Let's Learn Numbers up to 1000 and Fractions Together!

Back in 1st grade, you learned how to count up to \(100\). In this chapter, we will learn about even bigger numbers up to \(1000\) (one thousand), as well as fractions, which we use when sharing things like pizza or origami paper!
At first, big numbers and fractions might seem a little tricky, but don't worry! Let's take it step by step together.

1. How to Show Numbers Greater Than 100

When counting large numbers, it becomes much easier if you make "groups of \(10\)" and "groups of \(100\)".

Rules for Grouping Numbers:
・ When you gather \(10\) ones (\(1\)s) ... \(10\) (ten)
・ When you gather \(10\) tens (\(10\)s) ... \(100\) (one hundred)
・ When you gather \(10\) hundreds (\(100\)s) ... \(1000\) (one thousand)

[Key Point] Align by "Place Value"!
When writing numbers, each position (place value) is fixed.
From right to left, they line up as the ones place, the tens place, and the hundreds place.

For example, a number made of "\(3\) hundreds, \(4\) tens, and \(5\) ones" is written as \(345\) and read as "three hundred forty-five."

[Common Mistake] Don't forget the "\(0\)"!
For example, what happens when a number is made of "\(4\) hundreds and \(7\) ones"?
There is nothing in the tens place, right? In this case, skipping the tens place and writing \(47\) is incorrect.
When a place value is empty, put a \(0\) there and write \(407\) (four hundred seven).

2. Comparing Numbers (Inequality Signs: \(＞\) and \(＜\))

When comparing two numbers, compare them starting from the largest place value (the hundreds place).

Steps for Comparing:
1. First, compare the hundreds place (the bigger digit means the bigger number!).
2. If the hundreds place is the same, next compare the tens place.
3. If the tens place is also the same, finally compare the ones place.

There are handy symbols to show which number is greater. They are \(＞\) and \(＜\).

[Key Point] Chomp with the Big Mouth!
・ \(520 ＞ 380\) (\(520\) is greater than \(380\))
・ \(245 ＜ 260\) (\(245\) is less than \(260\))
Just remember: the open side of the symbol (the big open mouth) always chomps down on the larger number!

3. Looking at Numbers in Groups

It is also very important to look at a number as a whole group.
For example, let's look at the number \(350\) in different ways.

・ \(350\) is the number made by putting \(3\) hundreds and \(5\) tens together.
・ \(350\) is the number made of \(35\) tens.
・ \(350\) is the number that is \(50\) less than \(400\).

[Fun Fact] It's easy to understand when you think of money!
Ten \(10\)-yen coins make \(100\) yen, and ten \(100\)-yen coins make a \(1000\)-yen bill!
"Gathering \(10\) to transform into the next place value" works just like the money in your wallet!

4. Your Very First Fractions (One-Half, One-Fourth)

Up until now, we have learned about whole numbers (like \(1\), \(2\), or \(100\)). Now, let's learn about fractions, which show the size of a part when one whole thing is divided.

What is One-Half?

When you divide a single sheet of origami paper or a pizza into \(2\) equal parts, \(1\) of those parts is called one-half, and we write it as \(\frac{1}{2}\).

What is One-Fourth?

In the same way, when you divide one whole thing into \(4\) equal parts, \(1\) of those parts is called one-fourth (or one quarter), and we write it as \(\frac{1}{4}\).

[Common Mistake] They MUST be divided into "equal parts"!
Just splitting something into \(2\) pieces doesn't automatically make each piece one-half (\(\frac{1}{2}\)).
If you share a cake with your brother or sister and one piece is big while the other is small, you might end up in an argument!
When making fractions, the most important golden rule is to divide things into exactly equal sizes.

[Key Point] Helpful Fraction Tips
・ Fold the original size in half, and you get one-half (\(\frac{1}{2}\)).
・ Fold it in half one more time, and it becomes one-fourth (\(\frac{1}{4}\)).
・ If you put \(2\) one-halves (\(\frac{1}{2}\)) together, it goes back to the original "\(1\)"!

5. Chapter Summary

・ \(10\) tens make \(100\), and \(10\) hundreds make \(1000\).
・ Line up the place values (hundreds, tens, ones), and write a \(0\) in any empty place.
・ When comparing sizes, the open mouth of \(＞\) or \(＜\) faces the larger number.
・ \(1\) of \(2\) equal parts is one-half (\(\frac{1}{2}\)), and \(1\) of \(4\) equal parts is one-fourth (\(\frac{1}{4}\)).

Big numbers and fractions are important friends you'll be using in math from now on. Practice reading them out loud and writing them down in your notebook to get used to them!