NZ Level 3
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Tenths and Hundredths (equivalent fractions)
Lesson

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:

Write $\frac{7}{10}$710 as an equivalent fraction out of $100$100:

  1. $\frac{7}{10}=\frac{\editable{}}{100}$710=100

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

Write $\frac{20}{100}$20100 as an equivalent fraction out of $10$10:

  1. $\frac{20}{100}=\frac{\editable{}}{10}$20100=10

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:

We want to put the fractions $\frac{7}{10}$710, $\frac{56}{100}$56100 and $\frac{6}{10}$610 in ascending order.

  1. First write $\frac{7}{10}$710 and $\frac{6}{10}$610 as equivalent fractions out of $100$100:

    $\frac{7}{10}=\frac{\editable{}}{100}$710=100

    $\frac{6}{10}=\frac{\editable{}}{100}$610=100

  2. Which of the options has the three fractions in ascending order?

    $\frac{7}{10},\frac{6}{10},\frac{56}{100}$710,610,56100

    A

    $\frac{56}{100},\frac{6}{10},\frac{7}{10}$56100,610,710

    B

    $\frac{6}{10},\frac{7}{10},\frac{56}{100}$610,710,56100

    C

    $\frac{7}{10},\frac{56}{100},\frac{6}{10}$710,56100,610

    D

    $\frac{7}{10},\frac{6}{10},\frac{56}{100}$710,610,56100

    A

    $\frac{56}{100},\frac{6}{10},\frac{7}{10}$56100,610,710

    B

    $\frac{6}{10},\frac{7}{10},\frac{56}{100}$610,710,56100

    C

    $\frac{7}{10},\frac{56}{100},\frac{6}{10}$710,56100,610

    D

Remember!

To convert from tenths to hundredths we multiply by ten

To convert from hundredths to tenths we divide by ten

Outcomes

NA3-4

Know how many tenths, tens, hundreds, and thousands are in whole numbers.

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