What is Division?
Division is one of the four basic arithmetic operations, alongside addition, subtraction, and multiplication. It is the process of splitting a number into equal parts or groups. When we divide, we are essentially asking how many times one number can fit into another. For example, if you have 12 apples and want to share them equally among 3 friends, how would you divide it?
You can start giving 1 apple to each friend until you run out.
Here’s how it looks:
- Friend 1: 🍏🍏🍏🍏
- Friend 2: 🍏🍏🍏🍏
- Friend 3: 🍏🍏🍏🍏
After sharing, you find that each friend gets 4 apples. This shows that 12 divided by 3 gives the result 4. This can be written as
12 ÷ 3 = 4
Visualizing Division
One effective way to understand division is through visual aids. Using objects, like counters or blocks, can help children grasp the concept. For example, if you have 20 blocks and want to divide them into groups of 5, you can physically group the blocks to see that there are 4 groups of 5.
Division as the Inverse of Multiplication
Division is the opposite, or inverse, of multiplication. While multiplication tells us how many groups of a certain size we have, division helps us find out how many groups can be made from a total. For example, if we know that 4 multiplied by 3 equals 12 (4 × 3 = 12), we can use this information to solve the division problem 12 ÷ 4. Since 12 is the total and 4 is the size of each group, we can say there are 3 groups of 4 in 12.
Thus, we can use multiplication tables to help us with division. By looking at the multiplication table, we can quickly find the answers to division problems. For instance, if we want to know what 18 ÷ 3 is, we can check the multiplication table and see that 3 times 6 equals 18 (3 × 6 = 18), which tells us that 18 ÷ 3 equals 6.
Understanding this connection between multiplication and division makes it easier to solve division problems!
Division with Remainders
Sometimes, when you divide, the numbers don’t fit perfectly. For example, if you have 14 candies and want to share them among 3 children:
Count How Many Fit:
- Each child can get 4 candies (because 3 x 4 = 12, which is less than 14).
Child 1: 🍬🍬🍬🍬
Child 2: 🍬🍬🍬🍬
Child 3: 🍬🍬🍬🍬
See What’s Left:
- After giving 4 candies to each child (3 children × 4 candies = 12 candies), you have 2 candies left. 🍬🍬
Write the Answer with a Remainder:
- You can write this as:
- 14 ÷ 3 = 4 R2
- This means each child gets 4 candies, and there are 2 candies remaining.
- You can write this as:
Key Terms in Division
- Dividend: The number you want to divide (e.g., in 12 ÷ 3, 12 is the dividend).
- Divisor: The number you are dividing by (e.g., in 12 ÷ 3, 3 is the divisor).
- Quotient: The result of the division (e.g., in 12 ÷ 3, 4 is the quotient).
- Remainder: The amount left over if the dividend does not divide evenly by the divisor (e.g., in 14 ÷ 3, the quotient is 4, and the remainder is 2).
Long Division
Long division is a method used to divide larger numbers by breaking the problem down into smaller steps. It involves dividing each part of the number, one digit at a time, making it easier to handle big numbers. To perform long division, we start by seeing how many times the divisor (the number we are dividing by) can fit into the first few digits of the dividend (the number being divided). We then write the result, or quotient, above the dividend and subtract to see what’s left. We repeat this process, bringing down each new digit from the dividend until there’s nothing left.
Step-by-step Explanation
Let’s use the example 625 ÷ 5.
Set Up the Problem:
- Write 625 (the dividend) under the long division bar.
- Write 5 (the divisor) outside the bar.
Divide the First Digit:
- Look at the first digit of 625, which is 6.
- Ask how many times 5 fits into 6. The answer is 1.
- Write 1 above the division bar, above the first digit (6) of 625.
Multiply and Subtract:
- Multiply 1 × 5 = 5 and write 5 below the 6.
- Subtract 6 – 5 = 1. Write 1 below the 5.
Bring Down the Next Digit:
- Bring down the next digit in 625, which is 2, making the new number 12.
Divide the Next Part:
- Now, see how many times 5 fits into 12. The answer is 2.
- Write 2 above the division bar, next to the 1, so now the partial answer reads 12.
Multiply and Subtract:
- Multiply 2 × 5 = 10 and write 10 below the 12.
- Subtract 12 – 10 = 2. Write 2 below the 10.
Bring Down the Last Digit:
- Bring down the last digit of 625, which is 5, making the new number 25.
Divide Again:
- Now, see how many times 5 fits into 25. The answer is 5.
- Write 5 above the division bar, next to the 12, so the answer reads 125.
Multiply and Subtract:
- Multiply 5 × 5 = 25 and write 25 below the 25.
- Subtract 25 – 25 = 0. There’s nothing left to bring down, so you’re done.
Write the Final Answer:
- The final answer is the number above the division bar, which is 125. So, 625 ÷ 5 = 125.
By dividing each part step-by-step, multiplying, subtracting, and bringing down the next number, long division helps break down a big problem into smaller steps, making it easier to solve.
Division is everywhere in our daily lives! Whether it’s sharing snacks, dividing a bill, or figuring out how many rows of seats are needed in a theater, understanding division helps us solve problems efficiently. Division is an essential skill that allows us to share, organize, and understand quantities in our world. By learning how to divide numbers, children can develop critical thinking and problem-solving skills that will benefit them in many areas of life.
FAQs on Division
- No, division is not commutative. Changing the order of the numbers changes the result.
- Example: 12÷4=3 is not the same as 4÷12=0.333.
- The result is always zero.
- Example: 0÷7=0.
- No, division by zero is undefined because there is no number that can multiply with zero to give a non-zero result.
- Example: 124 = 3 because 4 x 3 = 12; but 120 = undefined, because 0 multiplied by any number does not gives the result 12.
- Ratios can be expressed as fractions, which are a form of division.
- Example: A ratio of 3:4 can be written as 34.