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Grade 7/ Mathematics/ Working with Fractions
Chapter 8 · NCERT Ganita Prakash

Working with
Fractions

A fraction is just a part of a whole — and once you can see it on a bar, equivalent fractions, comparing, and adding all stop being scary. Drag the bar and watch.

➗ 3 topics⏱ ~25 min📝 12-question quiz
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Play with it

See the fraction

Set the denominator (how many equal parts) and the numerator (how many you take). Watch the bar fill — and see the same amount written as a decimal and in its simplest form.

Explore · Fraction bardrag the sliders

3/4 = 0.75 — a proper fraction, already in simplest form.

Learn

The three big ideas

A fraction names a part of a whole (or of a collection). In 3/4, the denominator (4) is how many equal parts the whole is cut into; the numerator (3) is how many of those parts you take.

  • Proper — numerator < denominator (3/4): less than one whole.
  • Improper — numerator ≥ denominator (7/4): one whole or more.
  • Mixed number — a whole plus a proper fraction (1 3/4). 7/4 = 1 3/4.

Multiply or divide the top and bottom by the same number and the value doesn't change — these are equivalent fractions: 1/2 = 2/4 = 3/6. Divide by the HCF to reach the simplest form (6/8 → 3/4).

To compare two fractions, give them the same denominator (use the LCM), then just compare the numerators:

  • 3/4 vs 2/3 → LCM 12 → 9/12 vs 8/12 → 3/4 is bigger.
  • Same denominator: add/subtract the numerators, keep the denominator: 1/5 + 2/5 = 3/5.
  • Different denominators: make them equal first (LCM), then add: 1/4 + 1/6 = 3/12 + 2/12 = 5/12.
  • "Fraction of" means multiply: 2/3 of 12 = 2/3 × 12 = 8.

Worked example. Add 1/4 + 1/6.

LCM of 4 and 6 is 12. Rewrite: 1/4 = 3/12 and 1/6 = 2/12.

Now the denominators match: 3/12 + 2/12 = 5/12.

Common mistake: adding the denominators — 1/4 + 1/6 is not 2/10. You only add the numerators, and only once the denominators are equal.

Where you'll meet it

Fractions are everywhere

Cooking & sharing

Half the recipe? Every quantity halves: 3/4 cup becomes 3/8. Splitting 3 rotis among 4 people gives each 3/4 of a roti — a fraction is literally "share fairly".

Sales & time

"1/3 off" a ₹600 shirt saves ₹200. "Three-quarters of an hour" is 45 minutes. Knowing "fraction of" turns these into one quick multiplication.

Check yourself

Competency quiz

Modelled on the competency-based pattern — MCQ, assertion–reason and a case study, testing whether you can use fractions, not just recall the rules.

Score 0/12

Interactive built to the OpenMAIC approach (THU-MAIC, MIT). Content from the NCERT Class 7 Maths textbook, Ganita Prakash (ncert.nic.in).

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