Hello Math Superstars! Let's Dive into Division!
Welcome to the exciting world of division! You've already learned how to share things into small groups. Now, we're going to level up and learn how to divide bigger numbers, especially by numbers that have two digits. Think of it like sharing a giant bag of 96 sweets among your 12 best friends. How many does each friend get? By the end of this, you'll be a division pro!
Division is a super useful skill for sharing fairly, solving puzzles, and understanding the world around you. Let's get started!
Quick Review: The Parts of a Division Problem
Remember when you first learned about division? It's all about sharing. Let's quickly review the special names for each part of a division problem. Imagine you have 17 cookies to share among 5 friends.
Example: 17 ÷ 5 = 3 with 2 left over
- Dividend: This is the total number you start with. (Here, it's the 17 cookies).
- Divisor: This is the number you are dividing by. (Here, it's the 5 friends).
- Quotient: This is the main answer, or how many each group gets. (Here, it's 3, so each friend gets 3 cookies).
- Remainder: This is the amount that is left over because it can't be shared equally. (Here, it's the 2 leftover cookies).
Key Takeaway
Division is just a fancy word for equal sharing or equal grouping.
The Main Event: Long Division with Two-Digit Divisors
Dividing by a two-digit number might look scary, but it's just a few simple steps repeated. Don't worry if it seems tricky at first, we'll go through it together. To remember the steps, we can use a fun memory aid: Dad, Mom, Sister, Brother!
- Dad = Divide
- Mom = Multiply
- Sister = Subtract
- Brother = Bring Down
Let's see how it works with an example!
Example 1: A 2-digit number divided by a 2-digit number
Let's solve $$84 \div 21$$
Step 1: Set it up
Write the problem in the long division format (sometimes called the "bus stop" method).
Step 2: D-M-S-B Cycle
- Divide: How many times does 21 go into 84? This is tricky to guess! Let's try rounding. 21 is close to 20. How many 20s are in 80? Let's guess 4. Write the 4 on top, above the 4 in 84.
- Multiply: Now multiply your guess (4) by the divisor (21). $$4 \times 21 = 84$$. Write this 84 underneath the 84 in the dividend.
- Subtract: Subtract the numbers. $$84 - 84 = 0$$.
- Bring Down: Is there another number to bring down from the dividend? No! We're done.
The number on top is our answer! So, $$84 \div 21 = 4$$. There is no remainder.
Example 2: A 3-digit number divided by a 2-digit number (with a remainder)
Let's solve $$165 \div 15$$
Step 1: Set it up
Write the problem in the long division format.
Step 2: D-M-S-B Cycle (First Round)
- Divide: How many times does 15 go into 1? It can't. How many times does 15 go into 16? It goes in 1 time. Write the 1 on top, above the 6.
- Multiply: $$1 \times 15 = 15$$. Write 15 under the 16.
- Subtract: $$16 - 15 = 1$$.
- Bring Down: Bring down the next digit from the dividend, which is 5. Place it next to the 1, making the new number 15.
Step 3: D-M-S-B Cycle (Second Round)
- Divide: Now, how many times does 15 go into our new number, 15? It goes in 1 time. Write this 1 on top, next to the other 1.
- Multiply: $$1 \times 15 = 15$$. Write this 15 under the other 15.
- Subtract: $$15 - 15 = 0$$.
- Bring Down: Nothing left to bring down.
The answer is the number on top. So, $$165 \div 15 = 11$$.
Key Takeaway
Long division is just repeating the four steps: Divide, Multiply, Subtract, Bring Down until you can't bring down any more numbers. You've got this!
Your Superpower: Smart Guessing (Estimation)
The hardest part of two-digit division is the "Divide" step. How do you guess how many times 32 goes into 195? Here's a trick!
Round the divisor to the nearest 10.
Let's try $$97 \div 29$$
- The divisor is 29. Let's round it to 30.
- Now the question is easier: "How many 30s are in 97?"
- You can even cover the zeros and think "How many 3s are in 9?". The answer is 3!
- So, our first guess should be 3.
Now we can try it: $$3 \times 29 = 87$$. That's very close to 97, so it's a great guess!
What if my guess is wrong?
- If you subtract and the result is bigger than the divisor, your guess was too small. Try the next number up.
- If you can't subtract because the bottom number is bigger, your guess was too big. Try the next number down.
Estimation is a skill. The more you practice, the better your guesses will be!
Become a Math Detective: Checking Your Answer!
How do you know if your answer is correct? You can use multiplication to check! It's the opposite (or inverse) of division.
The secret formula is: (Quotient × Divisor) + Remainder = Dividend
Let's say we solved $$78 \div 14$$ and got the answer 5 with a remainder of 8.
Let's check it:
- Quotient = 5
- Divisor = 14
- Remainder = 8
$$ (5 \times 14) + 8 $$
$$ 70 + 8 = 78 $$
Our final number (78) is the same as our original dividend! That means our answer is correct! Hooray!
Awesome Math Shortcuts: Divisibility Rules
Sometimes, you can tell if a number can be divided perfectly just by looking at it! These tricks are called divisibility rules. They are super helpful for checking your work quickly.
A number is divisible by...
- 2 if the last digit is an even number (0, 2, 4, 6, or 8).
Example: 58 is divisible by 2 because it ends in 8. - 3 if the sum of all its digits is divisible by 3.
Example: 135. Let's add the digits: 1 + 3 + 5 = 9. Since 9 can be divided by 3, 135 can too! - 5 if the last digit is a 0 or a 5.
Example: 195 is divisible by 5 because it ends in 5. - 10 if the last digit is a 0.
Example: 340 is divisible by 10 because it ends in 0.
Did you know?
Using these rules can help you estimate better in long division. If you are solving $$135 \div 15$$, you know 135 ends in a 5 and 15 ends in a 5. This tells you that the quotient might be a whole number with no remainder!
Solving Real-World Problems
Let's use our new division skills to solve a word problem.
Problem: A school has 320 students going on a trip. Each bus can hold 40 students. How many buses are needed for the trip?
- Read and Find: We have a total of 320 students and we are making equal groups of 40.
- Decide: This is a grouping problem, so we need to divide.
- Solve: We need to calculate $$320 \div 40$$.
Hint: You can use estimation! How many 40s in 320? Or, how many 4s in 32? The answer is 8!
Let's check with multiplication: $$8 \times 40 = 320$$. It's a perfect match. - Answer: The school will need 8 buses for the trip.
Key Takeaway
When you see a word problem, look for clues about sharing or grouping. This usually means it's time to divide!