What Does “Of” Mean in Fractions? The Word That Confuses Every Child

In fractions, “of” means multiply. When a problem says “find 1/3 of 12,” it means 1/3 × 12 = 4. This is one of the most common confusion points in CBSE Class 5-7 maths, because “of” sounds like a description word, not a mathematical operation. Once your child realises that “of” translates directly to multiplication, fraction word problems get dramatically easier.

Why this confuses children

In everyday language, “of” describes belonging or connection: “a piece of cake,” “the colour of the sky.” It doesn’t suggest multiplication. So when a maths problem says “1/4 of 20,” your child doesn’t instinctively think “multiply.” They might try to divide, or subtract, or just freeze.

The confusion deepens when problems use different phrasings:

“What is 2/5 of 30?” — 2/5 × 30 = 12. “Find 3/4 of one hour.” — 3/4 × 60 minutes = 45 minutes. “A shop gives 1/3 off on a ₹900 item. What is the discount?” — 1/3 × 900 = ₹300.

All three use “of” to mean multiplication. But a child who hasn’t been explicitly taught this rule tries to solve each problem differently, often guessing.

The simplest way to teach it

Use physical objects. Put 12 coins on a table.

“I want 1/3 of these coins.” Divide into 3 equal groups. Each group has 4 coins. So 1/3 of 12 = 4.

“I want 2/3 of these coins.” Same 3 groups. Take 2 groups — that’s 8 coins. So 2/3 of 12 = 8.

Now connect it to the maths: 2/3 × 12 = 8. Your child sees that “of” means “take that fraction’s share.”

Once this clicks with physical objects, move to numbers without objects. The mental model carries over.

The misconception that gets it half-right

Some children learn that “1/3 of 12 means divide 12 by 3,” which gives the right answer for unit fractions like 1/3 or 1/4 but breaks for non-unit fractions. “2/3 of 12” doesn’t mean “divide 12 by 2/3.”

Teaching “of equals multiply” works for all cases, not just the simple ones. It’s worth being precise from the start.

What you can do today

Give your child this problem: “A school has 40 students. 3/8 of them wear glasses. How many wear glasses?”

If they set up 3/8 × 40 = 15, they understand “of.” If they try to divide 40 by 8 and then by 3, or freeze, the “of equals multiply” connection needs building with physical examples first.

How GuruMode handles this

GuruMode’s fraction missions explicitly teach the “of equals multiply” translation through interactive visual problems. Your child sees a group of objects, takes a fraction’s share, and watches the multiplication happen in real time. When they misinterpret “of,” the app catches the specific error and routes to visual recovery.

Try it free

Try the chapter as an interactive mission.

Let your child try a free fractions mission on GuruMode and see how visual practice makes “of” finally click. Visit gurumode.com and click ‘Try GuruMode’ to start. (http://gurumode.com)

Frequently asked questions

By the end of Class 5 (NCERT Math-Magic), children should understand “of” for unit fractions like 1/2 of 10 or 1/4 of 20. By Class 6-7, it should extend to all fractions like 3/5 of 25. If a Class 7 child still struggles with “of,” the gap needs immediate attention.
In fraction and percentage contexts, yes. “50% of 200” = 0.5 × 200. “3/4 of 60” = 3/4 × 60. Teaching this as a consistent rule simplifies a lot of word problems.
Absolutely. It’s a translation problem, not a computation problem. Your child can multiply but doesn’t recognise that the word “of” is telling them to multiply. The fix is explicit teaching of the translation rule, followed by varied practice.