Albert Teen YOU ARE LEARNING:  Relationships between Numbers  # Relationships between Numbers ### Relationships between Numbers

We use a system of notation to indicate whether numbers are equal, greater than or less than each other.

1

Notation lets us write things without words. There is some maths notation here, how else could we describe them?  2

These are also symbols. Which one means equal to?  3

We've seen that $=$ means equal to, but which symbol means not equal to?  4

The equal sign means that what is on the left side is the same as what is on the right side. Which of these statements is not true? 5

We saw that the statement $2\times 3=4$ is not true.

But we have another symbol and the statement $2\times 3 \neq 4$ is true.

6

Which of the symbols means less than?  7

The opposite of less than is greater than.

The greater than symbol is $>$. The open end points to the larger part and the closed end to the smaller part. 8

The symbol $\leq$ is very similar to the less than symbol, $<$. How does the extra line change it?  9

We can now give names to all these symbols.

Remember that we read these from left to right in a calculation. If we have an unknown number which we call $y$, how can we show that it is not equal to zero? We often use these symbols when we have an unknown number which we might call $x$. We might know that it is either greater than or equal to $3$ and so we write:

$x\ge3$

How would you write down "$x$ is greater than $3$"? How would you write down " $y$ is less than $15$"? 1

What if we wanted to write that our unknown number, $x$, is less than $8$ but greater than $4$?

We can use multiple symbols to achieve this and start with the smallest number.

2

Which option is the correct statement using symbols to say that $x$ is less than $8$ but greater than $4$? This time, $x$ is greater than $2$, but less than $10$. How do you write this using symbols? 1

We can use symbols to group data together.

The table shows four groups of data about the people's height. 2

If a person is $155cm$ tall, which group would they be in?  3

If a person is $170cm$ tall, which group would they be in?  4

This is where the difference between the symbols $\leq$ and $<$ is important.

When gathering data we need to make sure that each person can only be in one group. Someone who is $170cm$ tall just falls into Group $D$. How would you write "$x$ is less than $4$, but greater than or equal to $2$"? 1

In summary...

Symbols are often used when we have an unknown number, $x$ or $y$ or other letter. 2

Symbols form part of expressions.

The expression $x\neq 2$ means that our unknown number $x$ cannot be $2$ or is not equal to $2$. 3

Symbols can be used to show a range of values

No one can be in more than one group so the symbols are used carefully. 