Civil Service Exam (Subprofessional) Numerical Ability — Fractions — Operations, Conversion & ComparisonMemory Anchors

Tags

• classification
• definition

Topic

Types of Fractions

Concept

Types of Fractions (Proper, Improper, Mixed)

Anchor Id

A1

Difficulty

easy

Memory Aid

PIM - 'Proper Is Mini, Improper is Massive, Mixed is Both!' Think of PIM as a tiny person (proper) growing into a giant (improper) who becomes a superhero with both human and super powers (mixed).

Anchor Type

acronym

Why It Works

The visual transformation from small to large mirrors how fractions change from less than 1 to greater than 1, with mixed being the combination.

Example Usage

See 3/8? Think 'PIM' - numerator 3 is smaller than denominator 8, so it's Proper (mini person). See 8/3? Numerator is bigger, so Improper (giant). See 2 3/8? Mixed (superhero).

Recall Trigger

When you see any fraction, ask 'Is this PIM?' and picture the tiny person growing.

Tags

• process
• formula

Topic

Converting Mixed to Improper

Concept

Converting Mixed to Improper Fractions

Anchor Id

A2

Difficulty

medium

Memory Aid

The Whole Family Recipe: Papa Whole marries Mama Denominator and adopts Baby Numerator. To find their new family name, Papa multiplies himself by Mama, then adds Baby. The family keeps Mama's last name (denominator). So 2 3/5 becomes: Papa(2) × Mama(5) = 10, plus Baby(3) = 13, keeping Mama's name = 13/5.

Anchor Type

micro_story

Why It Works

The family story creates emotional connection and the multiplication/addition steps mirror real family dynamics of combining resources.

Example Usage

Convert 4 1/3: Papa(4) marries Mama(3), so 4×3=12, plus Baby(1)=13, family name stays 3, answer: 13/3.

Recall Trigger

Picture a wedding ceremony when you see mixed fractions - the whole number is getting married!

Tags

• process
• division

Topic

Converting Improper to Mixed

Concept

Converting Improper to Mixed Fractions

Anchor Id

A3

Difficulty

medium

Memory Aid

The Pizza Division Game: You have 17 slices of pizza (numerator) and tables for 4 people each (denominator). How many complete tables can you fill? 17÷4=4 complete tables (whole number) with 1 slice left over (remainder becomes new numerator). So 17/4 = 4 1/4.

Anchor Type

analogy

Why It Works

Pizza division is concrete and familiar - everyone understands sharing food equally among groups.

Example Usage

Convert 23/7: Picture 23 pizza slices for tables of 7. 23÷7=3 complete tables, remainder 2 slices. Answer: 3 2/7.

Recall Trigger

When you see an improper fraction, visualize pizza slices being distributed to tables.

Tags

• process
• multiplication

Topic

Equivalent Fractions

Concept

Finding Equivalent Fractions

Anchor Id

A4

Difficulty

easy

Memory Aid

The Twin Magic Wand: Picture two identical magic wands that must always do the same trick. Whatever you do to the top number (numerator), you MUST do to the bottom number (denominator). If you multiply the top by 3, the bottom wand automatically multiplies by 3 too. The fractions look different but have the same magical power (value).

Anchor Type

visual_association

Why It Works

The twin wand image reinforces the critical rule that both numerator and denominator must be treated equally.

Example Usage

Find equivalent of 2/3: Wave both wands with '×4' spell. Top: 2×4=8, Bottom: 3×4=12. Answer: 8/12.

Recall Trigger

See equivalent fraction problems? Visualize twin magic wands moving in perfect synchronization.

Tags

• process
• LCD

Topic

Addition of Dissimilar Fractions

Concept

Addition of Fractions with Different Denominators

Anchor Id

A5

Difficulty

medium

Memory Aid

The School Uniform Problem: Two students want to combine their allowances, but one has pesos (denominator 1) and another has coins in groups of 4 (denominator 4). Before they can add their money, they need the same currency! Find the LCD (Least Common Denominator) like finding a common currency both can use, then convert both amounts to that currency before adding.

Anchor Type

analogy

Why It Works

Currency conversion is a real-world parallel that students understand from daily life in the Philippines.

Example Usage

Add 1/2 + 1/3: Different currencies! LCD=6 (common currency). Convert: 3/6 + 2/6 = 5/6.

Recall Trigger

Different denominators = different currencies. Think 'money exchange' first!

Tags

• process
• multiples

Topic

Finding LCD

Concept

Finding LCD (Least Common Denominator)

Anchor Id

A6

Difficulty

medium

Memory Aid

The Jeepney Route Story: Two jeepneys (denominators 4 and 6) start from the same terminal but follow different routes. When will they meet again at the same stop? List their stops: Jeepney 4 stops at 4,8,12,16,20,24... Jeepney 6 stops at 6,12,18,24... They first meet at stop 12! That's your LCD.

Anchor Type

micro_story

Why It Works

Jeepneys are iconic in Filipino culture, making this a culturally relevant and memorable image.

Example Usage

LCD of 4 and 6: Jeepney routes 4: 4,8,12... Route 6: 6,12... First meeting point: 12.

Recall Trigger

Finding LCD? Picture jeepneys meeting at a common terminal.

Tags

• formula
• rhyme

Topic

Multiplication of Fractions

Concept

Multiplication of Fractions

Anchor Id

A7

Difficulty

easy

Memory Aid

Multiply fractions, it's so easy-peasy! Top times top, bottom times bottom - that's the key! No LCD needed, just straight multiply, then simplify your answer by and by!

Anchor Type

rhyme

Why It Works

Rhymes create musical memory patterns that stick better than plain rules.

Example Usage

Multiply 2/3 × 4/5: Top times top: 2×4=8, Bottom times bottom: 3×5=15. Answer: 8/15.

Recall Trigger

Hear 'multiply fractions' and sing the rhyme in your head.

Tags

• process
• reciprocal

Topic

Division of Fractions

Concept

Division of Fractions (Reciprocal Method)

Anchor Id

A8

Difficulty

medium

Memory Aid

The Flip Phone Trick: Division is like an old flip phone - when you divide, the second fraction does a complete flip! The phone flips from 3/4 to 4/3, then you multiply. Remember: 'Keep, Change, Flip' - Keep the first fraction, Change ÷ to ×, Flip the second fraction.

Anchor Type

visual_association

Why It Works

The physical flip motion creates a strong visual memory, and flip phones are familiar technology.

Example Usage

Divide 2/5 ÷ 3/4: Keep 2/5, Change to ×, Flip 3/4 to 4/3. Now multiply: 2/5 × 4/3 = 8/15.

Recall Trigger

See division of fractions? Picture flipping an old phone.

Tags

• comparison
• numerator

Topic

Comparing Fractions

Concept

Comparing Fractions with Same Denominators

Anchor Id

A9

Difficulty

easy

Memory Aid

The Pizza Slice Competition: Two friends order the same size pizza cut into 8 slices each. Friend A gets 3 slices (3/8), Friend B gets 5 slices (5/8). Same size slices (same denominators), so just count who has more slices (compare numerators). More slices = bigger fraction!

Anchor Type

analogy

Why It Works

Pizza comparison is intuitive - everyone understands that more slices of the same-sized pizza means more food.

Example Usage

Compare 4/7 and 6/7: Same pizza size (denominator 7), but 6 slices > 4 slices, so 6/7 > 4/7.

Recall Trigger

Same denominators? Think equal pizza slices - just count!

Tags

• comparison
• denominator

Topic

Comparing Fractions

Concept

Comparing Fractions with Same Numerators

Anchor Id

A10

Difficulty

medium

Memory Aid

The Chocolate Bar Paradox: You have 3 pieces of chocolate, but from different bars. One bar was cut into 4 pieces (3/4), another into 8 pieces (3/8). Same number of pieces (3), but which gives you more chocolate? The bar cut into fewer pieces (smaller denominator) gives bigger pieces! So 3/4 > 3/8.

Anchor Type

visual_association

Why It Works

The chocolate visual helps students see that fewer cuts means bigger pieces when you take the same number.

Example Usage

Compare 2/3 and 2/7: Same pieces (2), but 3 cuts vs 7 cuts. Fewer cuts wins: 2/3 > 2/7.

Recall Trigger

Same numerators? Think chocolate bars - fewer cuts = bigger pieces!

Tags

• conversion
• division

Topic

Converting Fractions to Decimals

Concept

Converting Fractions to Decimals

Anchor Id

A11

Difficulty

medium

Memory Aid

The Math Classroom Journey: Start at the door (fraction), walk to the teacher's desk (division setup), sit at your seat (perform division), walk to the board (write decimal), return to your desk (check answer). The journey path: Fraction → Division → Calculation → Decimal → Verification.

Anchor Type

method_of_loci

Why It Works

Method of loci uses spatial memory, one of the strongest memory systems humans have.

Example Usage

Convert 3/4: Door (3/4) → Teacher's desk (3÷4) → My seat (0.75) → Board (write 0.75) → Desk (check!).

Recall Trigger

Converting fraction to decimal? Start your classroom journey at the door.

Tags

• process
• GCF

Topic

Simplifying Fractions

Concept

Simplifying Fractions

Anchor Id

A12

Difficulty

medium

Memory Aid

The Number Detective Story: Detective GCF is hunting for the biggest criminal (Greatest Common Factor) hiding in both the numerator and denominator buildings. Once caught, this criminal is eliminated (divided) from both buildings simultaneously. The buildings become smaller but keep the same proportions. Detective GCF keeps working until no more common criminals remain.

Anchor Type

micro_story

Why It Works

Detective stories create narrative tension and the 'criminal elimination' mirrors the mathematical process.

Example Usage

Simplify 12/18: Detective finds criminal '6' in both buildings. Eliminate: 12÷6=2, 18÷6=3. Result: 2/3.

Recall Trigger

Simplifying fractions? Call Detective GCF to catch the common criminals!

Tags

• process
• application

Topic

Word Problems

Concept

Word Problems with Fractions

Anchor Id

A13

Difficulty

hard

Memory Aid

The FACT Method: F-ind what you're looking for, A-nalyze the given information, C-hoose the operation (of, is, than = clues), T-ranslate to math and solve. Break every word problem into these 4 chunks and process them in order.

Anchor Type

chunking

Why It Works

Chunking breaks overwhelming word problems into manageable steps, reducing cognitive load.

Example Usage

Problem: 'What is 2/3 of 45?' F-ind: the product, A-nalyze: 2/3 and 45 given, C-hoose: 'of' means multiply, T-ranslate: 2/3 × 45 = 30.

Recall Trigger

Word problem panic? Remember: just get the FACT!

Tags

• process
• cross multiplication

Topic

Division Methods

Concept

Cross Multiplication for Division

Anchor Id

A14

Difficulty

medium

Memory Aid

The X-Pattern Fighter: When dividing fractions, imagine an X-shaped fighter jet. The jet's wings cross-multiply: top-left wing hits bottom-right wing, bottom-left wing hits top-right wing. Draw the X and follow the wings to get your multiplication: (a/b) ÷ (c/d) = (a×d)/(b×c).

Anchor Type

visual_association

Why It Works

The X visual pattern matches the mathematical cross-multiplication pattern perfectly.

Example Usage

Divide 3/5 ÷ 2/7: Draw X, wings cross: (3×7)/(5×2) = 21/10.

Recall Trigger

Division problem? Draw the X-fighter and let the wings show you the way!

Tags

• process
• conversion

Topic

Mixed Number Operations

Concept

Mixed Number Operations

Anchor Id

A15

Difficulty

hard

Memory Aid

The Transformer Robot Strategy: Mixed numbers are like transformer robots - they look complete but must transform into improper fractions (battle mode) before they can fight (perform operations). After the battle, transform back to mixed form if needed (peace mode). Always: Mixed → Improper → Operate → Mixed (if required).

Anchor Type

analogy

Why It Works

Transformer imagery appeals to students and mirrors the conversion process perfectly.

Example Usage

Add 1 2/3 + 2 1/4: Transform to battle mode: 5/3 + 9/4 = 20/12 + 27/12 = 47/12. Peace mode: 3 11/12.

Recall Trigger

Mixed numbers in operations? Time for transformer battle mode!

Tags

• process
• mnemonic

Topic

Addition Process

Concept

Fraction Addition Pattern

Anchor Id

A16

Difficulty

medium

Memory Aid

LCD-SAME: Find LCD, Convert to SAME denominators, Add Numerators, Maintain denominator, Evaluate (simplify). Remember: 'Lahat Dapat Consistent, Sabay-sabay Add, Maintain, Evaluate!'

Anchor Type

mnemonic

Why It Works

The Filipino phrase helps local students remember the English steps, creating dual-language memory pathways.

Example Usage

Add 1/4 + 2/6: LCD(12), Convert(3/12 + 4/12), Add(7), Maintain(12), Evaluate(7/12).

Recall Trigger

Adding fractions? Think 'LCD-SAME' and remember the Filipino hint!

Tags

• classification
• visual

Topic

Fraction Classification

Concept

Proper vs Improper Recognition

Anchor Id

A17

Difficulty

easy

Memory Aid

The Seesaw Test: Imagine a seesaw with the numerator on one side and denominator on the other. If numerator is lighter (smaller), it goes up and the fraction is 'proper' (well-behaved, less than 1). If numerator is heavier (bigger), it crashes down and the fraction is 'improper' (misbehaving, more than 1).

Anchor Type

visual_association

Why It Works

Seesaws provide immediate visual feedback about which number is bigger, and the up/down motion reinforces the concept.

Example Usage

Is 7/5 proper or improper? Seesaw: 7 is heavier than 5, crashes down = improper.

Recall Trigger

Classifying fractions? Picture the seesaw and see which side crashes down!

Tags

• process
• multiples

Topic

Common Denominators

Concept

Finding Common Denominators

Anchor Id

A18

Difficulty

medium

Memory Aid

The Basketball Team Formation: Coach needs to put players from two different schools (denominators 6 and 8) into equal-sized practice groups. She lists possible group sizes for School A (6,12,18,24...) and School B (8,16,24,32...). The first size that works for both schools is 24 - that's when both teams can practice together using the same group formation (common denominator).

Anchor Type

micro_story

Why It Works

Basketball is popular in Philippines, and team formation mirrors the mathematical process of finding common multiples.

Example Usage

Find common denominator for 1/6 and 3/8: List multiples, find first match at 24. Convert both fractions to denominator 24.

Recall Trigger

Need common denominators? Think coach forming practice groups!

Formula

Mixed to Improper: (Whole × Denominator) + Numerator / Denominator

Mnemonic

Wedding Math: Papa marries Mama, adopts Baby, keeps Mama's name. (W×D)+N/D

When To Use

Converting mixed numbers before operations or when simplifying complex expressions

What Each Part Means

W=Whole number (Papa), D=Denominator (Mama), N=Numerator (Baby), Result=New family

Formula

Improper to Mixed: Numerator ÷ Denominator = Quotient Remainder/Denominator

Mnemonic

Pizza Division: Total slices ÷ Table size = Full tables + Leftover slices/Table size

When To Use

Converting improper fractions to mixed form for final answers or easier interpretation

What Each Part Means

Numerator=Total items, Denominator=Group size, Quotient=Whole groups, Remainder=Leftover

Formula

Fraction Addition: a/b + c/d = (a×d + b×c)/(b×d)

Mnemonic

Cross Pattern: Draw an X, multiply along the arms for top, multiply straight across for bottom

When To Use

Adding fractions with different denominators when LCD method is complex

What Each Part Means

a,c=numerators, b,d=denominators, Cross multiply then add for numerator, multiply denominators

Formula

Fraction Division: a/b ÷ c/d = a/b × d/c

Mnemonic

Keep Change Flip: Keep first fraction, Change ÷ to ×, Flip second fraction

When To Use

All fraction division problems - most reliable method

What Each Part Means

a/b=dividend, c/d=divisor becomes d/c=reciprocal, ×=new operation

Chain Title

Steps for Adding Unlike Fractions

Recall Test

What are the 5 steps to add fractions with different denominators?

Memory Chain

Filipino kids Learn Different Cultures: Find LCD (Lahat), Convert (Different), Add (Cultures), Keep (denominator constant), Simplify (make it clean)

Items To Remember

• Find LCD
• Convert fractions
• Add numerators
• Keep denominator
• Simplify

Chain Title

Order of Fraction Operations

Recall Test

What's the proper order for complex fraction operations?

Memory Chain

Careful Filipino Police Officers Succeed: Convert, Find, Perform, Simplify, Convert back

Items To Remember

• Convert mixed to improper
• Find common denominators
• Perform operation
• Simplify
• Convert back if needed

Chain Title

Types of Fractions in Size Order

Recall Test

List the four main types of fractions from smallest to largest typical size

Memory Chain

Please Use Internet Messages: Proper (small), Unit (exactly 1), Improper (big), Mixed (combination)

Items To Remember

• Proper (less than 1)
• Unit (equals 1)
• Improper (greater than 1)
• Mixed (whole + proper)

Chain Title

Fraction Comparison Rules

Recall Test

What are the four main rules for comparing fractions?

Memory Chain

Smart Students Need Creative thinking: Same denominator (compare tops), Same numerator (smaller bottom wins), Need LCD (when different), Creative cross multiply

Items To Remember

• Same denominators - compare numerators
• Same numerators - smaller denominator wins
• Different both - find LCD first
• Cross multiply for quick check

Chain Title

Simplifying Fraction Process

Recall Test

What are the steps to simplify a fraction to lowest terms?

Memory Chain

Great Detectives Catch Villains: Find GCF, Divide both, Check further, Verify result

Items To Remember

• Find GCF of numerator and denominator
• Divide both by GCF
• Check if further reduction possible
• Verify answer