L.3 Divide 2-digit numbers by 1-digit numbers: word problems
What is division?
Division is the process of splitting a number into equal groups. It is one of the four basic operations in math, along with addition, subtraction, and multiplication. When we divide, we are asking two important questions: “How many in each group?” or “How many groups can I make?” The number being divided is called the dividend. The number we are dividing by is the divisor. The result is the quotient. Sometimes, a number is left over, which is called the remainder.
- In the problem 42 ÷ 6 = 7, the dividend is 42, the divisor is 6, and the quotient is 7.
- If you have 36 apples and want to put them into 4 baskets with the same number in each, you divide: 36 ÷ 4 = 9 apples per basket.
- If you have 27 pencils and you give 5 pencils to each student, you can find how many students get pencils: 27 ÷ 5 = 5 with 2 left over (the remainder).
Division is the opposite of multiplication. If you know your multiplication facts, you can use them to solve division problems. For example, since 8 × 4 = 32, then 32 ÷ 8 = 4 and 32 ÷ 4 = 8.
Dividing 2-digit numbers by 1-digit numbers
When we divide a 2-digit number (like 45, 72, or 83) by a 1-digit number (like 3, 6, or 9), we are finding how many equal groups we can make. The quotient may be a 1-digit or 2-digit number. We can use a method called the standard algorithm (also known as long division) to solve these problems step by step.
- Step 1: Look at the tens digit of the dividend (4). How many times does the divisor (4) go into 4? It goes in 1 time. Write 1 above the tens place.
- Step 2: Multiply 1 × 4 = 4. Write that below the 4. Subtract: 4 − 4 = 0.
- Step 3: Bring down the ones digit (8). Now you have 8.
- Step 4: How many times does 4 go into 8? It goes in 2 times. Write 2 above the ones place.
- Step 5: Multiply 2 × 4 = 8. Subtract: 8 − 8 = 0. There is no remainder.
- Quotient: 12. So, 48 ÷ 4 = 12.
Always divide starting from the left (the tens place) and move to the right. This is different from addition or subtraction, where we start from the right.
Understanding remainders
A remainder is the amount left over after dividing when the divisor does not divide the dividend evenly. The remainder must always be less than the divisor. If the remainder is greater than or equal to the divisor, you can continue dividing.
- Step 1: How many times does 6 go into 5? It does not go into 5 because 6 is larger than 5. So we look at the first two digits: 59.
- Step 2: How many times does 6 go into 59? Use multiplication facts: 6 × 9 = 54, and 6 × 10 = 60 (too high). So, 6 goes into 59 nine times.
- Step 3: Write 9 above the ones place. Multiply 9 × 6 = 54. Write 54 below 59.
- Step 4: Subtract: 59 − 54 = 5. Since 5 is less than the divisor (6), this is the remainder.
- Quotient: 9 remainder 5. This is written as 9 R5 or sometimes as 9 with a remainder of 5.
A remainder can be written in different ways: as “R5,” as a fraction (5/6), or as a decimal (0.833). In fourth grade, you will usually write remainders using the “R” format unless told otherwise.
The long division algorithm step by step
The long division algorithm follows a repeating pattern: divide, multiply, subtract, bring down. You repeat these steps until there are no more digits to bring down. This method works for any division problem, whether there is a remainder or not.
- Divide: How many times does 3 go into 8? 2 times (since 2 × 3 = 6). Write 2 above the tens place.
- Multiply: Multiply 2 × 3 = 6. Write 6 below the 8.
- Subtract: 8 − 6 = 2.
- Bring down: Bring down the 7 from the ones place. Now you have 27.
- Repeat: How many times does 3 go into 27? 9 times (since 9 × 3 = 27). Write 9 above the ones place.
- Multiply: 9 × 3 = 27. Write 27 below the 27.
- Subtract: 27 − 27 = 0. No remainder.
- Quotient: 29. So, 87 ÷ 3 = 29.
Some students remember the steps with the phrase “Does McDonald’s Sell Burgers?” which stands for Divide, Multiply, Subtract, Bring down. Use whatever trick helps you remember the order.
Using multiplication to check division
Because division is the inverse (opposite) of multiplication, you can always check your division answer by multiplying. If your division has a remainder, you must add the remainder back after multiplying.
- Problem: 64 ÷ 4 = 16
- Check: Multiply the quotient (16) by the divisor (4): 16 × 4 = 64. This matches the dividend, so the answer is correct.
- Problem: 73 ÷ 5 = 14 R3
- Check: Multiply the quotient (14) by the divisor (5): 14 × 5 = 70.
- Add the remainder: 70 + 3 = 73. This matches the dividend, so the answer is correct.
Checking your work with multiplication is a powerful habit. It helps you catch mistakes and builds your confidence in your math skills.
Common mistakes and how to avoid them
When dividing 2-digit numbers by 1-digit numbers, students often make a few common errors. Recognizing these mistakes early will help you solve problems accurately.
- Example: In 56 ÷ 4, a student might divide 4 into 5 to get 1, subtract, and then stop without bringing down the 6. The correct answer is 14, but they might incorrectly say 1 R1.
- Fix: Always bring down the next digit before repeating the steps.
- Example: In 72 ÷ 3, a student might write the quotient as 24 but place the 2 above the ones place instead of the tens place.
- Fix: Remember that each digit of the quotient should line up with the digit you are dividing into. The first digit of the quotient goes above the last digit of the first group you divided.
- Example: In 85 ÷ 9, a student might say 9 R4, which is correct, but some students might incorrectly write 8 R13 because they stop too early.
- Fix: After subtracting, always check that the remainder is smaller than the divisor. If it is not, you can divide further.
Mistakes are part of learning. When you find an error, go back through the steps slowly. Use multiplication to check your work.
Real-world applications of division
Division is used every day in many real-life situations. Understanding how to divide helps you solve problems involving sharing, grouping, budgeting, and measuring.
- Four friends earned $95 together for a lemonade stand. They want to split the money equally. How much does each friend get? 95 ÷ 4 = 23 R3. Each friend gets $23, and there is $3 left over that they can donate or save.
- A teacher has 78 index cards. If each student needs 6 index cards, how many students can receive cards? 78 ÷ 6 = 13. Thirteen students will get a full set of index cards.
- There are 86 students going on a field trip. Each van holds 9 students. How many vans are needed? 86 ÷ 9 = 9 R5. This means 9 vans will be full, and 1 more van will be needed for the remaining 5 students. So, 10 vans are required.
In real-world problems, sometimes you need to ignore the remainder, sometimes you need to use it as a fraction, and sometimes you need to round up to the next whole number. Always read the problem carefully to decide what to do with the remainder.
Practice strategies for division fluency
Becoming fluent with division takes practice. Using a variety of strategies will help you build speed and accuracy. The goal is to be able to divide 2-digit numbers by 1-digit numbers with confidence.
- If you know that 7 × 8 = 56, then you automatically know that 56 ÷ 7 = 8 and 56 ÷ 8 = 7. Strong multiplication facts are the foundation of strong division skills.
- Before solving, estimate the quotient. For 93 ÷ 4, think: 4 × 20 = 80 and 4 × 25 = 100. The quotient will be between 20 and 25, close to 23. Estimating helps you know if your answer is reasonable.
- For 84 ÷ 6, you can break 84 into 60 and 24. Then 60 ÷ 6 = 10 and 24 ÷ 6 = 4. Add them together: 10 + 4 = 14. This mental math strategy works well for many problems.
Practice a few division problems every day. Over time, the steps will become automatic, and you will be able to solve problems more quickly without having to write every small step.
Common Core alignment: CCSS.MATH.CONTENT.4.NBT.B.6 – Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division.
Notes for teachers
This lesson is aligned with CCSS.MATH.CONTENT.4.NBT.B.6. All content is 100% free, use it for whole-class instruction, independent study and practice, or homework.