “How many more does Sara have than Tom?” means Sara’s number minus Tom’s, not the other way around.

Related Topics

• Word Problems: Fractions
• Order of Operations
• One-Step Equations
• The Ultimate 6th Grade Math Course

Frequently Asked Questions

How do you do long division with 2-digit numbers?

Divide, multiply, subtract and bring down, just as with one-digit divisors, but estimate each quotient digit by rounding the divisor. For 672 ÷ 24, think 67 ÷ 24 is about 2, so write 2, subtract 48 to get 19, bring down the 2 to make 192, and 192 ÷ 24 = 8. The answer is 28, and 28 × 24 = 672 confirms it.

How do you solve word problems with two-digit divisors?

Decide what is being shared or grouped, write the division, then solve and make sure the answer fits the story. If 384 chairs are set up in rows of 16, then 384 ÷ 16 = 24 rows. Multiply back, 24 × 16 = 384, to confirm. Labeling the answer with its unit, such as rows, teams or boxes, catches many setup mistakes.

What do you do with a remainder in a long division word problem?

Let the question decide. If 250 students ride buses that hold 48 each, 250 ÷ 48 = 5 R10. To get everyone there you need 6 buses, so you round up. If the question asks how many buses are completely full, the answer is 5. If it asks how many students are on the last bus, the answer is the remainder, 10.

How do you check a long division answer with a 2-digit divisor?

Multiply the quotient by the divisor and add the remainder; the result should equal the dividend. For 500 ÷ 32 = 15 R20, check 15 × 32 = 480 and 480 + 20 = 500. If a remainder ever comes out equal to or larger than the divisor, the quotient digit was too small, so go back and raise it by one.

Practice Problems

1. A bakery sold 67 muffins on Friday and 84 on Saturday. How many in all? (Answer: 151)
2. There were 95 students at a field trip. After 38 went home early, how many remained? (Answer: 57)
3. Mark biked 24 miles each day for 13 days. Total miles? (Answer: 312)
4. A garden has 72 tulips and 39 daffodils. How many more tulips? (Answer: 33)

Recommended EffortlessMath Books

For a workbook that builds long division skills with worked examples, the Mastering Grade 5 Math walks through two-digit divisor problems step by step. For pure word-problem practice, the Mastering Grade 5 Math Word Problems packs in hundreds of division scenarios with full solutions.

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Related EffortlessMath Lessons

If a topic on this page feels rusty, these short lessons go deeper:

• How to divide multi-digit numbers
• How to multiply multi-digit numbers
• How to solve division word problems with facts up to 12
• How to solve multi-digit by one-digit division word problems
• How to solve multi-step word problems