FEUCAT Mathematics — Ratio & ProportionMemory Anchors

Tags

• definition
• notation
• basics

Topic

Ratio basics

Concept

Ratio definition and notation

Anchor Id

A1

Difficulty

easy

Memory Aid

Imagine a RATIO as a rice cooker with two compartments - one for rice, one for water. The ratio 3:5 means 3 cups of rice to 5 cups of water. You can write it three ways: using a colon (3:5), as a fraction (3/5), or with 'to' (3 to 5) - just like you can describe your rice cooker three ways: 'colon style', 'fraction style', or 'to style'.

Anchor Type

visual_association

Why It Works

Visual imagery combined with a familiar Filipino cooking reference creates multiple retrieval pathways in memory.

Example Usage

When you see 4:7 in an exam, imagine 4 cups rice to 7 cups water in your mental rice cooker, then choose whichever notation the problem requires.

Recall Trigger

Think of cooking rice when you see a ratio

Tags

• formula
• proportion
• solving

Topic

Cross multiplication

Concept

Cross-multiplication rule for proportions

Anchor Id

A2

Difficulty

medium

Memory Aid

Captain Cross-Multiply is a superhero who fights proportion problems. When he sees a/b = c/d, he draws a giant X across the equation and multiplies diagonally: 'a times d equals b times c!' He shouts 'Cross my heart and hope to die, diagonal products never lie!' His cape has an X on it, and his power comes from making diagonal connections.

Anchor Type

micro_story

Why It Works

Superhero narratives are memorable, and the visual X connects to the mathematical operation.

Example Usage

For 3/4 = x/20, imagine Captain Cross-Multiply drawing his X: 3×20 = 4×x, so 60 = 4x, therefore x = 15.

Recall Trigger

Visualize Captain Cross-Multiply drawing an X when you see equal fractions

Tags

• concept
• identification
• relationship

Topic

Direct vs inverse proportion

Concept

Direct vs Inverse proportion identification

Anchor Id

A3

Difficulty

medium

Memory Aid

Direct proportion is like dancing with your partner - when you move forward, they move forward too (same direction). Inverse proportion is like a seesaw - when you go up, your friend goes down (opposite directions). If more workers means less time, it's seesaw-style (inverse). If more jeepney fare means more distance, it's dance-style (direct).

Anchor Type

analogy

Why It Works

Physical movement analogies help students visualize mathematical relationships through familiar experiences.

Example Usage

Problem says '6 workers finish in 8 days, how long for 12 workers?' Think seesaw - more workers, less time = inverse proportion.

Recall Trigger

Ask yourself: 'Is this like dancing together or playing seesaw?' when identifying proportion types

Tags

• method
• sequence
• calculation

Topic

Partitive proportion

Concept

Partitive proportion method

Anchor Id

A4

Difficulty

hard

Memory Aid

Remember 'ADD-DIVIDE-MULTIPLY' or ADM for partitive proportion: ADD up all ratio parts, DIVIDE the total by this sum to get one share, then MULTIPLY each ratio part by the share size. Think of ADM as 'Automatic Dividing Machine' that splits money fairly according to ratios.

Anchor Type

acronym

Why It Works

The acronym creates a clear sequence, and the machine metaphor makes the process concrete.

Example Usage

Split ₱840 in ratio 2:3:7. ADM: ADD (2+3+7=12), DIVIDE (840÷12=70), MULTIPLY (2×70=140, 3×70=210, 7×70=490).

Recall Trigger

When splitting totals by ratios, think 'I need my ADM machine'

Tags

• connection
• conversion
• disguise

Topic

Percentages and ratios

Concept

Percent as ratio disguised

Anchor Id

A5

Difficulty

medium

Memory Aid

Imagine percentages wearing a mask at a costume party - underneath, they're really ratios! 25% is just 25:100 in disguise. When you unmask the percentage, you see its true ratio face. Every 'percent of' problem is secretly a proportion problem playing dress-up.

Anchor Type

visual_association

Why It Works

The disguise metaphor helps students see through surface complexity to underlying simplicity.

Example Usage

See '30% of 80'? Unmask it: 30% = 30:100 = 30/100, so 30/100 = x/80, cross-multiply to get x = 24.

Recall Trigger

When you see a percentage, mentally 'unmask' it to reveal the hidden ratio

Tags

• trap
• units
• conversion

Topic

Common errors

Concept

Unit mismatch trap

Anchor Id

A6

Difficulty

medium

Memory Aid

UMT: 'Units Must Transform!' Like a Transformer robot, units must change form before ratios can work. Hours vs minutes? Transform first! The UPCAT loves hiding different units like a magician - always check if units match before calculating.

Anchor Type

mnemonic

Why It Works

The Transformer reference makes unit conversion memorable, and the warning about UPCAT tricks is practical.

Example Usage

Problem mixes hours and minutes? Stop! Transform first. 2 hours = 120 minutes, then proceed with ratio calculation.

Recall Trigger

Before solving any ratio problem, ask 'Do I need to transform my units?'

Tags

• trap
• shares
• calculation

Topic

Common errors

Concept

Ratio vs total confusion

Anchor Id

A7

Difficulty

hard

Memory Aid

Ricky and Tina are siblings whose allowances are in ratio 3:2. Their mom says 'You two get ₱40 total.' Ricky thinks he gets ₱3 - wrong! The ratio means 3 SHARES to 2 SHARES = 5 total shares. So ₱40 ÷ 5 = ₱8 per share. Ricky gets 3×₱8 = ₱24, Tina gets 2×₱8 = ₱16. Ratio parts are shares, not actual amounts!

Anchor Type

micro_story

Why It Works

The sibling story is relatable, and the common mistake is explicitly corrected within the narrative.

Example Usage

Boys to girls = 3:2 with 40 students total. Think shares: 3+2=5 shares, 40÷5=8 per share, so 24 boys and 16 girls.

Recall Trigger

When you see a ratio with a total, think of Ricky and Tina sharing allowance by shares, not by ratio numbers

Tags

• formula
• direct
• relationship

Topic

Direct proportion formula

Concept

Direct proportion formula y = kx

Anchor Id

A8

Difficulty

medium

Memory Aid

'Why equals K times X, that's the direct effect! When one goes up, the other follows, like jeepney fare to distance traveled. K is the constant rate, X and Y increase their fate!' The rhyme helps remember that in direct proportion, Y and X grow together with constant K.

Anchor Type

rhyme

Why It Works

Rhymes create strong memory hooks, and the jeepney reference is culturally familiar to Filipino students.

Example Usage

3 notebooks cost ₱45, how much for 7? Think y=kx: 45=k×3, so k=15. Then y=15×7=₱105.

Recall Trigger

When identifying direct proportion, chant 'Why equals K times X'

Tags

• formula
• inverse
• relationship

Topic

Inverse proportion formula

Concept

Inverse proportion formula xy = k

Anchor Id

A9

Difficulty

medium

Memory Aid

Inverse proportion is like a hydraulic press - when you squeeze X down (smaller), Y shoots up (bigger), but their product XY stays constant like the total pressure K. Picture a seesaw with weights: heavy weight (big X) needs short arm (small Y), light weight (small X) needs long arm (big Y), but the balance point K never moves.

Anchor Type

visual_association

Why It Works

Physical metaphors make abstract mathematical relationships tangible and memorable.

Example Usage

6 workers finish in 8 days. How long for 12 workers? xy=k: 6×8=48, so 12×y=48, therefore y=4 days.

Recall Trigger

Think of a hydraulic press or balanced seesaw when you see inverse relationships

Tags

• process
• simplification
• GCD

Topic

Simplifying ratios

Concept

Simplifying ratios

Anchor Id

A10

Difficulty

easy

Memory Aid

Walk through your house to simplify ratios: At the FRONT DOOR, find the GCD (Greatest Common Divisor) of both numbers. In the LIVING ROOM, divide the first number by the GCD. In the KITCHEN, divide the second number by the GCD. In the BEDROOM, write your simplified ratio. Like cleaning house - you're removing common factors to make everything neat and tidy.

Anchor Type

method_of_loci

Why It Works

The method of loci uses spatial memory to organize the simplification process into memorable steps.

Example Usage

Simplify 12:18. Front door: GCD is 6. Living room: 12÷6=2. Kitchen: 18÷6=3. Bedroom: simplified ratio is 2:3.

Recall Trigger

When simplifying ratios, take a mental walk through your house

Tags

• multiple parts
• simplification
• proportion

Topic

Continued ratios

Concept

Continued ratios with three parts

Anchor Id

A11

Difficulty

medium

Memory Aid

A continued ratio like 2:3:5 is like a three-flavor halo-halo recipe: 2 scoops ube, 3 scoops buko, 5 scoops leche flan. To simplify, you find what divides ALL flavors equally - like adjusting a recipe for more servings. The proportion between flavors stays the same, just like mathematical ratios.

Anchor Type

analogy

Why It Works

Food analogies are memorable, and the halo-halo reference is culturally relevant to Filipino students.

Example Usage

Ratio 6:9:12 simplifies like adjusting recipe portions - divide all by 3 to get 2:3:4.

Recall Trigger

Think of adjusting a halo-halo recipe when working with continued ratios

Tags

• strategy
• sequence
• systematic

Topic

Problem solving strategy

Concept

Problem-solving strategy sequence

Anchor Id

A12

Difficulty

easy

Memory Aid

RAPID problem solving: READ the problem completely first, ASK yourself 'same direction or opposite direction?', PROPORTION setup (write the equation), IMPLEMENT cross-multiplication, DOUBLE-check by plugging back in. RAPID like a race car - but don't skip steps or you'll crash into wrong answers!

Anchor Type

acronym

Why It Works

The acronym provides a systematic approach, and the race car metaphor emphasizes both speed and precision.

Example Usage

New problem appears: READ it fully, ASK if it's direct/inverse, set up PROPORTION, cross-multiply to IMPLEMENT, then DOUBLE-check the answer.

Recall Trigger

Before starting any ratio problem, remember to go RAPID

Tags

• verification
• equality
• check

Topic

Checking proportions

Concept

Proportion equality check

Anchor Id

A13

Difficulty

easy

Memory Aid

Two ratios are equal if their 'diagonal twins' are equal. Picture an equals sign as a bridge connecting two fractions: a/b = c/d. The diagonal twins (a×d and b×c) must weigh exactly the same for the bridge to balance. If the diagonal twins don't match, the bridge collapses and the proportion is false.

Anchor Type

visual_association

Why It Works

The bridge metaphor creates a clear visual test for proportion validity.

Example Usage

Is 2/3 = 8/12? Check diagonal twins: 2×12 = 24, 3×8 = 24. Bridge balances - they're equal!

Recall Trigger

When checking if two ratios are equal, visualize balancing them on a bridge using diagonal twins

Tags

• application
• scale
• maps

Topic

Scale and maps

Concept

Scale and map problems

Anchor Id

A14

Difficulty

medium

Memory Aid

Captain Scale is a tiny superhero who lives in maps. When the map says '1 cm = 5 km', Captain Scale explains: 'In my tiny world, every centimeter I walk equals 5 kilometers in the real world!' He sets up proportions to help travelers: map distance / real distance = 1 cm / 5 km. His motto: 'Small measurements, big adventures!'

Anchor Type

micro_story

Why It Works

The character makes abstract scaling concepts concrete and memorable through storytelling.

Example Usage

Map shows 3 cm between cities, scale is 1 cm = 5 km. Captain Scale says: 1/5 = 3/x, so x = 15 km real distance.

Recall Trigger

When solving scale problems, think of Captain Scale explaining the tiny-to-big relationship

Tags

• application
• mixtures
• scaling

Topic

Mixtures and alloys

Concept

Mixture and alloy problems

Anchor Id

A15

Difficulty

hard

Memory Aid

Mixture problems are like making the perfect buko pie recipe. You have ingredients in certain ratios (coconut to sugar = 3:2), and you want to scale up or combine recipes while keeping the taste the same. The total changes, but the ratio of flavors must stay constant. Just like mathematical mixtures - quantities change, ratios stay the same.

Anchor Type

analogy

Why It Works

Cooking analogies make abstract mixture problems concrete and relatable to everyday experience.

Example Usage

Mixing metals in 2:3 ratio. Need 50kg total. Think buko pie: 2+3=5 parts, 50÷5=10kg per part, so 20kg of first metal, 30kg of second.

Recall Trigger

When solving mixture problems, think of scaling up your favorite recipe while keeping flavors balanced

Tags

• application
• motion
• chunking

Topic

Speed-time-distance

Concept

Speed-time-distance in proportions

Anchor Id

A16

Difficulty

hard

Memory Aid

Speed problems chunk into three families: 1) SAME SPEED, different times → distances are proportional to times (direct). 2) SAME DISTANCE, different speeds → speeds and times are inversely proportional. 3) SAME TIME, different speeds → distances are proportional to speeds (direct). Chunk by what stays SAME, then identify the proportion type.

Anchor Type

chunking

Why It Works

Chunking reduces cognitive load by organizing similar problems into recognizable patterns.

Example Usage

Car travels 120 km in 2 hours. Distance in 5 hours? Same speed chunk: distance ∝ time, so 120/2 = x/5, therefore x = 300 km.

Recall Trigger

In speed problems, first identify what stays SAME, then apply the appropriate proportion chunk

Tags

• application
• work
• inverse

Topic

Work and time

Concept

Work rate problems

Anchor Id

A17

Difficulty

hard

Memory Aid

Work problems are like filling a swimming pool with garden hoses. More hoses = faster filling (inverse proportion between workers and time). Each worker is a hose with a certain 'filling rate.' If 6 hoses fill the pool in 8 hours, then 12 hoses fill it in 4 hours. The total 'hose-hours' (worker-hours) stays constant at 48.

Anchor Type

visual_association

Why It Works

The swimming pool metaphor makes abstract work concepts visual and intuitive.

Example Usage

6 workers complete job in 8 days. How long for 12 workers? Pool thinking: 6×8=48 worker-days total, so 12×t=48, therefore t=4 days.

Recall Trigger

When solving work problems, visualize workers as hoses filling a pool

Tags

• solving
• unknown
• cross-multiplication

Topic

Missing terms

Concept

Finding missing terms in proportions

Anchor Id

A18

Difficulty

medium

Memory Aid

Cross-Diagonal-Solve: 'When one term hides, Cross multiply the sides, Diagonal products are your guide, Solve to make the unknown ride!' This rhyme reminds you that finding missing terms always uses cross multiplication, no matter how complex the proportion looks.

Anchor Type

mnemonic

Why It Works

Rhyming mnemonics create strong recall pathways and make mathematical procedures memorable.

Example Usage

Find x in 7/x = 3/6. Cross-Diagonal-Solve: 7×6 = 3×x, so 42 = 3x, therefore x = 14.

Recall Trigger

When you see an unknown in a proportion, chant 'Cross-Diagonal-Solve'

Formula

a/b = c/d → a×d = b×c

Mnemonic

Cross My Heart And Hope To Die, Diagonal Products Never Lie! Picture drawing an X across equal fractions - multiply the ends that the X connects.

When To Use

Whenever you have two equal ratios and need to find a missing value. This is the master key for all proportion problems.

What Each Part Means

a and d are diagonal partners, b and c are diagonal partners. When fractions are equal, diagonal products are equal.

Formula

y = kx (direct proportion)

Mnemonic

Why Koalas eXplore - they move together! When X goes up, Y goes up too. K is the 'koala constant' that never changes.

When To Use

When two quantities increase or decrease together at a constant rate (more workers → more output, more distance → more fuel).

What Each Part Means

y is the dependent variable, k is the constant of proportionality, x is the independent variable.

Formula

xy = k (inverse proportion)

Mnemonic

X times Y equals K-onstant. When X grows big, Y grows small, but their product K stays tall! Like a seesaw - one up, one down, balance stays around.

When To Use

When one quantity increases while the other decreases (more workers → less time, faster speed → less time).

What Each Part Means

x and y are inversely related variables, k is the constant product that never changes.

Formula

Part/Whole = %/100

Mnemonic

Part of Whole equals Percent over hundred - like slicing cake into a hundred pieces, then counting your share!

When To Use

For all percentage problems - finding parts, wholes, or percentages. Convert every percent problem to this proportion.

What Each Part Means

Part is the portion you want, Whole is the total amount, % is the percentage, 100 is the percent base.

Chain Title

Steps for Partitive Proportion

Recall Test

How do you split ₱100 in ratio 2:3:5? Use ADM!

Memory Chain

ADM - Automatic Dividing Machine: First it ADDS all the parts together, then DIVIDES the total by this sum to find one share, then MULTIPLIES each original part by the share size.

Items To Remember

• Add ratio parts
• Divide total by sum
• Multiply each part by quotient

Chain Title

RAPID Problem-Solving Strategy

Recall Test

What's the first step when you see any ratio problem?

Memory Chain

RAPID like a race car: READ the track, ASK which direction to turn, set up your PROPORTION engine, IMPLEMENT the cross-multiplication gear, DOUBLE-check you reached the finish line correctly.

Items To Remember

• Read completely
• Ask direction type
• Proportion setup
• Implement cross-multiply
• Double-check answer

Chain Title

Types of Proportion Problems

Recall Test

What type is 'more workers, less time'?

Memory Chain

DIPC - Dance In Philippine Culture: DIRECT (dancers move together), INVERSE (seesaw players), PARTITIVE (sharing food fairly), COMPOUND (complex folk dances with multiple moves).

Items To Remember

• Direct proportion
• Inverse proportion
• Partitive proportion
• Compound proportion

Chain Title

Common UPCAT Proportion Contexts

Recall Test

Name three contexts where proportions commonly appear in UPCAT.

Memory Chain

Mama Rosa's Work Schedule: She reads MAPS to plan routes, cooks RECIPES for mixtures, manages WORK schedules, calculates SPEED for deliveries, handles MONEY for exchanges - all using proportions!

Items To Remember

• Maps and scale
• Recipes and mixtures
• Work and time
• Speed and distance
• Money and exchange

Chain Title

Ratio Notation Methods

Recall Test

What are the three ways to write a ratio?

Memory Chain

CFW - Come From Wisdom: COLON is the clearest punctuation, FRACTION is mathematical wisdom, WORD notation explains everything clearly - all express the same ratio relationship.

Items To Remember

• Colon notation (3:5)
• Fraction notation (3/5)
• Word notation (3 to 5)