How to connect fractions, decimals and percentages

Connect fractions, decimals and percentages by showing all three names on the same picture. One quarter, 0.25 and 25% can describe the same share of a whole. A hundred-square grid makes that connection visible because both hundredths and percentages relate to groups of one hundred.

Start with familiar amounts such as a half and a quarter. Your child needs to understand those parts before a conversion rule will mean much.

Understand the idea

A fraction expresses a number using a numerator and denominator. A decimal uses place value, including tenths and hundredths. A percentage expresses an amount relative to one hundred.

For this activity, the entire grid is one whole. Each of its 100 equal squares is one hundredth of that whole, written as 1/100 or 0.01. It is also 1% of the grid.

Say: "We are looking at one amount and learning three ways to name it. The shaded squares will stay where they are."

For the amounts in this activity, the fraction, decimal and percentage are three ways to name the same value.

See it worked through

A quarter on a hundred-square grid

Shade 25 squares on a hundred-square grid. That is 25 out of 100 squares, so write 25/100.

Divide the grid's 100 squares into four equal groups of 25. The shaded amount is one of those four groups, so 25/100 = 1/4.

Twenty-five hundredths is written 0.25. The two after the decimal point represents two tenths, and the five represents five hundredths. Two tenths are 20 hundredths, making 25 hundredths altogether.

Because 25 squares are shaded out of every 100, this is also 25%.

All the names describe the same value: 1/4 = 25/100 = 0.25 = 25%.

Ask your child to point to the picture while explaining each name. If they can repeat the equation but cannot show the quarter, return to the four equal groups of squares.

Try it together

Shade it, then name it

Draw another hundred-square grid and shade 50 squares. Ask your child to write a fraction, a decimal and a percentage for the shaded amount.

Then shade 10 squares on a fresh grid and ask for the same three descriptions.

Use the question "How many out of one hundred?" when they get stuck. Keep each grid as a separate whole so the shaded squares do not get mixed together.

Check the answer

Fifty shaded squares give 50/100 = 1/2 = 0.50 = 50%. The decimal 0.50 can also be written 0.5; five tenths and fifty hundredths have the same value.

Ten shaded squares give 10/100 = 1/10 = 0.10 = 10%. The decimal 0.10 can also be written 0.1.

Check their understanding

Ask whether 0.25 is greater or smaller than 0.5. Your child can compare 25 shaded squares with 50 shaded squares. The answer is smaller, even though the digits "25" look larger than "5".

Next, ask them to explain 75% without using a conversion shortcut. It means 75 out of one hundred. On this grid, 75 squares cover three of the four groups of 25, so 75% = 3/4 = 0.75.

Make it easier or harder

Make it easier by using half a grid only. Match 1/2, 0.5 and 50% before adding quarters. Let your child use words as well as symbols.

Make it harder by shading 20 squares and finding 20/100 = 1/5 = 0.2 = 20%. Then ask for 25% of 20 counters. Divide the counters into four equal groups; one group contains five.

Do not force every fraction into a hundred-square model. One third, for example, does not cover a whole number of the grid's tiny squares and has a recurring decimal representation.

Teaching notes

VCAA's guidance on equivalent representations describes connecting fractions, decimals and percentages as representations of the same value. The grid activities here use original examples to help children describe equal values.

Numeracy practice

Help your child apply their maths understanding with practice questions and explanations.

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