Comparing multiplication statements with decimals
Comparing statements
You may have already looked at how to compare decimal statements with hundredths or thousandths. Now we're going to look at how to compare two statements with number problems. When we compare statements with number problems, it means we are looking at one number problem, and deciding if it is:
- greater than (>)
- equal to (=), or
- less than (<)
the other number problem.
Comparing statements with number problems that contain addition and subtraction is a great way to get into the swing of comparing statements with number problems. Now let's look at some decimal statements that include multiplication.
Comparing statements without solving
We can often decide on what mathematical symbol to use without even solving the number problem! Imagine if we needed to compare these statements:
| Statement A | Statement B | |
|---|---|---|
| $2\times0.05$2×0.05 | $12\times0.5$12×0.5 |
We can see that Statement A has $2$2 groups of $5$5 hundredths, but Statement B has $12$12 groups of $5$5 tenths. Since hundredths are $10$10 times smaller than tenths, and we only have $2$2 groups of $0.05$0.05, Statement A is less than Statement B.
In this case, the $<$< symbol is used. Though we haven't solved either number problem, we have made the statement below true!
| Statement A | Statement B | |
|---|---|---|
| $2\times0.05$2×0.05 | $<$< | $12\times0.5$12×0.5 |
Now let's compare some more statements with multiplication in our number problems. In Video 1, we look at what the numbers are, to see how many groups we are making.
In Video 2, we look at whether the order of our numbers in the number problem makes a difference. We also solve a problem right through, to check that our understanding is correct.
Using place value to compare numbers
Place value is also useful in considering which sign will make our statement true. In Video 3, we look at comparing a number problem with tenths to one with hundredths.
When working out what symbol will make a mathematical statement true, you can always solve each side. However, you can also check what the question is asking to see whether we can tell what symbol we need without solving it.
Worked Examples
Question 1
Consider the following statement:
$1\times3.7$1×3.7$\editable{}$$5\times3.7$5×3.7
Which one of the symbols $=$=, $<$< or $>$> will make the statement true?
$1\times3.7\editable{}5\times3.7$1×3.75×3.7
Question 2
Consider the following statement:
$7\times3\times6.4$7×3×6.4$\editable{}$$21\times5.8$21×5.8
Which one of the symbols $=$=, $<$< or $>$> will make the statement true?
$7\times3\times6.4\editable{}21\times5.8$7×3×6.421×5.8
Question 3
Consider the following statement:
$0.1\times0.2\times0.9$0.1×0.2×0.9$\editable{}$$0.9\times0.1\times0.2$0.9×0.1×0.2
Which one of the symbols $=$=, $<$< or $>$> will make the statement true?
$0.1\times0.2\times0.9\editable{}0.9\times0.1\times0.2$0.1×0.2×0.90.9×0.1×0.2