Fractions: pictures to name here or print

How a fraction is written

• The bottom number (the denominator) says how many equal parts the whole shape is cut into.
• The top number (the numerator) says how many of those parts are counted. In these pictures, they are the shaded ones.
• So 3/4 means the shape is cut into 4 equal parts and 3 of them are shaded. This page writes a fraction on one line with a slash, like 3/4. On paper it is often written with the 3 over a short line and the 4 under it.
• The parts are equal. Each part of a circle here is the same slice turned around the middle, and each part of a bar is the same width. The shaded parts do not have to sit side by side: any 3 of the 4 parts make 3/4.
• One amount can have more than one name. 2/4 of a shape covers as much of it as 1/2. This page counts parts, so a shape cut into 4 with 2 shaded is 2/4 here, and 1/2 is not offered as a wrong answer for it.

The three kinds of sheet

• Halves, thirds and fourths: shapes cut into 2, 3 or 4 parts. There are only 6 such fractions (1/2, 1/3, 2/3, 1/4, 2/4 and 3/4), so on a sheet of 12 a fraction can come up more than once, with different parts shaded.
• Up to eighths: shapes cut into 2, 3, 4, 5, 6 or 8 parts.
• Up to twelfths: shapes cut into 2, 3, 4, 5, 6, 8, 10 or 12 parts, which makes 42 fractions.
• Shapes: circles, bars, or some of each.
• The sheet number: any whole number from 1 to 999999. The same fractions, shapes and number make the same twelve pictures on any device, so a whole class can have the same sheet, and no two pictures on a sheet are the same. If we change how the page picks fractions, a number will make a different sheet.
• How big they print: on a Letter sheet, each of 6 or 9 pictures sits in a square about 6 cm wide, and each of 12 pictures in a square about 4 cm wide.

Every time the page is built, a program makes 1,200 sheets (400 of each kind) and counts all 14,400 pictures back from their drawings, with code written apart from the page’s own: it counts the parts drawn and the parts shaded, checks that the parts are the same size and fill the whole shape, and that count has to be the fraction on the answer sheet. It does the same for each of the 42 fractions in both shapes, checks that the four answers on the screen are four different fractions with the right one among them and no other of the same amount, and measures the 6 ways the page can lay pictures out on a sheet.

What this page does not do

• It does not put fractions in lowest terms: 2/4 stays 2/4. It does not compare, order, add or take away fractions.
• It has no fraction as big as a whole or bigger in its pictures, no mixed numbers, no decimals and no percents. For percents there is the percent tool.
• It draws only circles and bars: no groups of things to count, and no number line.
• It does not check parts you shade. On paper, any parts will do as long as the count is right; the answer sheet shows one way. On the screen there are only pictures to name.
• It does not keep score after you close or reload the page, or pick another sheet. The sheet number brings back the pictures, not your answers.
• It is not a lesson plan and follows no school’s program or grade. It makes no promise about what anyone will know after using it. It is pictures to practice on.
• It cannot be read from the picture by a screen reader. “What is in the picture?” says in words the shape, how many equal parts it has and how many are shaded. An answer is written like 3/4; how a screen reader says that aloud depends on the reader, and the page has not been tried with one.
• It cannot see your printer. The shaded parts are grey, and how dark they come out depends on the printer. It has been tried in one browser’s print preview (Chromium, saved as PDF), where each sheet came out on one page; it has not been tried on paper from a real printer.