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Pattern 01·Foundation·L1

Fraction ↔ Decimal ↔ Percentage

High FrequencyMust Master 45–60 sec

USE WHEN

Question asks you to move quickly between fractions, decimals and percentages or compare them.

BEST METHOD

Shortcut Table Method

TARGET

45–60 sec

MASTERY

not started

Recognition Cues

  • fraction, decimal, percent comparison
  • convert quickly / compare values
  • part of whole hidden as fraction

How to Recognise

Question asks you to move quickly between fractions, decimals and percentages or compare them.

Core Concept

A percentage is simply a fraction with denominator 100. Fast conversion reduces calculation time across almost every Arithmetic chapter.

x%=x/100;a/b=(a÷b)×100%x\% = x/100; a/b = (a \div b) \times 100\%x%=x/100;a/b=(a÷b)×100%

Athena Shortcut

Memorise common conversions: 1/2=50%, 1/3≈33.33%, 1/4=25%, 1/5=20%, 1/6≈16.67%, 1/8=12.5%, 1/9≈11.11%, 1/11≈9.09%.

Alternative Method · Shortcut Table Method

Use memorised common conversions and benchmark fractions like 1/8, 3/8, 5/8.

Timed drill

Identify the base or invariant before you calculate.

1:00

Attempt first · Standard Example

What percentage is 3/8?

Attempt first · CAT-Level Example

A value increases from 5/8 of a base to 3/4 of the same base. By what percentage does the value increase?

Common Trap

  • Do not measure the change against the common external base; percentage change is measured against the original value.

3-level practice ladder

Attempt all three before checking solutions

Foundation

Convert 7/16 into a percentage.

CAT Standard

Express 62.5% as a fraction in lowest terms.

Advanced / Hybrid

A quantity rises from 9/20 of a base to 3/5 of the same base. Find the percentage increase.

PYQ Mapping

Related archetypeCAT

fraction–percentage fluency is foundational across cat arithmetic; no exact year/slot is asserted here.

Pattern Connections

#02 Percentage of a Quantity #03 A as a Percentage of B #04 Percentage Increase / Decrease
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Learning flow

  1. 1Recognition Cues
  2. 2How to Recognise
  3. 3Core Concept
  4. 4Formula
  5. 5Athena Shortcut
  6. 6Alternative Method
  7. 7Timed Drill
  8. 8Standard Example
  9. 9CAT-Level Example
  10. 10Common Trap
  11. 11Practice Ladder
  12. 12PYQ Mapping
  13. 13Connections
  14. 14Mastery

Attempt every example before opening its answer.