Decimals

NZ Level 5

Compare statements with decimals (4 operations)

Lesson

When we are comparing statements, we can often work out if they are equal, or if one side is larger, without even solving them. By thinking about the number problem on each side, there are some ways of working out which symbol to use, to make the statement true. We need to decide if one side is:

- equal to (=)
- less than (<), or
- greater than (>)

the other side.

We have seen how to work out number problems with multiplication in our number statements and if we have division in our number problems, there are some ways to figure out how the two statements compare, including:

- looking at the total we have to share
- looking at the number we are dividing by (the divisor),
- whether one number is similar to another, or has been multiplied by a factor of 10, for example.

In Video 1, we look at how to use these ideas to see what symbol makes the statement true.

When we have more than one operator in our number problem, we need to remember the order of operations before we can estimate or decide which side of our statement is greater. Then there are some ways to help us decide which symbol to use, without solving our number problem. We can:

- round our decimals to the nearest unit, to work out an estimated total for each side
- look at how the numbers in our number problems are changing, depending on which operators we have to solve

In Video 2, we look at some statements where our number problems have more than one part and decide which symbol to use without solving them.

Remember!

Don't forget the order of operations when solving number problems.

Consider the following statement:

$32.59\div6.2$32.59÷6.2$\editable{}$$32.59\div6.8$32.59÷6.8

Which one of the symbols $=$=, $<$< or $>$> will make the statement true?

$32.59\div6.2\editable{}32.59\div6.8$32.59÷6.232.59÷6.8

Consider the following statement:

$61\div2.3$61÷2.3$\editable{}$$61\div23$61÷23

Which one of the symbols $=$=, $<$< or $>$> will make the statement true?

$61\div2.3\editable{}61\div23$61÷2.361÷23

Consider the following statement:

$3.4+5.1\times8.2$3.4+5.1×8.2$\editable{}$$3.4\times5.1+8.2$3.4×5.1+8.2

Which one of the symbols $=$=, $<$< or $>$> will make the statement true?

$3.4+5.1\times8.2\editable{}3.4\times5.1+8.2$3.4+5.1×8.23.4×5.1+8.2

Understand operations on fractions, decimals, percentages, and integers