Tenths and Hundredths (equivalent fractions)

Equivalence

Watch this video to understand more about tenths, hundredths and equivalence.

Equivalence is when things might not look the same, but they have the same value.

Take a look back at fractions as area models or on a number line to review your understanding of fractions up to tenths.

The diagram below shows four tenths shaded (because there are ten columns and four are shaded). You can see there are ten hundredths in each tenth, so it also shows forty hundredths.

Example 1

How many hundredths are in $\frac{7}{10}$710​?

To convert tenths to hundredths we can multiply by ten because there are ten hundredths in every tenth. So $\frac{7}{10}=\frac{70}{100}$710​=70100​

Try this question for yourself.

question 1:

Example 2

How many tenths are in $\frac{60}{100}$60100​?

To convert from hundredths to tenths we do the opposite (divide by ten). So $\frac{60}{100}=\frac{6}{10}$60100​=610​

Try this question for yourself.

question 2

Using equivalence to solve problems

$\frac{43}{100}$43100​  $\frac{4}{10}$410​  $\frac{49}{100}$49100​  $\frac{5}{10}$510​  $\frac{3}{10}$310​

When fractions have different denominators it is difficult to compare and use them. So we can convert the fractions above to show hundredths. We do this by multiplying the tenths by ten to get their equivalent fractions in hundredths.

Now they look like this

$\frac{43}{100}$43100​  $\frac{40}{100}$40100​  $\frac{49}{100}$49100​  $\frac{50}{100}$50100​  $\frac{30}{100}$30100​

This makes it much easier to work with the fractions when they look the same.

Try this question for yourself

question 3: