Arithmetic — Multiples, Factors, PEMDAS, Fractions & Decimals - Memory anchors
Memory techniques transform abstract arithmetic concepts into unforgettable mental images and stories. By creating vivid associations, mnemonics, and visual patterns, students can instantly recall formulas, procedures, and key facts during high-pressure exams. These memory anchors tap into your brain's natural ability to remember stories, patterns, and familiar experiences, making complex mathematical concepts as easy to remember as your favorite song lyrics.
Memory anchors
PEMDAS Order of Operations
Memory aid
Please Excuse My Dear Aunt Sally - Picture your favorite tita (aunt) serving you a meal in this exact order: Parentheses (she serves soup in bowls first), Exponents (she adds extra rice on top), Multiplication/Division (she multiplies the ulam portions and divides them equally), Addition/Subtraction (she adds more vegetables and removes what you don't like)
Why it works
Associates mathematical operations with a familiar family scenario that Filipino students experience regularly during meals
Example usage
When solving 2 + 3 × 4², think 'Tita serves soup (parentheses) first, then extra rice (exponents: 4² = 16), then multiplies ulam (3 × 16 = 48), finally adds (2 + 48 = 50)'
Recall trigger
Think of your tita serving food in order
Finding GCF using Prime Factorization
Memory aid
Finding GCF is like finding the common ingredients in your favorite adobo recipes from two different lolas. List all ingredients (prime factors) for each recipe, then keep only the common ones with the smallest amount used. For example, if Lola A uses 3 bay leaves and Lola B uses 2 bay leaves, you can only use 2 bay leaves in your combined recipe.
Why it works
Connects abstract math to familiar cooking scenarios, making the 'common factors' concept tangible
Example usage
For GCF of 24 and 30: 24 = 2³×3, 30 = 2×3×5. Common ingredients are 2 and 3. Take the smallest amount: 2¹×3¹ = 6
Recall trigger
Think of two lolas comparing their adobo ingredients
Finding LCM using Prime Factorization
Memory aid
Finding LCM is like planning a bayanihan (community work) where you need enough supplies for everyone. Take ALL different ingredients (prime factors) from both recipes, but use the LARGEST amount of each ingredient mentioned. If one recipe needs 3 bay leaves and another needs 2, bring 3 bay leaves to satisfy both.
Why it works
Uses the familiar concept of community preparation where you need maximum supplies
Example usage
For LCM of 24 and 30: 24 = 2³×3, 30 = 2×3×5. Take maximum of each: 2³×3¹×5¹ = 8×3×5 = 120
Recall trigger
Think of preparing supplies for bayanihan - take the maximum of each item
Prime vs Composite Numbers
Memory aid
In the Kingdom of Numbers, Prime numbers are like hermit crabs - they live alone and can only be divided by 1 and themselves. Composite numbers are like families in a bahay kubo - they have many divisors living together. The number 1 is the village chief who doesn't belong to either group, and 0 is the empty lot.
Why it works
Creates a memorable visual story that clearly distinguishes between number types
Example usage
When asked if 17 is prime, think: 'Is 17 a hermit crab? Yes, it only has factors 1 and 17, so it lives alone - it's prime!'
Recall trigger
Picture the Kingdom of Numbers with hermit crabs and families
Divisibility Rule for 3
Memory aid
Add the digits, don't you wait, if the sum divides by three, then the number's really great! Like a jeepney route that's planned, where all passengers (digits) must add up to stations divisible by 3 to make the trip complete.
Why it works
Rhythmic pattern makes the rule memorable and the jeepney analogy provides familiar context
Example usage
For 243: 2+4+3 = 9, and 9÷3 = 3, so 243 is divisible by 3. Like counting 9 passengers on a jeepney!
Recall trigger
Think of passengers boarding a jeepney - count them up
Converting Mixed Numbers to Improper Fractions
Memory aid
MAD method: Multiply, Add, Drop! Picture a basketball player (the whole number) holding basketballs (numerator) while standing on a court divided into sections (denominator). To find total basketballs: Multiply player number × court sections, Add the basketballs he's already holding, Drop the answer over the same court sections.
Why it works
Visual sports imagery makes the abstract process concrete and memorable
Example usage
For 3²⁄₅: Player #3 on a 5-section court holding 2 balls. MAD: 3×5=15, 15+2=17, Drop over 5 = ¹⁷⁄₅
Recall trigger
Picture a basketball player on a sectioned court
Adding Fractions with Different Denominators
Memory aid
Two sari-sari store owners want to combine their rice supplies. Owner A has ¾ sack, Owner B has ⅖ sack. But their sacks are different sizes! They must first find identical sacks (LCD) that both portions can fit into. ¾ becomes ¹⁵⁄₂₀ and ⅖ becomes ⁸⁄₂₀. Now they can add: 15 + 8 = 23 portions in 20-portion sacks = ²³⁄₂₀ sacks total.
Why it works
Familiar business scenario makes the need for common denominators logical
Example usage
For ¾ + ⅖: Find LCD (20), convert (¹⁵⁄₂₀ + ⁸⁄₂₀), add numerators (23), result = ²³⁄₂₀
Recall trigger
Think of two store owners combining different-sized supplies
Multiplying Fractions
Memory aid
FANT: Fraction multiplication is so FANTASTIC! Just multiply Across (numerators together, denominators together). No need for common denominators - it's like crossing the street straight across, not diagonally!
Why it works
Simple acronym with a clear visual of crossing straight across
Example usage
For ²⁄₃ × ⁴⁄₅: Multiply across - (2×4)/(3×5) = ⁸⁄₁₅. Straight across like crossing the street!
Recall trigger
Think FANT and crossing straight across the street
Dividing Fractions
Memory aid
Dividing fractions, here's the key - flip the second, then multiply! Like doing tinikling dance steps: when the second bamboo pole comes down, you flip it up and step-step (multiply) through!
Why it works
Traditional Filipino dance provides memorable physical action for the flip-and-multiply rule
Example usage
For ³⁄₄ ÷ ²⁄₅: Flip the second (²⁄₅ becomes ⁵⁄₂), then multiply: ³⁄₄ × ⁵⁄₂ = ¹⁵⁄₈
Recall trigger
Think of flipping bamboo poles in tinikling dance
Decimal Place Values
Memory aid
Think of the decimal point as the Rizal Monument in Luneta. To the left (west) are the whole number provinces: ones, tens, hundreds. To the right (east) are the decimal barangays: tenths, hundredths, thousandths. The farther you go from the monument, the smaller/larger the place value becomes.
Why it works
Uses familiar Manila landmark to create spatial memory for place values
Example usage
In 423.567, the 5 is in the first barangay east of Rizal (tenths place), worth 5/10 = 0.5
Recall trigger
Picture Rizal Monument with provinces on left, barangays on right
Converting Fractions to Decimals
Memory aid
Journey through your house: Start at the door (fraction), walk to the kitchen (divide numerator by denominator), cook using long division, serve the decimal result on a plate. If the division doesn't end, you have a repeating decimal - like a broken record player in your living room.
Why it works
Creates a memorable journey through familiar spaces with clear action steps
Example usage
For ³⁄₈: Door (³⁄₈) → Kitchen (3 ÷ 8) → Cook with long division → Serve 0.375 on plate
Recall trigger
Start your house journey at the front door with a fraction
Rounding Decimals
Memory aid
The Digit Detective Story: You're a detective looking at the digit in the rounding place. Look to your right at the next digit - this is your witness. If the witness is 5 or more, they're telling the truth, so round UP (add 1 to your digit). If the witness is 4 or less, they're lying, so round DOWN (keep your digit the same). All digits to the right of your rounding place disappear - they've left the scene!
Why it works
Detective story makes the decision-making process memorable and logical
Example usage
Round 3.247 to nearest tenth: Detective looks at 2 (tenths), witness 4 is lying, so keep 2. Answer: 3.2
Recall trigger
Picture yourself as a detective questioning digit witnesses
Properties of Real Numbers
Memory aid
ADAM DI CA: Associative, Distributive, Additive identity, Multiplicative identity, Distributive, Identity, Commutative, Additive inverse. Like remembering the names of your barkada members for group work assignments!
Why it works
Creates a memorable name-like acronym that sounds Filipino
Example usage
When asked about properties, recall ADAM DI CA and expand: A=Associative (grouping), D=Distributive, etc.
Recall trigger
Think of your friend ADAM DI CA joining your study group
Prime Factorization Process
Memory aid
Build a family tree, but for numbers! Start with the big kuya (original number) at the top. He has two anak (factors) below him. Keep splitting each anak until you reach the bunso (prime numbers) who can't be split anymore. These bunso are your prime factors - the youngest generation of the number family.
Why it works
Filipino family structure provides familiar hierarchical framework
Example usage
For 60: Kuya 60 has anak 6 and 10, 6 splits to bunso 2 and 3, 10 splits to bunso 2 and 5. Prime factors: 2, 2, 3, 5
Recall trigger
Picture a family tree with kuya at top, bunso at bottom
Comparing Fractions
Memory aid
Comparing fractions is like comparing heights of students from different classes. You can't directly compare unless they're standing on the same floor level (common denominator). Cross multiplication is like using a measuring tape that works across different floors - multiply the numerator of each fraction by the denominator of the other to get comparable measurements.
Why it works
Height comparison is intuitive, and the measuring tape analogy explains cross multiplication
Example usage
Compare ³⁄₄ vs ²⁄₃: Cross multiply (3×3=9, 4×2=8). Since 9>8, we have ³⁄₄ > ²⁄₃
Recall trigger
Picture students on different floors needing a measuring tape
Absolute Value
Memory aid
The Security Guard Story: Absolute value bars | | are like security guards at a mall entrance. No matter which direction you come from (positive or negative), the security guard only cares about your distance from the entrance (zero). If you're 5 steps to the left (-5) or 5 steps to the right (+5), the guard records your distance as simply 5 steps.
Why it works
Familiar mall security scenario makes the distance-from-zero concept clear
Example usage
For |-7|: Security guard sees you're 7 steps away from entrance (zero), records distance as 7
Recall trigger
Picture security guards measuring distance from mall entrance
Divisibility by 6
Memory aid
6 = 2×3 Marriage: For a number to be divisible by 6, it must be 'married' to both 2 and 3. Like a Filipino wedding, both families (2 and 3) must approve! Check: Is it even? (divisible by 2) AND Do digits sum to multiple of 3? Both must say 'Oo' for the marriage to happen!
Why it works
Marriage metaphor makes the 'both conditions must be met' rule memorable
Example usage
For 42: Even? Yes (family 2 approves). Digit sum 4+2=6, divisible by 3? Yes (family 3 approves). Wedding approved - 42÷6 = 7!
Recall trigger
Think of a wedding where both families must approve
Number System Hierarchy
Memory aid
Picture the Philippine archipelago: Natural numbers are like main islands (1,2,3...), Whole numbers add the surrounding water (includes 0), Integers add the ocean depths (negative numbers), Rational numbers add all the boats and ships (fractions), Irrational numbers are the mysterious sea creatures (π, √2), Real numbers include everything in our ocean world, and Complex numbers add the sky above (imaginary).
Why it works
Uses familiar geographic metaphor to show expanding number system
Example usage
When classifying -3/4: It's in the rational ocean (fraction), which includes the integer depths and natural islands
Recall trigger
Picture the Philippine islands expanding to include ocean and sky
Revision game
I'm the Filipino tita who serves food in a specific order to help you remember mathematical operations
Answer
Aunt Sally (PEMDAS)
Memory link
A1 - Please Excuse My Dear Aunt Sally mnemonic
Like hermit crabs in the Kingdom of Numbers, I live alone with only 1 and myself as company
Answer
Prime numbers
Memory link
A4 - Kingdom of Numbers story
I'm the basketball method where you Multiply, Add, and Drop to convert mixed numbers
Answer
MAD method
Memory link
A6 - Basketball player visual association
I'm the security guard who only cares about your distance from zero, not which direction you came from
Answer
Absolute value
Memory link
A16 - Mall security guard story
Like two sari-sari store owners combining rice supplies, we need the same size containers before adding
Answer
Common denominators for adding fractions
Memory link
A7 - Sari-sari store owners story
I'm the tinikling dance move where you flip the second bamboo pole before stepping through
Answer
Dividing fractions (flip and multiply)
Memory link
A9 - Tinikling dance analogy
I'm the detective who questions digit witnesses to decide whether to round up or down
Answer
Rounding decimals process
Memory link
A12 - Digit Detective story
For me to approve a number for division by 6, both family 2 and family 3 must say 'Oo' at the wedding
Answer
Divisibility by 6 rule
Memory link
A17 - Filipino wedding approval analogy
Formula mnemonics
LCM × GCF = Product of the two numbers
Mnemonic
Love Conquers Great Fear - Product! Picture lovers (LCM and GCF) whose love multiplied equals the product of their family numbers. The stronger their love bond, the more their families are connected!
When to use
To verify your LCM and GCF calculations, or to find one when you know the other
What each part means
LCM (Least Common Multiple) × GCF (Greatest Common Factor) always equals the product of the original two numbers
Mixed number to improper: (whole × denominator) + numerator / denominator
Mnemonic
MAD formula: Multiply, Add, Drop! Basketball player (whole) × court sections (denominator) + balls held (numerator), all over court sections (denominator)
When to use
Converting mixed numbers to improper fractions for easier calculation
What each part means
Whole number multiplied by denominator, plus the existing numerator, all over the same denominator
Cross multiplication for comparing fractions: a/b vs c/d → compare a×d vs b×c
Mnemonic
X marks the spot! Draw an X across the fractions - multiply along each arm of the X to compare. Like treasure hunting where X shows you the way!
When to use
Comparing fractions with different denominators
What each part means
Multiply numerator of first fraction by denominator of second, compare to numerator of second by denominator of first
a/b ÷ c/d = a/b × d/c
Mnemonic
Keep Change Flip (KCF): Keep the first fraction, Change division to multiplication, Flip the second fraction. Like driving - Keep your lane, Change gears, Flip your turn signal!
When to use
Dividing fractions
What each part means
Division by a fraction equals multiplication by its reciprocal
Prime factorization method for GCF: multiply common prime factors with lowest powers
Mnemonic
Common Ground Minimum Power: Take only the common prime factors and use the minimum power each appears. Like sharing - take only what everyone has, in the smallest amount anyone has!
When to use
Finding GCF using prime factorization
What each part means
Find prime factors that appear in all numbers, use the lowest exponent for each common factor
Prime factorization method for LCM: multiply all prime factors with highest powers
Mnemonic
All Maximum Power: Take ALL prime factors from all numbers, use the maximum power each appears. Like party planning - bring everything anyone mentioned, in the largest quantity anyone suggested!
When to use
Finding LCM using prime factorization
What each part means
Include every prime factor that appears in any number, using the highest exponent for each factor
Quick recall chains
PEMDAS Order of Operations
Recall test
What operation comes after exponents in 2 + 3 × 4²?
Memory chain
Please Excuse My Dear Aunt Sally - Picture your tita serving a traditional meal in perfect order: bowls (parentheses) first, extra rice piled high (exponents), portions multiplied and divided fairly, then final additions and subtractions of condiments
Items to remember
- Parentheses
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Steps to Check if Number is Prime
Recall test
What's the first step to check if 97 is prime?
Memory chain
Square Root Detective Agency: First FIND the square root boundary, LIST all prime suspects, TEST each suspect as potential factor, IF none work, declare the number PRIME and close the case!
Items to remember
- Find square root
- List prime numbers up to square root
- Test each prime as factor
- If no factors found, number is prime
Converting Fractions to Decimals
Recall test
After setting up division for ⅜, what's the next step?
Memory chain
Kitchen Division Recipe: SET up your ingredients (division), DIVIDE the main ingredient (numerator) by servings (denominator), ADD the decimal seasoning, CONTINUE cooking until done, IDENTIFY if it's a complete dish (terminating) or needs repeating!
Items to remember
- Set up division
- Divide numerator by denominator
- Add decimal point
- Continue dividing
- Identify terminating or repeating
Prime Factorization Steps
Recall test
After finding two factors of a number, what should you check next?
Memory chain
Family Tree Building: START with the family patriarch (number), FIND his two children (factors), CHECK if children can have kids (composite) or are bunso (prime), CONTINUE building branches for composite children, LIST all the bunso (prime factors) at the bottom
Items to remember
- Start with the number
- Find two factors
- Check if factors are prime
- Continue factoring composite factors
- List all prime factors
Adding Fractions with Different Denominators
Recall test
After finding the LCD for ¼ + ⅓, what's the next step?
Memory chain
Sari-sari Store Merger: FIND common container size (LCD), CONVERT all portions to same container, ADD the portions together, KEEP using the same container size, SIMPLIFY by using smaller containers if possible
Items to remember
- Find LCD
- Convert fractions
- Add numerators
- Keep same denominator
- Simplify if needed
Diagrams
Arithmetic Concepts Overview
Complete overview of all arithmetic topics showing relationships between concepts
Prime Number Detection Process
Step-by-step flowchart for determining if a number is prime or composite
PEMDAS Decision Tree
Decision tree for applying PEMDAS order of operations correctly
Common UPCAT Arithmetic Question Types
Distribution of arithmetic question types commonly found in UPCAT exams
Problem-Solving Timeline for Complex Fraction Operations
Timeline showing the sequential steps for solving fraction problems systematically