【4th Grade】Let's Master Decimal Multiplication and Division!
Hello everyone!
So far, you’ve learned about "decimals," which are numbers used to express values smaller than 1.
Today, we’re going to challenge ourselves with multiplication and division using decimals!
You might think, "Decimals sound difficult...," but actually, the steps are almost the same as the integer calculations you already know.
Once you get the hang of it, you’ll be solving them in no time, so let’s learn together and have some fun!
1. Multiplying Decimals by Integers
Let's start by looking at how to multiply a decimal by an integer.
For example, think about this situation: "There are 3 bottles of juice, each containing 1.2 liters. How many liters are there in total?"
A Helpful Way to Think
The equation is \( 1.2 \times 3 \).
It’s easier to solve if you think about "how many 0.1s there are."
\( 1.2 \) is made up of 12 groups of \( 0.1 \).
Since \( 12 \times 3 = 36 \), that means we have 36 groups of \( 0.1 \).
So, the answer is \( 3.6 \)!
How to do long multiplication
When doing long multiplication, follow these steps:
1. Ignore the decimal point for a moment and multiply the numbers as if they were integers (\( 12 \times 3 \)).
2. Place the decimal point in the answer at the same position as it is in the original decimal (the multiplicand).
Tip:
Line up the numbers to the right. Don’t worry about the decimal point until the very end!
💡 Fun Fact:
"×3" is the same as adding the same number three times. If you calculate \( 1.2 + 1.2 + 1.2 \), you also get \( 3.6 \). If you’re ever stuck, thinking about it as "addition" is a great way to double-check!
2. Dividing Decimals by Integers
Next, let's look at dividing a decimal by an integer.
Think of this case: "We are sharing 5.2 meters of tape equally among 4 people. How many meters does each person get?"
How to do long division
The equation is \( 5.2 \div 4 \).
1. Just like with integers, calculate from left to right.
2. The most important point: Bring the decimal point in the quotient (the answer) straight up to the same position as it is in the dividend (the number being divided).
【Steps】
・Since 4 goes into 5 once, write 1 above the 5.
・Bring down the remainder of 1 and the 2 from the next place to make 12.
・Since 4 goes into 12 three times, write 3 above the 2.
・Place the decimal point in the answer \( 13 \) in the same spot it was originally, making it \( 1.3 \).
⚠ A common mistake:
Many people forget to place the decimal point and end up with "13." Once you finish your calculation, remember to look straight up from the original decimal point and place it in your answer!
3. Dividing Further (Dividing until it ends!)
Sometimes when you divide, you end up with a remainder. But with decimal division, you can add a "0" and keep dividing until there is no remainder left.
Example: \( 6 \div 5 \)
"5 goes into 6 once," leaving a remainder of 1.
Instead of stopping there, think of \( 6 \) as \( 6.0 \), write down a "0," and bring it down.
Now, "5 goes into 10 twice," so the answer is \( 1.2 \).
Tip:
Integers have "invisible" decimals like ".000..." hidden behind them. Use as many zeros as you need to finish your calculation!
4. Division with Remainders (Pay extra attention here!)
Sometimes you’ll see problems like "Find the quotient to the nearest whole number (or the first decimal place) and find the remainder."
Here is a tricky point that trips a lot of people up: "The position of the decimal point in the remainder."
Example: \( 13.5 \div 4 \) (Finding the answer as a whole number)
1. \( 13 \div 4 = 3 \) with a remainder of 1.
2. If you bring down the ".5" from the first decimal place, the remainder looks like "15," but...
The correct answer:
The decimal point for the remainder must be brought straight down from the original decimal point.
Therefore, the answer is "3 with a remainder of 1.5."
Tip:
Decimal point for the quotient (answer) goes UP.
Decimal point for the remainder goes DOWN.
Remember this as your motto!
🌟 Summary: Remember these!
・Multiplication: Calculate as you would with integers, then place the decimal point at the end.
・Division: Move the decimal point from the dividend straight up to the quotient (answer).
・Remainder: Move the decimal point from the dividend straight down to the remainder.
・Dividing further: If you get a remainder, add a "0" and keep going.
At first, you might get confused about where to put the decimal point.
But if you practice, it will start to feel like solving a puzzle—and you’ll even start to enjoy it!
Take it slow and work at your own pace. I’m cheering for you!