Maths
Why is 1/4 smaller than 1/3?
Four is bigger than three. So why is one quarter smaller than one third?
The bottom number in a fraction tells you how many equal pieces the whole has been divided into. If you divide the same whole into more equal pieces, each piece must be smaller. One of four equal pieces is smaller than one of three equal pieces. That is why 1/4 < 1/3.
Let's make that idea visible before using a calculation.
Start with two identical strips
Cut two paper strips of exactly the same length. Imagine that each strip represents one whole.
Divide the first strip into three equal sections. Shade one section. You have shaded one third, written 1/3.
Divide the second strip into four equal sections. Shade one section. You have shaded one quarter, written 1/4.
Place the strips underneath each other with their left edges lined up. The shaded third reaches farther along its strip than the shaded quarter does. You have taken one piece from each whole, but the pieces have different sizes.
The top number, called the numerator, is 1 in both fractions. It tells you that you are counting one piece. The bottom number, called the denominator, tells you the size of those pieces by naming how many equal pieces make the whole.
Why the whole matters
Now imagine one quarter of a very large pizza and one third of a small pizza. Which slice contains more food? The fractions alone cannot tell you. You also need the sizes of the pizzas.
For a simple numerical example, one quarter of a 120-gram bar is 30 grams. One third of a 60-gram bar is 20 grams. The quarter of the larger bar contains more chocolate.
This does not change the number fact 1/4 < 1/3. It changes the quantities you are finding fractions of. When comparing shaded amounts in a picture, check that both pictures use the same-sized whole. Also check that the parts within each whole are equal. Four uneven pieces do not each represent a quarter.
Put both fractions on one number line
Draw a line from 0 to 1. This distance represents one whole unit.
Mark one quarter of the way along the line. Then mark one third of the way along it. The 1/4 mark sits to the left of the 1/3 mark. Numbers farther to the right on a number line are greater, so the picture shows the same comparison as the paper strips.
You can make the marks exact by splitting the unit into 12 equal intervals. One quarter lands at the third mark because 1/4 = 3/12. One third lands at the fourth mark because 1/3 = 4/12. Three twelfths is less than four twelfths.
If you want to explore why different fraction names can mark the same point, read our guide to equivalent fractions. Here, those equal names help us compare two different amounts.
A rule, and its limit
Fractions with 1 on top are called unit fractions. For positive whole-number denominators, a larger denominator makes a smaller unit fraction. For example, 1/8 < 1/5: one of eight equal pieces is smaller than one of five equal pieces of the same whole.
Be careful about using that shortcut when the numerators differ. It cannot decide whether 3/4 or 1/3 is larger just by looking at 4 and 3. Three quarters includes three pieces. A drawing or common denominator shows that 3/4 > 1/3.
Before comparing, ask: are we counting the same number of pieces? Are the pieces the same size? Answering those questions is more useful than treating the numerator and denominator as separate whole numbers.
Three questions to try
Try explaining each answer with a sketch before reading the explanation.
1. Which is larger: 1/5 or 1/8?
Answer: 1/5. Divide identical strips into five and eight equal pieces. One fifth is the longer piece. Both fractions count one piece, so the strip divided into fewer pieces gives the larger fraction.
2. A line from 0 to 1 has 12 equal intervals. Where do 1/4 and 1/3 go?
Answer: the third and fourth marks after 0. One quarter is 3/12; one third is 4/12. The fourth mark is farther right, confirming that 1/3 is greater.
3. Sam says, “A quarter always contains less chocolate than a third.” What is missing?
Answer: the size of the whole bar. The statement works when both bars have the same mass. With different-sized bars, compare the actual amounts, not just the fractions.
Try it together
Ask someone to draw a fraction comparison with one deliberate mistake: unequal pieces, different-sized wholes or a misplaced number-line mark. Find the mistake and explain how to fix it.
Parents can see how Edny works: spoken explanations on a shared whiteboard. Check important work: AI explanations can be mistaken.
Further reading
References for the maths ideas; these are not endorsements or curriculum certifications.