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CBSE Class 8 · Mathematics

Fractions in Disguise

Official NCERT chapter from Ganita Prakash Part II (book code hegp2). ExamMaster notes are original teaching at CBSE Class 8 depth.

This lesson follows the official chapter “Fractions in Disguise” in Ganita Prakash Part II. The words below are ExamMaster’s teaching, not a paste from the book. Use the NCERT chapter for the classroom sequence; use these notes to hold the idea without copying exercises or figures.

  • CBSE Class 8
  • Easy level
  • 8 concepts

1Fractions as Percentages

A percentage is a fraction with a 100-house: 25% = 25/100 = 1/4. The disguise is the % mark; the maths is parts per hundred.

25% is not 25, and not 1/25 unless you compute that and it happens to match another fact.

How it works

  1. Write the percent as /10025/100.
  2. Simplify if you wish1/4.
  3. Keep “per hundred” as the meaningThe disguise off.

2Percentage of Some Quantity

A percentage of a quantity is that fraction of it: 25% of 80 is (25/100)×80 = 20. Of means ×. 25% of 80 is not 25, and not 80−25.

Adding 25 to 80 is not 25% of 80.

How it works

  1. Write p/100 × the quantityThe of.
  2. Compute20.
  3. Name the unit of the quantity20 of whatever 80 was.

25% of 80

Find 25% of 80.

  • 25/1001/4
  • (1/4)×8020
  • Check20 is a quarter of 80

Pro tip. Percent of is multiply by p/100.

3Using Percentages

Using percentages: compare two of-jobs, or find the whole from a part (if 20 is 25% then the whole is 80), or a change as a percent of the start as taught. Each use still writes /100.

A “% off” story that subtracts the percent-number from the price (₹100 − 25 = ₹75 when 25% was meant) may luckily match 25% of 100, but 25% of ₹80 is not ₹80 − 25.

How it works

  1. Name the useOf, or find-the-whole, or change.
  2. Write the /100 sentenceThe maths.
  3. Compute; check a find-the-whole by taking the % of your answerThe use.

4A definition is a test you can run

Percent is a test: parts per hundred you can write as p/100. If you cannot write the hundred, you have a % sticker.

A badge “25%” with no hundred is not the definition.

How it works

  1. Write p over 100The object.
  2. Of a quantity, multiplyThe test.
  3. If the hundred is missing, it is not yet percent-mathsName 100.

5Name the given before the unknown

The given are p% and the quantity (or the part). The unknown is the of-amount or the whole. Copy 80 before you treat 25 as 25 ones to subtract.

Subtracting 25 from 80 because “percent off” sounded like minus 25 is a silent given.

How it works

  1. Copy p and the quantityThe given.
  2. Name of-amount or wholeThe unknown.
  3. Then × p/100 or undo itGiven first.

6One worked case is enough at this class

One of-job is enough. A page of 25% of 80 clones does not add a new hundred-house.

Ten twins of 20 are still one idea.

How it works

  1. Compute one percent-ofThe case.
  2. A second only as a check (maybe find-the-whole)Optional.
  3. StopThis class.

7A miss: swapping the school name for the picture

A shop-window % sticker is a setting. The maths is p/100 × price. Reading the sticker and subtracting p rupees from every price is the swap-miss.

A red badge is not 20.

How it works

  1. Keep the shop as a storyA setting.
  2. Write p/100 × the given priceThe maths.
  3. ComputeDo not swap.

8Check by the opposite action or the opposite test

Check an of-job by asking “is this a sensible part?”: 25% should be a quarter, so 20 vs 80 fits; 70 would not. Check a whole by taking the same % again.

Staring at 20 and saying “looks small” is not the opposite test.

How it works

  1. State the of-amount or the wholeThe claim.
  2. Take the % the other way, or compare to a simple fractionThe check.
  3. Mend if it failsHonest.
25% of 80 is
  1. 20
  2. 25
  3. 55

A quarter of 80, or (25/100)×80.

Notes

  • The official chapter title is “Fractions in Disguise”. Teach the school test for that title, not a contest shortcut.
  • If a step needs a later class, stop. The next official chapter will pick it up.

Formulas

  • p% = p/100
  • p% of N = (p/100) × N

Recap

Hold these pegs from the official chapter “Fractions in Disguise”. The wording is ExamMaster’s teaching, not a textbook recap.

Fractions as Percentages
A percentage is a fraction with a 100-house: 25% = 25/100 = 1/4.
Percentage of Some Quantity
A percentage of a quantity is that fraction of it: 25% of 80 is (25/100)×80 = 20.
Using Percentages
Using percentages: compare two of-jobs, or find the whole from a part (if 20 is 25% then the whole is 80), or a change as a percent of the start as taught.
A definition is a test you can run
Percent is a test: parts per hundred you can write as p/100.
Name the given before the unknown
The given are p% and the quantity (or the part).
One worked case is enough at this class
One of-job is enough. A page of 25% of 80 clones does not add a new hundred-house.

Practise Fractions in Disguise

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