Maths Week Scotland 2026 - Challenge 5 - Painting the flats

Challenge 5 is all about fractions.

Maths teacher Chris Smith and pupils from Grange Academy are here to explain.

The Maths Week Scotland Daily Challenges have been set by the Scottish Mathematical Council.

So here's the challenge:

This problem is all about fractions.

The Hillside Estate on the edge of the city consists of eight tower blocks.

Each tower block has nine floors and each floor has ten flats.

The council painters have just arrived and they’re wondering just how many flats need to be painted this year.

Two in five of the flats are privately owned, so they will not be painted by the council.

Of the rest, one in four flats will be left to next year.

How many flats are to be painted by the council this year?

• You could draw this out or use blocks to help you visualise this problem.
• It might help to work through this in separate stages.
• Think about how you work with fractions.

Worked out the answer? Here's how you can do it.

Step 1

We can work this out in stages, so first let's work out the total number of flats.

There are eight blocks of flats, with nine floors, and ten flats on each floor.

So that's 8 x 9 x 10 = 720

Step 2

Two in five flats are privately owned, so three in five, or 3/5 need to be painted.

3/5 x 720 = 432

Step 3

One in four flats are being left until next year.

That means three out of four, or three quarters of the flats are to be painted,

¾ x 432 = 324

324 flats are to be painted this year.