Equivalent decimals of halves and quarters – KS2 Maths resources for Year 5

Finding equivalent decimals and fractions

Fractions and decimals are both ways of representing parts of a whole.

Even though they look different, a fraction can have the same value as a decimal and a decimal can have the same value as a fraction.

These are called equivalent fractions and equivalent decimals.

A boy and a girl stand next to a whiteboard. On the board, 1/2 = 0.5.

To find equivalent decimals for halves and quarters, you can use division or remember some common conversions:

\(\frac {1} {2}\) = 0.5

\(\frac {1} {4}\) = 0.25

\(\frac {3} {4}\) = 0.75

Quiz: Equivalent decimals of halves and quarters

Test out your knowledge of equivalent decimals of halves and quarters with this quiz, then read on to complete the page.

One half as a decimal

The equivalent decimal of \(\frac {1} {2}\) is 0.5.

Let's explore why…

Take a look at these squares. Each one has been divided into a different number of parts, but one half of the overall square has been shaded.

There are 3 rectangles with fraction written below them. The first rectangle is split into two equal parts with one shaded, it is labelled 1/2. The second rectangle is split into ten equal parts with five shaded, it is labelled 5/10. The third rectangle is split into one hundred equal parts with fifty shaded, it is labelled 50/100.

\(\frac {1} {2}\) shows that 1 part out of 2 is shaded.

\(\frac {5} {10}\) shows that 5 parts out of 10 are shaded.

\(\frac {50} {100}\) shows that 50 parts out of 100 are shaded.

You can say that:

\(\frac {1} {2}\) = \(\frac {5} {10}\) = \(\frac {50} {100}\)

They are all equivalent fractions.

Now, let's take a look at how you can find the decimal equivalent of these fractions by using place value counters.

This is how \(\frac {5} {10}\) can be represented using place value counters:

Five circles, each labelled with the fraction 1/10.

The fraction \(\frac {1} {10}\) is one tenth and it is written as 0.1 in decimals.

So, this is how the fraction \(\frac {5} {10}\) can be represented using five 0.1 decimal counters:

Five circles, each labelled with the decimal 0.1.

When added together, the counters make the decimal 0.5.

As \(\frac {5} {10}\) is equivalent to 0.5, then \(\frac {1} {2}\) and \(\frac {50} {100}\) must also be equal to 0.5, as each of those fractions are equivalent.

\(\frac {1} {2}\) = \(\frac {5} {10}\) = \(\frac {50} {100}\) = 0.5

This means the decimal equivalent of \(\frac {1} {2}\) is 0.5.

One quarter as a decimal

The equivalent decimal of \(\frac {1} {4}\) is 0.25.

Let's explore why…

In each of the representations below, one quarter of the overall square has been shaded.

Two squares with fractions below them. The first square is divided into four equal parts with one part shaded, it is labelled 1/4. The second square is divided into one hundred parts with twenty-five parts shaded, it is labelled 25/100.

\(\frac {1} {4}\) shows that 1 part out of 4 has been shaded.

\(\frac {25} {100}\) shows that 25 parts out of 100 have been shaded.

You can see that:

\(\frac {1} {4}\) = \(\frac {25} {100}\)

So \(\frac {1} {4}\) and \(\frac {25} {100}\) are equivalent fractions.

Now let's take a look at \(\frac {25} {100}\) again, but let's rearrange the shaded parts into columns.

On the left, a square grid labelled 25/100. It is divided into 100 parts with 25 parts shaded. Those parts are the first 5 squares in each of the first 5 columns. In the centre of the image is an arrow pointing to another square grid also labelled 25/100. It is divided into 100 parts with 25 parts shaded. 10 of those parts are arranged in 2 vertical columns next to each other fully shaded in pink. Then 5 individual squares, next to each other, from the next column are shaded in green.

When the shaded parts are rearranged like this, you can see that you have two column of 10 and one column of 5. Or:

\(\frac {10} {100}\) + \(\frac {10} {100}\) + \(\frac {5} {100}\)

\(\frac {10} {100}\) is the same as \(\frac {1} {10}\).

You can represent this with a 0.1 decimal counter. You will need 2 of these to represent the 2 tenths.

\(\frac {5} {100}\) can be represented with 0.01 decimal counters. You will need 5 of these to represent the 5 hundredths.

Two counters in one row labelled 0.1 and five counters in another row underneath labelled 0.01.

Let’s put these counters into a place value chart to help us read this as a decimal number.

A chart with the labels ones, tenths, and hundredths. The one's column has nothing in its top row and the number 0 written in the next row below it. The tenths column has two circles each labelled 0.1 in its first row and has the number 2 written in the next row below it. The hundredths column has five circles each labelled 0.01 in the first row, with the number 5 written in the next row below it.

Can you see that:

\(\frac {1} {4}\) = \(\frac {25} {100}\) = 0.25

So the decimal equivalent of \(\frac {1} {4}\) is 0.25.

Three quarters as a decimal

The equivalent decimal of \(\frac {3} {4}\) is 0.75

Let's explore why…

In each of the representations below three quarters of the overall square has been shaded.

The first square is divided into four equal parts with three parts shaded, it is labelled 3/4. The next square is divided into 100 parts with 75 parts shaded, it is labelled 75/100.

\(\frac {3} {4}\) shows that 3 parts out of 4 have been shaded.

\(\frac {75} {100}\) shows that 75 parts out of 100 have been shaded.

Finding the equivalent decimal of \(\frac {3} {4}\) is easy, when you already know the equivalent decimal of \(\frac {1} {4}\) is 0.25.

\(\frac {1} {4}\) + \(\frac {1} {4}\) + \(\frac {1} {4}\) = \(\frac {3} {4}\)

So:

0.25 + 0.25 + 0.25 = 0.75

Now, let’s use a place value chart to represent this using decimal counters.

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Image caption,
Each row in this place value table contains the counters equivalent to one quarter. You know this is 0.25 or two tenths and five hundredths.
Image caption,
When the counters from each row are combined into one row you can see both the total number of tenths and hundredths. In the last column, you can see that there are 15 hundredths.
Image caption,
15 hundredths is 0.15. It is made up of 1 tenth and 5 hundredths. This 1 tenth will then be moved and added to the tenths column.
Image caption,
The 10 hundredths counters have been exchanged for one tenths counter. Now that the counters are rearranged, you can see that they represent the decimal 0.75.