Comparing addition or subtraction statements involving decimals and fractions

Lesson

When we compare statements, we are thinking of whether one part of our statement is greater than ($>$>), equal to ($=$=), or less than ($<$<) the other part of our statement. We might have only fractions in our statement, or only decimals, but other times we might have a mixture of fractions and decimals to work with.

Before we compare

If we are comparing one fraction to another fraction, we may notice that our fractions have different denominators. That means we may need an extra step, so that they are expressed with the same denominator. The fractions are still equivalent, and have the same value, but are expressed differently.

If we are comparing one decimal to another decimal, we might also need to rename one of them. This allows us to think about the value of our numbers, so we can compare tenths with tenths, or hundredths with hundredths, for example.

If we are comparing a decimal and a fraction, it may be useful to convert the fraction to a decimal, or the decimal to a fraction.

Let's look at how to do this now.

Comparing values with whole numbers and decimals or fractions

With those tools under our belt, we can now look at comparing numbers with a mixture of fractions and decimals. Video 2 works through some examples of how to use those tools.

Making statements true with equality and inequality symbols

You may have already looked at how to make statements true with whole numbers. The process for doing this with decimals and fractions is just the same. Let's look at how to do it now in this video.

Remember!

When a decimal has a zero at the end, to the right of the decimal point, it doesn't change the value of the number.

Worked Examples

QUESTION 1

Write the decimal $0.3$0.3 as a fraction.

QUESTION 2

Choose the larger decimal.

1. $3.3$3.3

A

$3.38$3.38

B

$3.3$3.3

A

$3.38$3.38

B

QUESTION 3

Write $\frac{49}{10}$4910 as a decimal.

Outcomes

NA4-6

Know the relative size and place value structure of positive and negative integers and decimals to three places.