Civil Service Exam (Subprofessional) Numerical Ability — Integers, PEMDAS & DivisibilityMemory Anchors

Tags

• formula
• sequence
• process

Topic

Order of Operations

Concept

PEMDAS Order of Operations

Anchor Id

A1

Difficulty

easy

Memory Aid

Please Excuse My Dear Aunt Sally - or in Filipino context: 'Paki Excuse Mo Dear Ate Sally'

Anchor Type

acronym

Why It Works

The acronym creates a memorable sentence that maps directly to the order: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction

Example Usage

For 2 + 3 × 4², think 'Ate Sally': First exponents (4² = 16), then multiplication (3 × 16 = 48), finally addition (2 + 48 = 50)

Recall Trigger

When you see a complex expression, think 'Ate Sally' to remember the order

Tags

• definition
• process

Topic

Integer Operations

Concept

Negative number addition rules

Anchor Id

A2

Difficulty

medium

Memory Aid

Adding negative numbers is like debt and money. Same sign friends stick together and add up their values. Opposite sign friends fight, and the stronger one wins but loses some strength.

Anchor Type

analogy

Why It Works

The debt/money analogy makes abstract positive/negative relationships concrete and relatable

Example Usage

For (-5) + (-3), both are debts so they stick together: -8. For (-5) + 8, debt fights money, money wins: +3

Recall Trigger

Think 'debt vs money' when adding integers with different signs

Tags

• formula
• process

Topic

Integer Operations

Concept

Multiplication of integers sign rules

Anchor Id

A3

Difficulty

medium

Memory Aid

Same signs make it positive, Different signs make it negative. Like attracts like, opposites fight!

Anchor Type

rhyme

Why It Works

The rhyme creates a musical pattern that's easy to remember, and the 'like attracts like' concept is intuitive

Example Usage

For (-3) × (-4), same signs (both negative) = positive 12. For (-3) × 4, different signs = negative 12

Recall Trigger

When multiplying integers, think 'like attracts like'

Tags

• definition
• process

Topic

Divisibility Rules

Concept

Divisibility by 2

Anchor Id

A4

Difficulty

easy

Memory Aid

Picture a pair of shoes - everything even can be paired up perfectly. If the last digit is even (0,2,4,6,8), it's divisible by 2, like shoes that come in pairs.

Anchor Type

visual_association

Why It Works

Visual imagery of pairs connects to the concept of even numbers being divisible by 2

Example Usage

For 1,234, look at the last digit (4). Think shoes - yes, 4 shoes make 2 pairs, so 1,234 is divisible by 2

Recall Trigger

See the last digit, think 'can it pair up like shoes?'

Tags

• process
• definition

Topic

Divisibility Rules

Concept

Divisibility by 3

Anchor Id

A5

Difficulty

medium

Memory Aid

Three friends (3, 6, 9) love to share everything equally. To check if a number likes them, add up all its digits. If that sum is a friend of 3 (divisible by 3), then the original number will share with them too.

Anchor Type

micro_story

Why It Works

The story personifies numbers and creates a logical connection between digit sum and divisibility

Example Usage

For 576: 5+7+6=18. Since 18 likes the three friends (18÷3=6), so does 576

Recall Trigger

Think 'three friends sharing' when checking divisibility by 3

Tags

• definition
• process

Topic

Divisibility Rules

Concept

Divisibility by 5

Anchor Id

A6

Difficulty

easy

Memory Aid

Five pesos coin and ten pesos coin - money that ends in 5 or 0. Any number ending in 5 or 0 is 'valuable' to 5 (divisible).

Anchor Type

visual_association

Why It Works

Connects to familiar Philippine currency and the visual pattern of 5 and 0 endings

Example Usage

For 1,275, it ends in 5 like a 5-peso coin, so it's divisible by 5

Recall Trigger

Think 'pesos ending in 5 or 0' when checking divisibility by 5

Tags

• process
• definition

Topic

Divisibility Rules

Concept

Divisibility by 9

Anchor Id

A7

Difficulty

medium

Memory Aid

NINE DINES when the digit sum is fine (divisible by 9). Nine is very picky - only numbers whose digit sum is also divisible by 9 can join its dinner table.

Anchor Type

mnemonic

Why It Works

The rhyme 'nine dines when digit sum is fine' creates a memorable rule pattern

Example Usage

For 729: 7+2+9=18, and 18÷9=2, so 729 can join nine's dinner table (is divisible by 9)

Recall Trigger

Think 'nine's picky dinner table' when checking divisibility by 9

Tags

• formula
• process

Topic

Scientific Notation

Concept

Scientific notation structure

Anchor Id

A8

Difficulty

medium

Memory Aid

Scientific notation is like a moving truck: the mantissa (1-10) is the cargo that stays the same size, and the exponent is the number of houses you move left or right on the number street.

Anchor Type

analogy

Why It Works

The moving analogy helps visualize decimal point movement and maintains the relationship between parts

Example Usage

For 45,000: move the decimal 4 houses right to get 4.5, so it's 4.5 × 10⁴

Recall Trigger

Think 'moving truck on number street' when converting to scientific notation

Tags

• formula
• process

Topic

Scientific Notation

Concept

Converting positive to negative exponents

Anchor Id

A9

Difficulty

hard

Memory Aid

Positive exponents are like going UP a building (bigger numbers), negative exponents are like going DOWN to the basement (smaller numbers, towards zero). Moving the decimal left goes up, moving right goes down.

Anchor Type

micro_story

Why It Works

The up/down building metaphor makes the inverse relationship between decimal movement and exponent signs clear

Example Usage

For 0.0045: move decimal right 3 places to get 4.5, so we went 'down' 3 floors: 4.5 × 10⁻³

Recall Trigger

Think 'building floors' when dealing with positive/negative exponents

Tags

• definition
• formula

Topic

Integer Properties

Concept

Absolute value definition

Anchor Id

A10

Difficulty

easy

Memory Aid

Absolute value is like a mirror - it only shows positive reflections. No matter if you're happy (+) or sad (-), your reflection in the absolute value mirror is always positive distance from zero.

Anchor Type

visual_association

Why It Works

The mirror metaphor makes the 'always positive' concept intuitive and memorable

Example Usage

For |-7|, imagine -7 looking in the absolute value mirror and seeing +7 looking back

Recall Trigger

Think 'positive mirror reflection' when seeing absolute value bars |n|

Tags

• definition
• formula

Topic

Integer Properties

Concept

Zero properties in operations

Anchor Id

A11

Difficulty

medium

Memory Aid

Zero's Seven Special Powers: Addition (no change), Subtraction (no change), Multiplication (becomes zero), Division by zero (forbidden/undefined), Divided by others (becomes zero), Exponent (makes one), Any number to power zero (equals one).

Anchor Type

chunking

Why It Works

Chunking the seven properties into 'powers' makes them easier to memorize as a group

Example Usage

For 5 × 0, think zero's multiplication power - everything becomes zero. For 5⁰, think zero exponent power - becomes one

Recall Trigger

Think 'Zero's Seven Special Powers' when dealing with zero in operations

Tags

• definition
• classification

Topic

Factors and Multiples

Concept

Prime vs Composite numbers

Anchor Id

A12

Difficulty

medium

Memory Aid

Prime numbers are like introverted people - they only have two real friends (1 and themselves). Composite numbers are like popular people at parties - they have many factor friends who can multiply together to make them.

Anchor Type

analogy

Why It Works

The personality analogy makes the mathematical distinction relatable and memorable

Example Usage

For 17, it's introverted (only friends: 1 and 17), so it's prime. For 12, it's popular (friends: 1,2,3,4,6,12), so it's composite

Recall Trigger

Think 'introvert vs popular person' when classifying numbers as prime or composite

Tags

• process
• formula

Topic

Factors and Multiples

Concept

Finding GCF using prime factorization

Anchor Id

A13

Difficulty

hard

Memory Aid

Imagine a factory assembly line: First station breaks numbers into prime parts, Second station compares the parts from both numbers, Third station picks only the common parts, Fourth station multiplies common parts together for the final GCF product.

Anchor Type

method_of_loci

Why It Works

The assembly line creates a spatial memory sequence that maps to the mathematical process

Example Usage

For GCF of 12 and 18: Factory breaks them (12=2²×3, 18=2×3²), compares parts, picks common ones (2¹×3¹), final product: GCF=6

Recall Trigger

Think 'GCF factory assembly line' when finding greatest common factors

Tags

• process
• definition

Topic

Divisibility Rules

Concept

Divisibility by 4

Anchor Id

A14

Difficulty

medium

Memory Aid

Four wheels on a car - look at the last TWO digits like the back two wheels. If those two digits can be divided by 4 evenly, the whole car (number) can roll smoothly with 4.

Anchor Type

visual_association

Why It Works

The car wheel visual connects the concept of looking at last two digits with the rule for divisibility by 4

Example Usage

For 1,236, look at the back wheels (36). Since 36÷4=9 exactly, the car 1,236 rolls smoothly with 4

Recall Trigger

Think 'back two wheels of a car' when checking divisibility by 4

Tags

• process
• formula

Topic

Factors and Multiples

Concept

LCM using prime factorization

Anchor Id

A15

Difficulty

hard

Memory Aid

The LCM Hotel needs to accommodate all guests (numbers) comfortably. The hotel manager takes the HIGHEST power of each prime factor from all numbers to ensure everyone fits. It's like booking the biggest room size that each family needs.

Anchor Type

micro_story

Why It Works

The hotel story explains why we take the highest powers - to accommodate all requirements

Example Usage

For LCM of 12 and 18: Hotel needs 2² rooms (for 12's family) and 3² rooms (for 18's family), so LCM = 2² × 3² = 36

Recall Trigger

Think 'LCM Hotel with biggest rooms' when finding least common multiple

Tags

• process
• formula

Topic

Fractions and Decimals

Concept

Converting fractions to decimals to percentages

Anchor Id

A16

Difficulty

medium

Memory Aid

FDP Chain: Fraction Divides to Decimal, then Decimal × 100 to Percentage. Remember: F→D (divide), D→P (×100), P→D (÷100), D→F (make fraction)

Anchor Type

mnemonic

Why It Works

The chain acronym creates a clear conversion pathway between all three forms

Example Usage

For ¾: F→D (3÷4=0.75), D→P (0.75×100=75%). Reverse: 75%→D (75÷100=0.75), D→F (75/100=¾)

Recall Trigger

Think 'FDP Chain' when converting between fractions, decimals, and percentages

Tags

• process
• definition

Topic

Divisibility Rules

Concept

Divisibility by 6

Anchor Id

A17

Difficulty

medium

Memory Aid

SIX = Sum (divisible by 3) + eXtra (even number). For a number to be divisible by 6, it must pass both the 3-test and 2-test.

Anchor Type

acronym

Why It Works

The acronym breaks down the compound rule into memorable components

Example Usage

For 342: Sum test (3+4+2=9, divisible by 3 ✓), eXtra test (ends in 2, even ✓), so 342 is divisible by 6

Recall Trigger

Think 'SIX = Sum + eXtra' when checking divisibility by 6

Tags

• process
• sequence

Topic

Order of Operations

Concept

Order of operations with nested grouping symbols

Anchor Id

A18

Difficulty

hard

Memory Aid

Nested groupings are like Russian nesting dolls (matryoshka) - you must open the innermost doll first, then work your way outward. Parentheses ( ) are the tiny inner doll, brackets [ ] are the middle doll, braces { } are the outer doll.

Anchor Type

analogy

Why It Works

The nesting doll analogy perfectly visualizes the inside-out approach to nested groupings

Example Usage

For {5 + [3 × (2 + 1)]}: Open inner doll (2+1=3), middle doll [3×3=9], outer doll {5+9=14}

Recall Trigger

Think 'Russian nesting dolls - innermost first' when seeing complex groupings

Tags

• process
• definition

Topic

Divisibility Rules

Concept

Divisibility by 11

Anchor Id

A19

Difficulty

hard

Memory Aid

Eleven is like a seesaw - alternating positions must balance. Add digits in odd positions, add digits in even positions, then check if their difference is 0 or divisible by 11. If balanced, the number works with 11.

Anchor Type

visual_association

Why It Works

The seesaw visual helps remember the alternating pattern and balance requirement

Example Usage

For 4,510: Odd positions (4+1=5), Even positions (5+0=5), Difference (5-5=0). Seesaw balanced, so divisible by 11

Recall Trigger

Think 'seesaw balance' when checking divisibility by 11

Tags

• definition
• classification

Topic

Factors and Multiples

Concept

Properties of multiples

Anchor Id

A20

Difficulty

easy

Memory Aid

Multiples are magic, here's what they do: Every number's a multiple of itself and one too! The smallest multiple is the number you see, They go on forever, infinitely free!

Anchor Type

rhyme

Why It Works

The rhyme encodes the four key properties in a memorable, musical pattern

Example Usage

For multiples of 7: 7 is multiple of itself (7×1=7), smallest is 7, they continue forever: 7,14,21,28...

Recall Trigger

Think 'multiples are magic' when listing properties of multiples

Formula

PEMDAS: P-E-M/D-A/S

Mnemonic

Please Excuse My Dear Ate Sally (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction)

When To Use

When evaluating any complex mathematical expression with multiple operations

What Each Part Means

P=Parentheses first, E=Exponents second, M/D=Multiplication and Division left to right, A/S=Addition and Subtraction left to right

Formula

Scientific Notation: a × 10^n (where 1 ≤ |a| < 10)

Mnemonic

Move decimal to make Mantissa between 1-10, Count moves for eXponent. Left moves = positive, Right moves = negative

When To Use

When expressing very large or very small numbers in compact form

What Each Part Means

a=mantissa (coefficient between 1-10), 10=base, n=exponent (number of decimal places moved)

Formula

|n| = n if n≥0, |n| = -n if n<0

Mnemonic

Absolute value Always Positive - mirror reflects only positive distances

When To Use

When finding distance from zero or removing negative signs

What Each Part Means

The absolute value bars |n| always give the positive distance from zero

Formula

GCF using prime factors: multiply all common factors with lowest powers

Mnemonic

Greatest Common Factor = Common factors with Least powers (GCF = CLp)

When To Use

When finding the largest number that divides two or more numbers evenly

What Each Part Means

Find prime factors of each number, identify common ones, use smallest power of each

Formula

LCM using prime factors: multiply all factors with highest powers

Mnemonic

Least Common Multiple = All factors with Highest powers (LCM = AHp)

When To Use

When finding the smallest number that is divisible by two or more numbers

What Each Part Means

Take all prime factors that appear, use the highest power of each factor

Chain Title

PEMDAS Order Steps

Recall Test

What operation comes after exponents but before addition in PEMDAS?

Memory Chain

Please Excuse My Dear Ate Sally - she always follows this order when cooking her famous adobo recipe

Items To Remember

• Parentheses
• Exponents
• Multiplication/Division
• Addition/Subtraction

Chain Title

Divisibility Rules for 2,3,4,5,6,9,10

Recall Test

Which divisibility rule requires checking if a number is both even and has digits that sum to a multiple of 3?

Memory Chain

Even Three-year-old Four-wheelers Stop at Six Nine-story buildings - a story connecting each rule's key feature

Items To Remember

• 2:even last digit
• 3:digit sum ÷ 3
• 4:last 2 digits ÷ 4
• 5:ends in 0 or 5
• 6:even AND ÷ 3
• 9:digit sum ÷ 9
• 10:ends in 0

Chain Title

Integer Operation Sign Rules

Recall Test

What is the result when you multiply or divide two numbers with different signs?

Memory Chain

Like attracts Like (same = positive), Opposites fight (different = negative), Works for both Multiply and Divide

Items To Remember

• Same signs = positive
• Different signs = negative
• This applies to both multiplication and division

Chain Title

Steps for Prime Factorization

Recall Test

After dividing repeatedly by 2, what should you do next in prime factorization?

Memory Chain

Small prime Starts, Divide repeatedly, Move to Next when stuck, Continue until One, Write the Product

Items To Remember

• Start with smallest prime (2)
• Divide repeatedly by same prime
• Move to next prime when no longer divisible
• Continue until quotient is 1
• Write as product of primes

Chain Title

Scientific Notation Conversion Steps

Recall Test

If you move the decimal point 3 places to the right, what sign should the exponent have?

Memory Chain

Place decimal, Count moves, Left = Positive, Right = Negative, Write the form

Items To Remember

• Place decimal after first non-zero digit
• Count places moved
• Left moves = positive exponent
• Right moves = negative exponent
• Write in a × 10^n form