Divide 2-digit numbers by 1-digit numbers: interpret remainders
Sometimes when you divide, there are leftovers! These are called remainders. The tricky part isn't finding the remainder, but figuring out what it means and what to do with it. 🤔
Do this: Read the concept below, then try the quiz or activity.
Concept
When a number doesn't divide evenly, the amount left over is called the remainder. In word problems, what you do with the remainder is the most important part.
Example Problem: You have 23 cookies to share equally among 4 friends. How many cookies does each friend get?
1. Divide: 23 ÷ 4
* Think: 4 x ? is close to 23.
* 4 x 5 = 20.
* 23 - 20 = 3. The remainder is 3.
* The answer is 5 R 3 (5 with a remainder of 3).2. Interpret the Remainder: What do the numbers mean?
* 5: Each friend gets 5 cookies.
* 3: There are 3 cookies left over.Three Ways to Interpret a Remainder:
1. Ignore the Remainder (The "How many full groups?" question) * Question: You have 23 apples and you need 4 apples to make a pie. How many full pies can you make? * Answer: 5 pies. The 3 leftover apples aren't enough for another full pie, so you ignore them.
2. Round Up (The "Everyone needs a spot" question) * Question: There are 23 students going on a trip. Each car can hold 4 students. How many cars are needed? * Answer: 6 cars. 5 cars will hold 20 students, but the last 3 students still need a ride. So, you need a 6th car for them. You have to round up the answer.
3. Use the Remainder (The "What's left over?" question) * Question: You have 23 toy cars and share them equally among 4 friends. After everyone gets their share, how many cars are left over for you? * Answer: 3 cars. The question is specifically asking for the leftover amount.
Key Idea: Read the question carefully! It will tell you what to do with the remainder. Are you looking for full groups, making sure everyone is included, or finding the leftovers?
Try it
Practice interpreting remainders!
Solve, then interpret: First, solve 26 ÷ 5. The answer is 5 R 1. Now use that to answer the following questions:
1. If you have 26 pencils to put into boxes that hold 5 pencils each, how many full boxes can you make? 2. If 26 people are going to a movie and each row holds 5 people, how many rows will they need? 3. If you share 26 strawberries equally among 5 friends, how many will be left over?
Word Problems (Decide what to do with the remainder): 4. A baker has 40 eggs. Each cake requires 6 eggs. How many full cakes can the baker make? 5. There are 53 students going on a field trip. Each van can hold 8 students. How many vans are needed to take all the students? 6. A farmer has 34 apples. He packs them into bags with 5 apples each. How many apples are not in a full bag? 7. You have 75 inches of ribbon. You need 9 inches of ribbon for each gift. How many gifts can you wrap?
Challenge Problems: 8. I am a number between 20 and 30. When you divide me by 4, the remainder is 3. What number am I? 9. A rope is 100 inches long. It is cut into 7 equal pieces. What is the length of each piece, and how much rope is left over?