K.2 Division facts up to 12: word problems
What is division?
Division is an operation that splits a number into equal groups. It helps you find out how many items are in each group or how many groups you can make. The symbol ÷ or a fraction bar (—) is used to show division.
- 12 ÷ 3 = 4 means “12 split into 3 equal groups gives 4 in each group.”
- 20 ÷ 5 = 4 means “20 split into 5 equal groups gives 4 in each group.”
- If you have 15 cookies and share them equally among 3 friends, each friend gets 5 cookies. This is 15 ÷ 3 = 5.
Division is the opposite of multiplication. If you know your multiplication facts, you can use them to solve division facts quickly. For example, since 4 × 3 = 12, you know 12 ÷ 3 = 4 and 12 ÷ 4 = 3.
Parts of a division equation
Every division problem has three important parts: the dividend, the divisor, and the quotient. The dividend is the number being split up. The divisor is the number you are dividing by. The quotient is the answer.
- In 24 ÷ 6 = 4, 24 is the dividend, 6 is the divisor, and 4 is the quotient.
- In 45 ÷ 9 = 5, 45 is the dividend, 9 is the divisor, and 5 is the quotient.
- When written as a fraction, like 328 = 4, 32 is still the dividend, 8 is the divisor, and 4 is the quotient.
The quotient tells you the size of each group or the number of groups. Always check that your quotient makes sense with the problem you are solving.
Division facts up to 12
Division facts are basic division equations that use numbers 1 through 12 as divisors and dividends up to 144. Memorizing these facts helps you solve more complex problems quickly. A division fact is related to a multiplication fact from the same fact family.
- 12 ÷ 1 = 12
- 24 ÷ 2 = 12
- 36 ÷ 3 = 12
- 48 ÷ 4 = 12
- 60 ÷ 5 = 12
- 72 ÷ 6 = 12
- 84 ÷ 7 = 12
- 96 ÷ 8 = 12
- 108 ÷ 9 = 12
- 120 ÷ 10 = 12
- 132 ÷ 11 = 12
- 144 ÷ 12 = 12
In fourth grade, you should be able to recall any division fact with divisors from 1 to 12 and quotients up to 12. Practice these until they feel automatic. Using flash cards or online games can make memorization easier.
Fact families: multiplication and division
A fact family is a set of related multiplication and division equations that use the same three numbers. Understanding fact families helps you see how multiplication and division are connected. If you know one fact, you can figure out the others.
- For the numbers 3, 4, and 12, the fact family is:
3 × 4 = 12, 4 × 3 = 12, 12 ÷ 3 = 4, 12 ÷ 4 = 3. - For the numbers 5, 6, and 30, the fact family is:
5 × 6 = 30, 6 × 5 = 30, 30 ÷ 5 = 6, 30 ÷ 6 = 5. - For the numbers 7, 8, and 56, the fact family is:
7 × 8 = 56, 8 × 7 = 56, 56 ÷ 7 = 8, 56 ÷ 8 = 7.
When you get stuck on a division fact, think of the related multiplication fact. Ask yourself, “What number times the divisor equals the dividend?” For 42 ÷ 6, think 6 × ? = 42. Since 6 × 7 = 42, the quotient is 7.
Dividing by 1 and by the number itself
There are two special rules in division that always hold true. When you divide a number by 1, the quotient is always the number itself. When you divide a number by itself (except zero), the quotient is always 1.
- Any number divided by 1 equals that number: 9 ÷ 1 = 9, 15 ÷ 1 = 15, 144 ÷ 1 = 144.
- Any number divided by itself equals 1: 8 ÷ 8 = 1, 25 ÷ 25 = 1, 121 ÷ 121 = 1.
Remember that division by zero is not allowed. You cannot divide a number by zero because it does not make sense mathematically. For example, 12 ÷ 0 has no answer.
Strategies for solving division facts
There are several strategies you can use to solve division facts quickly and accurately. Using these strategies builds your number sense and prepares you for long division and more complex math.
- Use multiplication: To find 56 ÷ 7, think 7 × ? = 56. Since 7 × 8 = 56, the quotient is 8.
- Skip counting: To find 24 ÷ 3, count by 3s: 3, 6, 9, 12, 15, 18, 21, 24. It takes 8 jumps to reach 24, so 24 ÷ 3 = 8.
- Use repeated subtraction: For 18 ÷ 6, subtract 6 repeatedly: 18 − 6 = 12, 12 − 6 = 6, 6 − 6 = 0. You subtracted 3 times, so 18 ÷ 6 = 3.
- Draw equal groups: Draw 20 circles and group them into 4 equal groups. Each group has 5 circles, so 20 ÷ 4 = 5.
Try different strategies to see which one works best for you. Over time, you will find that memorizing facts is the fastest way, but using strategies helps you understand why the answer is correct.
Understanding remainders
Sometimes a number cannot be divided into equal groups without having some left over. The amount left over is called a remainder. In fourth grade, you focus on division facts that divide evenly, but it is important to know what a remainder means.
- 13 ÷ 4 = 3 with a remainder of 1 because 4 × 3 = 12, and 13 − 12 = 1.
- 25 ÷ 6 = 4 with a remainder of 1 because 6 × 4 = 24, and 25 − 24 = 1.
- When division facts are even, the remainder is zero. For example, 36 ÷ 6 = 6 exactly with no remainder.
All division facts up to 12 that you practice should have a remainder of 0. This means the dividend is a multiple of the divisor. Knowing these exact facts prepares you for long division in later grades.
Common division patterns
Recognizing patterns in division facts can help you memorize them more quickly. Patterns appear when you look at divisors, dividends, and quotients across tables.
- Dividing by 2 is like finding half: 18 ÷ 2 = 9, 24 ÷ 2 = 12, 10 ÷ 2 = 5.
- Dividing by 5: the quotient ends in 0, 2, 4, 6, or 8 when the dividend is even, but often the result is a whole number. 35 ÷ 5 = 7, 45 ÷ 5 = 9.
- Dividing by 10: simply remove the zero from the dividend: 120 ÷ 10 = 12, 90 ÷ 10 = 9.
- Dividing by 11: look for patterns like 121 ÷ 11 = 11, 44 ÷ 11 = 4, 99 ÷ 11 = 9.
When you notice a pattern, write it down and test it with other numbers. Patterns make memorization faster and help you check your work.
Real-world applications of division facts
Knowing division facts is not just for math class. You use division in many everyday situations. Understanding division helps you organize, plan, and share fairly.
- Shopping: If a pack of 6 water bottles costs $12, how much is one bottle? 12 ÷ 6 = $2 per bottle.
- Cooking: A recipe makes 8 servings, but you only need 4 servings. You can divide the ingredients by 2.
- Sports: A coach has 24 players and wants to make 4 equal teams. 24 ÷ 4 = 6 players per team.
- Time: If you have 60 minutes and want to divide them into 12 equal blocks, each block is 60 ÷ 12 = 5 minutes.
When solving real-world problems, always check if the problem asks for the number of groups or the number in each group. This will help you set up the correct division equation.
Building fluency with division facts
Fluency means being able to recall a division fact quickly and accurately without having to stop and figure it out. Fluency with division facts up to 12 is a key goal in fourth grade because it makes harder math problems much easier.
- Set a goal to master one divisor at a time. Start with dividing by 1, then 2, then 3, and so on up to 12.
- Use timed practice: try to answer 20 division facts in one minute. Track your progress each week.
- Play math games with a partner: one person says a multiplication fact, and the other says the related division fact.
- Write the entire division table for 7: 7 ÷ 7 = 1, 14 ÷ 7 = 2, 21 ÷ 7 = 3, 28 ÷ 7 = 4, 35 ÷ 7 = 5, 42 ÷ 7 = 6, 49 ÷ 7 = 7, 56 ÷ 7 = 8, 63 ÷ 7 = 9, 70 ÷ 7 = 10, 77 ÷ 7 = 11, 84 ÷ 7 = 12.
Fluency does not mean rushing. It means knowing the fact so well that you can recall it confidently. Practice for just 10 minutes a day, and you will see great improvement.
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. Mastering division facts up to 12 provides the foundational fluency necessary for success with this fourth-grade standard.
Notes for teachers
This lesson supports CCSS.MATH.CONTENT.4.NBT.B.6 by building automaticity with division facts up to 12. Fluency with these facts allows students to focus on place value strategies and multi-digit division without being slowed down by basic fact recall. All content is 100% free; use it for whole-class instruction, independent study and practice, or homework.