Comparing and Ordering Numbers

What you will learn

• Say which of two numbers up to $100$ is bigger, using tens first and ones second.
• Use the signs $<$, $>$ and $=$ the right way round.
• Put a set of numbers in order, and find one more and one less.
• Spot a number as odd or even from its last digit (the full story is in Odd and Even Numbers).

Before you start: you should know what tens and ones are. If not, try Counting and Place Value first.

The idea

Two friends each have a bag of marbles. Who has more? You could line them up side by side and see which row is longer. Comparing numbers is the same job without the marbles: deciding which number is bigger, which is smaller, or whether they are the same.

Three useful signs

Writing “is bigger than” every time is slow, so there are three short signs.

• $<$ means is less than. $4 < 6$ says four is less than six.
• $>$ means is greater than. $6 > 4$ says six is greater than four.
• $=$ means is equal to. $6 = 6$ says the two sides are the same.

Here is how to remember which way round they go. The sign has a wide end and a narrow point. The wide end always faces the bigger number. The point always aims at the smaller one. Think of it as an arrow tip pointing at the smaller number.

Comparing with tens and ones

For numbers up to $100$, you compare in two steps.

1. Look at the tens digits first. More tens means a bigger number, whatever the ones say.
2. If the tens are the same, look at the ones.

So $62$ is bigger than $58$, even though $8$ is bigger than $2$. The $6$ tens beat the $5$ tens before the ones get a say.

Numbers on a line

A number line is a straight line with numbers marked along it in order, like a ruler. Smaller numbers sit on the left and bigger numbers on the right. If you can find two numbers on the line, the one further right is bigger. The line also shows you how far apart they are.

One more and one less

Every number has a neighbour just above and just below. One more than $36$ is $37$. One less than $36$ is $35$. The tricky ones are at the tens. One more than $49$ is $50$, and one less than $70$ is $69$. Count carefully across those boundaries.

Putting numbers in order

To order a set of numbers from smallest to biggest, find the smallest first and write it down. Cross it off. Then find the smallest of what is left. Keep going until none are left. Compare using tens first, then ones, just as before.

Odd and even

An even number can be split into two equal groups with nothing left over. $8$ is even because it makes $4$ and $4$. An odd number always leaves one over. $9$ makes $4$ and $4$ with $1$ spare.

You can spot odd and even from the ones digit alone. If it ends in $0, 2, 4, 6$ or $8$, the number is even. If it ends in $1, 3, 5, 7$ or $9$, it is odd. So $74$ is even and $67$ is odd.

Worked examples

Example 1: Which sign?

Put the right sign between $43$ and $47$.

1. Compare the tens. Both have $4$ tens, so the tens do not decide.
2. Compare the ones. $3$ is less than $7$.
3. So $43$ is less than $47$. The point of the sign aims at $43$.

Answer: $43 < 47$.

Example 2: Ordering

Put these race times, in seconds, from fastest to slowest: $31$, $29$, $34$, $30$. The fastest time is the smallest number.

1. Look at the tens. $29$ has only $2$ tens, so it is the smallest. Write it first and cross it off.
2. The rest all have $3$ tens, so use the ones: $31$, $34$, $30$ have ones of $1$, $4$, $0$.
3. Smallest ones digit is $0$, so $30$ comes next. Then $31$. Then $34$.

Answer: $29, 30, 31, 34$.

Example 3: Odd or even?

Sam and Priya want to share $23$ stickers equally. Can they?

1. Look at the ones digit of $23$. It is $3$.
2. $3$ is one of $1, 3, 5, 7, 9$, so $23$ is odd.
3. Odd numbers cannot be split into two equal groups. They would get $11$ each with $1$ left over.

Answer: No. $23$ is odd, so one sticker is left over.

A longer number is not always a bigger number. $9$ has one digit and $10$ has two, so $10$ is bigger. But $9$ is bigger than $7$, and both have one digit. Always compare the worth of the digits, not how many there are.

Why it matters

Comparing is how you make choices. Which queue is shorter? Which bag of sweets has more in it? Who won the game, and by how much? Who is older? Ordering lets you line up scores, ages and prices from smallest to biggest, and read a scoreboard or a league table. Knowing odd from even helps you share fairly, spot patterns in numbers and, later, find which numbers divide exactly by two.