NAPOLCOM PNPE Numerical Ability — Ratio, Proportion & PercentageMemory Anchors

Tags

• definition
• notation
• basic concept

Topic

Ratio Basics

Concept

Basic ratio definition and notation

Anchor Id

A1

Difficulty

easy

Memory Aid

A ratio is like a recipe for halo-halo. If you need 2 cups of ice to 3 cups of milk, that's the ratio 2:3. Just like how changing the recipe changes the taste, changing the ratio changes the relationship between quantities.

Anchor Type

analogy

Why It Works

Everyone knows halo-halo recipes, making the abstract concept of ratio concrete and relatable to Filipino students.

Example Usage

When you see '5:7', immediately think 'This is like a recipe - 5 parts of ingredient A to 7 parts of ingredient B.'

Recall Trigger

Think 'halo-halo recipe' whenever you see the colon (:) symbol.

Tags

• method
• solving
• cross multiplication

Topic

Proportion Solving

Concept

Cross multiplication method for proportions

Anchor Id

A2

Difficulty

medium

Memory Aid

Picture a giant 'X' made of bamboo poles crossing over the proportion. The 'X' tells you to multiply diagonally - top-left with bottom-right, top-right with bottom-left. The bamboo X is strong and stable, just like your answer will be when you cross multiply correctly.

Anchor Type

visual_association

Why It Works

The visual X directly matches the mathematical operation, and bamboo is familiar to Filipino students.

Example Usage

For 3/x = 5/15, visualize bamboo poles crossing to get 3 × 15 = 5 × x, so 45 = 5x, therefore x = 9.

Recall Trigger

See the proportion as a bamboo X crossing through it.

Tags

• conversion
• decimal
• percentage

Topic

Percentage Conversion

Concept

Converting percentage to decimal

Anchor Id

A3

Difficulty

easy

Memory Aid

Move the dot two places left, that's the way that's always best! Percent means 'out of one hundred', so divide and you'll be found!

Anchor Type

rhyme

Why It Works

Rhymes create rhythm and repetition that enhance memory retention.

Example Usage

For 25%, sing the rhyme and move decimal: 25.% → 2.5% → .25 = 0.25

Recall Trigger

Sing the rhyme while moving the decimal point.

Tags

• calculation
• multiplication
• percentage

Topic

Percentage Calculations

Concept

Finding percentage of a number

Anchor Id

A4

Difficulty

medium

Memory Aid

Use 'OF means MULTIPLY' - remember OMG! When you see 'of' in percentage problems, it's like saying 'OMG, I need to multiply!'

Anchor Type

acronym

Why It Works

OMG is universally known by students, creating an instant connection to the multiplication operation.

Example Usage

What is 30% of 80? OMG means multiply: 0.30 × 80 = 24

Recall Trigger

Say 'OMG!' when you see the word 'of' in percentage problems.

Tags

• discount
• original price
• problem solving

Topic

Discount Problems

Concept

Finding the original price from discounted price

Anchor Id

A5

Difficulty

hard

Memory Aid

Maria bought a bag for ₱800 at 20% off. To find the original price, she thinks: 'If I paid 80% (100% - 20%), then ₱800 is 80% of the original price.' She divides ₱800 by 0.80 to get ₱1000. Maria always remembers: 'What I paid divided by what percentage I paid gives the original price.'

Anchor Type

micro_story

Why It Works

The story provides context and a clear logical sequence that mirrors real shopping experiences.

Example Usage

Paid ₱1200 at 25% off. Think of Maria: ₱1200 ÷ 0.75 = ₱1600 original price.

Recall Trigger

Think of Maria shopping with her discount calculation.

Tags

• conversion
• ratio
• percentage

Topic

Ratio and Percentage

Concept

Ratio to percentage conversion

Anchor Id

A6

Difficulty

medium

Memory Aid

Walk through your house: (1) Kitchen - Add up all parts of the ratio like ingredients, (2) Living room - Divide each part by the total like sharing TV time, (3) Bedroom - Multiply by 100 like counting sheep to 100 for percentage.

Anchor Type

method_of_loci

Why It Works

Using familiar room locations creates a memorable sequence for the three-step process.

Example Usage

Ratio 3:7. Kitchen: 3+7=10 total. Living room: 3/10 and 7/10. Bedroom: 30% and 70%.

Recall Trigger

Visualize walking through your house from kitchen to bedroom.

Tags

• relationship
• direct proportion
• analogy

Topic

Direct Proportion

Concept

Direct proportion relationship

Anchor Id

A7

Difficulty

medium

Memory Aid

Direct proportion is like dancing the tinikling - when one bamboo pole goes up, the other goes up too. When one dancer jumps higher, the other must jump higher. They move in the same direction, just like directly proportional quantities.

Anchor Type

analogy

Why It Works

Tinikling is culturally familiar and visually demonstrates synchronized, same-direction movement.

Example Usage

If speed increases, distance increases too - like tinikling dancers jumping higher together.

Recall Trigger

Picture tinikling dancers moving together when you see 'directly proportional'.

Tags

• relationship
• inverse proportion
• visual

Topic

Inverse Proportion

Concept

Inverse proportion relationship

Anchor Id

A8

Difficulty

medium

Memory Aid

Picture a seesaw in the park - when one side goes up, the other must go down. Inverse proportion works exactly like this seesaw: as one quantity increases, the other decreases to maintain balance.

Anchor Type

visual_association

Why It Works

Seesaw motion is universally understood and perfectly demonstrates inverse relationships.

Example Usage

More workers means less time needed - like a seesaw where more weight on one side lifts the other side up (less time).

Recall Trigger

Visualize a seesaw when you see 'inversely proportional'.

Tags

• formula
• percentage increase
• calculation

Topic

Percentage Change

Concept

Percentage increase formula

Anchor Id

A9

Difficulty

medium

Memory Aid

NEW minus OLD, Over OLD, times ONE hundred - remember 'NO-O-OH!' like you're surprised by the increase!

Anchor Type

mnemonic

Why It Works

The exclamation creates emotional engagement while the acronym provides the formula structure.

Example Usage

Price went from ₱50 to ₱60. NO-O-OH: (60-50)/50 × 100 = 20% increase.

Recall Trigger

Shout 'NO-O-OH!' when calculating percentage increase.

Tags

• classification
• problem types
• percentage

Topic

Percentage Problem Types

Concept

Three types of percentage problems

Anchor Id

A10

Difficulty

medium

Memory Aid

Remember 'PRO' - P for Part (finding the percentage OF a number), R for Rate (finding what percent one number is of another), O for Original/Whole (finding the base when given part and rate).

Anchor Type

acronym

Why It Works

'PRO' suggests expertise and confidence, while organizing the three main problem types clearly.

Example Usage

What is 15% of 200? This is P-type (Part). What percent is 30 of 150? This is R-type (Rate). 24 is 40% of what? This is O-type (Original).

Recall Trigger

Think 'I'm a PRO at percentage problems' and identify which type you're solving.

Tags

• verification
• proportion
• method

Topic

Proportion Verification

Concept

Proportion equality test

Anchor Id

A11

Difficulty

easy

Memory Aid

To check if ratios are equal, use 'CROSS-CHECK': Cross multiply, Results should Equal, Otherwise Substitute Something else. Break it into chunks: CROSS (multiply diagonally) + CHECK (compare products).

Anchor Type

chunking

Why It Works

Chunking breaks complex processes into manageable parts while rhyming aids recall.

Example Usage

Is 2:3 = 6:9? CROSS-CHECK: 2×9 = 18, 3×6 = 18. Equal products mean equal ratios!

Recall Trigger

Say 'CROSS-CHECK' when verifying proportions.

Tags

• tax
• VAT
• real world application

Topic

Tax Calculations

Concept

Tax and VAT calculations

Anchor Id

A12

Difficulty

medium

Memory Aid

Lito buys a phone for ₱10,000. The cashier says 'Plus 12% VAT.' Lito thinks: 'VAT is ADDED to the price, so I pay MORE.' He calculates: ₱10,000 × 1.12 = ₱11,200. Lito remembers: 'Tax makes me pay MORE, so multiply by (1 + tax rate).'

Anchor Type

micro_story

Why It Works

The story clarifies the common confusion about whether tax is added to or subtracted from the base price.

Example Usage

₱5,000 item with 8% tax: Think of Lito paying MORE: ₱5,000 × 1.08 = ₱5,400.

Recall Trigger

Think of Lito paying MORE for his phone due to tax.

Tags

• profit
• loss
• percentage
• business

Topic

Profit and Loss

Concept

Profit and loss percentage

Anchor Id

A13

Difficulty

hard

Memory Aid

Imagine a jeepney driver's logbook with two columns: 'Cost' (what he paid) and 'Selling' (what he earned). Profit/Loss percentage always compares to the COST column (denominator). Picture the cost column highlighted in red as the base for comparison.

Anchor Type

visual_association

Why It Works

Jeepney drivers are familiar figures, and the visual logbook clarifies which value serves as the base.

Example Usage

Bought at ₱800, sold at ₱1000. Profit = ₱200. Percentage = (₱200/₱800) × 100 = 25% profit.

Recall Trigger

See the red-highlighted cost column in the jeepney driver's logbook.

Tags

• compound ratios
• multiplication
• combination

Topic

Compound Ratios

Concept

Compound ratios

Anchor Id

A14

Difficulty

hard

Memory Aid

Compound ratios are like mixing different halo-halo recipes. If recipe A uses 2:3 (ice:milk) and recipe B uses 4:5 (milk:fruit), combining them gives (2×4):(3×5) = 8:15 (ice:fruit). You multiply straight across like combining recipe ingredients.

Anchor Type

analogy

Why It Works

The familiar concept of mixing recipes makes the abstract multiplication of ratios concrete and logical.

Example Usage

A:B = 3:4 and B:C = 2:5. Combined A:C = (3×2):(4×5) = 6:20 = 3:10.

Recall Trigger

Think of combining halo-halo recipes when you see multiple ratios to combine.

Tags

• unitary method
• scaling
• problem solving

Topic

Unitary Method

Concept

Unitary method for proportions

Anchor Id

A15

Difficulty

medium

Memory Aid

Ana needs to buy fabric. The store says '3 meters costs ₱150.' Ana wants 7 meters. She thinks: 'First, find the cost of 1 meter (the UNIT), then multiply by 7.' So: ₱150 ÷ 3 = ₱50 per meter. Then: ₱50 × 7 = ₱350 for 7 meters. Ana's strategy: 'Always find the unit first, then scale up.'

Anchor Type

micro_story

Why It Works

The shopping scenario is relatable, and the step-by-step process mirrors the mathematical method exactly.

Example Usage

If 5 pens cost ₱75, what do 8 pens cost? Think of Ana: ₱75 ÷ 5 = ₱15 per pen. Then ₱15 × 8 = ₱120.

Recall Trigger

Think of Ana buying fabric and finding the unit price first.

Tags

• error
• measurement
• formula
• calculation

Topic

Percentage Error

Concept

Percentage error in measurements

Anchor Id

A16

Difficulty

hard

Memory Aid

ERROR = |Measured - Actual| divided by Actual, times 100. Remember 'MAD-A': Measured minus Actual gives Difference, Absolute value, divide by Actual. The chunks are: MAD (find the difference) + A (divide by actual).

Anchor Type

chunking

Why It Works

MAD helps remember the subtraction order, while chunking simplifies the multi-step formula.

Example Usage

Measured 98cm, actual 100cm. MAD-A: |98-100|/100 × 100 = 2/100 × 100 = 2% error.

Recall Trigger

Get MAD-A when calculating measurement errors.

Tags

• units
• conversion
• ratios
• standardization

Topic

Unit Conversion in Ratios

Concept

Mixed ratios with different units

Anchor Id

A17

Difficulty

medium

Memory Aid

Picture a market scale with different baskets: one has kilograms, another has grams, another has pounds. Before comparing ratios, all baskets must have the same unit label. Convert everything to matching units first, like organizing the market baskets by unit type.

Anchor Type

visual_association

Why It Works

Market scales are familiar, and the visual of organizing baskets by unit type reinforces the conversion requirement.

Example Usage

Ratio of 2kg:500g becomes 2000g:500g = 4:1 after converting to same units.

Recall Trigger

See the market vendor organizing baskets by unit type before weighing.

Tags

• successive changes
• multiplication
• percentage

Topic

Successive Percentages

Concept

Successive percentage changes

Anchor Id

A18

Difficulty

hard

Memory Aid

For successive percentages, remember 'MULTIPLY the MULTIPLIERS': If prices increase 10% then decrease 5%, multiply (1.10) × (0.95). Don't add percentages - MULTIPLY the change factors!

Anchor Type

mnemonic

Why It Works

The alliteration 'Multiply the Multipliers' creates a memorable rule that prevents the common error of adding percentages.

Example Usage

20% increase then 15% decrease: (1.20) × (0.85) = 1.02, so 2% net increase.

Recall Trigger

Chant 'Multiply the Multipliers' when seeing successive percentage changes.

Formula

Percentage = (Part/Whole) × 100

Mnemonic

PAWS-100: Part And Whole Separated by division, times 100

When To Use

When finding what percentage one quantity is of another

What Each Part Means

Part is the portion you're finding percentage for, Whole is the total amount, 100 converts decimal to percentage

Formula

Part = (Percentage × Whole) / 100

Mnemonic

POWER-100: Percentage Over Whole Equals Result, divided by 100

When To Use

When finding a specific percentage of a number

What Each Part Means

Percentage is the given percent, Whole is the total, Part is what you're finding

Formula

Whole = (Part × 100) / Percentage

Mnemonic

WHO-PAYS: Whole Has One-hundred times Part, And percentage Yields the answer

When To Use

When finding the total from a known part and percentage

What Each Part Means

Part is the known portion, 100 is the conversion factor, Percentage is the given rate

Formula

Cross multiplication: a/b = c/d means a×d = b×c

Mnemonic

ACROSS the X: A times D = B times C

When To Use

When solving proportions or checking if ratios are equal

What Each Part Means

Multiply the extremes (outer terms) and means (inner terms)

Chain Title

Steps to Solve Proportion Problems

Recall Test

What does Santa do after crossing the sky?

Memory Chain

Santa's Christmas Sleigh Checks - Santa Sets up his route, Crosses the sky, Solves delivery problems, Checks every house

Items To Remember

• Set up the proportion
• Cross multiply
• Solve the equation
• Check your answer

Chain Title

Types of Percentage Problems

Recall Test

What does the rabbit find in percentage problems?

Memory Chain

Peter Rabbit Was Playful - Peter finds Parts, Rabbit finds Rates, Was finds Wholes, Playful finds Percentage changes

Items To Remember

• Find the part
• Find the rate
• Find the whole
• Find percentage change

Chain Title

Converting Between Fractions, Decimals, and Percentages

Recall Test

What do dogs do to convert fractions to decimals?

Memory Chain

Dogs Dance Proudly Daily - Dogs Divide, Dance Multiplies by 100, Proudly divides by 100, Daily places over 10

Items To Remember

• Fraction to decimal: divide
• Decimal to percentage: multiply by 100
• Percentage to decimal: divide by 100
• Decimal to fraction: place over power of 10

Chain Title

Discount Problem Solution Steps

Recall Test

After finding and subtracting, what's the alternative method?

Memory Chain

Find Some Old Coins - Find discount amount, Subtract from original, Or use complement, Check if reasonable

Items To Remember

• Find discount amount
• Subtract from original
• Or multiply by complement percentage
• Check reasonableness

Chain Title

Ratio Simplification Process

Recall Test

After dividing both terms, what should you do next?

Memory Chain

Friendly Dogs Chase Wisely - Find common factors, Divide both terms, Check for more reduction, Write final answer

Items To Remember

• Find common factors
• Divide both terms
• Check if further reduction possible
• Write in simplest form