CEUET Mathematics — Ratio & ProportionSlides
Revision slides for CEUET Mathematics — Ratio & Proportion. Structured for quick scanning, with one idea per slide and the key formulas called out clearly. Good for the final week before the CEUET 2026 when you want to refresh the whole chapter in under an hour.
Exam context
The Centro Escolar University Entrance Test is conducted by Centro Escolar University and is scheduled for Q3–Q4 2026. The Mathematics subtest is marked as "Core" in the official pattern, and Ratio & Proportion appears in position 2nd of 9 in the CEUET Mathematics review rotation. Passing mark: Competitive overall score. Recent CEUET 2026 papers have drawn roughly a meaningful share of questions from this subject.
Ratio & Proportion - Slides
Ratio and proportion are fundamental mathematical concepts that appear in nearly every UPCAT Math problem involving mixtures, scale drawings, speed, percentages, and more. This chapter will teach you to recognize, set up, and solve ratio and proportion problems with confidence. Master these concepts once, and many other mathematical topics become much easier to understand and solve.
Slides
Introduction to Ratio & Proportion
Ratio and proportion form the foundation for many mathematical applications. They help us compare quantities, solve real-world problems, and understand relationships between different values. In UPCAT, these concepts are tested both directly and indirectly through various problem types.
Notes
Start by helping students understand that ratios and proportions are tools for comparing and relating quantities. Emphasize their practical importance in everyday life and academic success.
Topic
Chapter Overview
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S1
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mermaid
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mindmap root((Ratio & Proportion)) Applications Mixtures Scale Drawings Speed Problems Percentages Unit Conversions Types Simple Ratios Proportions Direct Proportion Inverse Proportion Partitive Proportion Skills Needed Cross Multiplication Simplification Problem Recognition Unit Matching
Type
mermaid_mindmap
Description
A comprehensive overview of ratio and proportion concepts, showing their applications, types, and required skills
What is a Ratio?
Think of a ratio as a way to compare two things. Just like fractions, ratios can be simplified to their lowest terms. The key is that both quantities must be of the same type (both lengths, both weights, both amounts, etc.).
Notes
Emphasize that ratios must compare like quantities and that simplification makes calculations easier. Practice with various examples to build confidence.
Topic
Ratio Basics
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mermaid
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flowchart TD A[Given Ratio 12:18] --> B[Find GCD of 12 and 18] B --> C[GCD = 6] C --> D[Divide both terms by 6] D --> E[12÷6 : 18÷6] E --> F[Simplified Ratio 2:3] G[Three Ways to Write] --> H[Colon 3:5] G --> I[Fraction 3/5] G --> J[Words 3 to 5]
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mermaid_flowchart
Description
Flowchart showing how to simplify ratios and the three different ways to express them
Continued Ratios
Continued ratios extend the concept of simple ratios to multiple quantities. They're particularly useful when dividing something among multiple people or comparing multiple components of a mixture.
Notes
Help students see that continued ratios are like recipes - each number tells us how much of each ingredient or share to use relative to the others.
Topic
Advanced Ratios
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flowchart TD A[Continued Ratio 6:9:12] --> B[Find GCD of all terms] B --> C[GCD = 3] C --> D[Divide each term by 3] D --> E[6÷3 : 9÷3 : 12÷3] E --> F[Simplified Ratio 2:3:4] G[Total Parts] --> H[2 + 3 + 4 = 9 parts] H --> I[Each part represents 1/9 of total]
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mermaid_flowchart
Description
Process of simplifying continued ratios and understanding how they represent proportional shares
What is a Proportion?
A proportion is like an equation but with ratios. The cross-product rule is your most powerful tool - it allows you to solve for any missing term when you know three of the four values.
Notes
The cross-product rule is the foundation of proportion solving. Practice this method extensively as it appears in many UPCAT problems. Always verify answers by substituting back.
Topic
Proportion Fundamentals
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4
Mermaid Diagram
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flowchart TD A[Proportion a/b = c/d] --> B[Cross multiply] B --> C[a × d = b × c] C --> D[Solve for unknown] E[Example 3/4 = x/20] --> F[Cross multiply] F --> G[3 × 20 = 4 × x] G --> H[60 = 4x] H --> I[x = 15] J[fa:fa-check Verify] --> K[3/4 = 0.75] J --> L[15/20 = 0.75] K --> M[Equal ✓] L --> M
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mermaid_flowchart
Description
Step-by-step process of solving proportions using cross-multiplication and verification
Direct Proportion - Worked Example
Direct proportion means 'same direction' - if you double one value, the other doubles too. If you triple one, the other triples. The ratio between them stays constant.
Notes
Emphasize the 'same direction' concept. When solving, always check if your answer makes logical sense - more items should cost more money.
Topic
Direct Proportion
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S5
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mermaid
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5
Mermaid Diagram
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flowchart TD A[Problem: 3 pens cost ₱45<br/>How much do 7 pens cost?] --> B[Set up proportion] B --> C[3 pens / ₱45 = 7 pens / x] C --> D[Cross multiply] D --> E[3x = 45 × 7] E --> F[3x = 315] F --> G[x = ₱105] H[fa:fa-lightbulb Key Insight] --> I[More pens = More cost<br/>Same direction] J[Verify] --> K[3:45 = 1:15] J --> L[7:105 = 1:15] K --> M[Both ratios equal ✓] L --> M
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mermaid_flowchart
Description
Complete solution process for a direct proportion problem with verification
Inverse Proportion - Worked Example
Inverse proportion means 'opposite direction' - if you double one value, the other becomes half. If you triple one, the other becomes one-third. Their product stays constant.
Notes
Help students identify inverse relationships by asking: 'If I double the first, does the second halve?' Common UPCAT topics include workers/time and speed/time problems.
Topic
Inverse Proportion
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flowchart TD A[Problem: 6 workers finish job in 8 days<br/>How long for 12 workers?] --> B[Find constant k] B --> C[k = 6 × 8 = 48 worker-days] C --> D[Use formula xy = k] D --> E[12 workers × x days = 48] E --> F[x = 48 ÷ 12 = 4 days] G[fa:fa-lightbulb Key Insight] --> H[More workers = Less time<br/>Opposite direction] I[Check] --> J[6 × 8 = 48] I --> K[12 × 4 = 48] J --> L[Same constant ✓] K --> L
Type
mermaid_flowchart
Description
Complete solution process for an inverse proportion problem showing the constant relationship
Identifying Direct vs Inverse Proportion
The ability to quickly identify whether a problem involves direct or inverse proportion is crucial for UPCAT success. This skill determines which formula and approach to use.
Notes
This identification skill is often what separates high scorers from average scorers in UPCAT. Practice with many examples until recognition becomes automatic.
Topic
Problem Recognition
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flowchart TD A[Read the Problem] --> B{If I double the first<br/>what happens to second?} B -->|Doubles| C[Direct Proportion<br/>y = kx] B -->|Halves| D[Inverse Proportion<br/>xy = k] B -->|Unsure| E[Look for Keywords] E --> F[workers, pipes, machines<br/>together, shared] F --> G[Probably Inverse] E --> H[cost, distance, amount<br/>more, less] H --> I[Probably Direct] C --> J[Set up: a/b = c/d] D --> K[Set up: a×b = c×d]
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mermaid_flowchart
Description
Decision tree for identifying whether a proportion problem is direct or inverse
Partitive Proportion - Step by Step
Partitive proportion is like dividing a pizza according to how much each person should get. The ratio tells you the relative sizes of each portion.
Notes
Partitive proportion appears frequently in UPCAT word problems about sharing money, dividing inheritance, or mixing ingredients. Always verify that parts add up to the original total.
Topic
Partitive Proportion
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S8
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Mermaid Diagram
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flowchart TD A[Problem: Divide ₱840 in ratio 2:3:7] --> B[Step 1: Add ratio parts] B --> C[2 + 3 + 7 = 12 parts] C --> D[Step 2: Find one share] D --> E[₱840 ÷ 12 = ₱70 per part] E --> F[Step 3: Calculate each portion] F --> G[A gets: 2 × ₱70 = ₱140] F --> H[B gets: 3 × ₱70 = ₱210] F --> I[C gets: 7 × ₱70 = ₱490] G --> J[fa:fa-check Verify] H --> J I --> J J --> K[₱140 + ₱210 + ₱490 = ₱840 ✓]
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mermaid_flowchart
Description
Complete step-by-step solution for partitive proportion with verification
Percentages as Ratios in Disguise
Don't treat percentage problems as completely separate from ratios. They're the same concept! This connection makes both topics easier to understand and solve.
Notes
This connection helps students see that they already know how to solve percentage problems if they understand proportions. It reduces the mental burden of learning separate methods.
Topic
Percentages and Ratios
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S9
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mermaid
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9
Mermaid Diagram
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flowchart TD A[25% of 80 = ?] --> B[Convert to ratio] B --> C[25% = 25/100] C --> D[Set up proportion] D --> E[25/100 = x/80] E --> F[Cross multiply] F --> G[100x = 25 × 80] G --> H[100x = 2000] H --> I[x = 20] J[Alternative Method] --> K[25% = 0.25] K --> L[0.25 × 80 = 20] I --> M[fa:fa-check Same Answer] L --> M
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mermaid_flowchart
Description
Two methods for solving percentage problems using ratio/proportion concepts
Common UPCAT Traps and How to Avoid Them
UPCAT test makers deliberately include these common mistakes as answer choices. Recognizing and avoiding these traps can significantly improve your score.
Notes
Teach students to be extra careful with units and to always do a sanity check on their answers. Many UPCAT questions are designed to catch these specific mistakes.
Topic
Common Mistakes
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S10
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mermaid
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flowchart TD A[Read Problem Carefully] --> B{Units Match?} B -->|No| C[Convert to Same Units] B -->|Yes| D[Identify Relationship Type] C --> D D --> E{Direct or Inverse?} E -->|Direct| F[Set up a/b = c/d] E -->|Inverse| G[Set up ab = cd] F --> H[Cross Multiply Carefully] G --> H H --> I[Solve for Unknown] I --> J[fa:fa-warning Check Answer Makes Sense] J --> K[Verify by Substitution] L[fa:fa-times Common Mistakes] --> M[Unit mismatch] L --> N[Ratio vs total] L --> O[Wrong relationship type] L --> P[Arithmetic errors]
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mermaid_flowchart
Description
Problem-solving flowchart highlighting common traps and verification steps
Mixed Practice Problem 1: Recipe Scaling
Recipe scaling is a classic direct proportion problem. Each ingredient increases proportionally with the number of servings.
Notes
Show students both the scale factor method and individual proportions. Both give the same answer, but scale factor is often faster for multiple ingredients.
Topic
Practice Problems
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S11
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flowchart TD A[Recipe: 6 servings needs<br/>2 cups flour, 3 eggs, 1 cup milk] --> B[Want: 10 servings] B --> C[Scale factor = 10/6 = 5/3] C --> D[Flour: 2 × 5/3 = 10/3 = 3⅓ cups] C --> E[Eggs: 3 × 5/3 = 15/3 = 5 eggs] C --> F[Milk: 1 × 5/3 = 5/3 = 1⅔ cups] G[Alternative Method] --> H[Set up proportions] H --> I[2/6 = x/10 → x = 3⅓] H --> J[3/6 = y/10 → y = 5] H --> K[1/6 = z/10 → z = 1⅔] D --> L[fa:fa-check Same Results] I --> L
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mermaid_flowchart
Description
Two solution methods for recipe scaling: scale factor multiplication and individual proportions
Mixed Practice Problem 2: Work and Time
Work problems are typically inverse proportion. The total amount of work (measured in worker-days) stays the same regardless of how it's distributed.
Notes
Work problems are very common in UPCAT. Help students remember that the total work (worker-days, machine-hours, etc.) remains constant in these problems.
Topic
Practice Problems
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S12
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mermaid
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12
Mermaid Diagram
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flowchart TD A[8 workers finish in 15 days<br/>How many workers for 10 days?] --> B[Identify: Inverse Proportion] B --> C[More workers = Less time] C --> D[Find total work] D --> E[8 workers × 15 days = 120 worker-days] E --> F[Set up equation] F --> G[x workers × 10 days = 120 worker-days] G --> H[Solve for x] H --> I[x = 120 ÷ 10 = 12 workers] J[Verify] --> K[8 × 15 = 120] J --> L[12 × 10 = 120] K --> M[Same total work ✓] L --> M
Type
mermaid_flowchart
Description
Complete solution for inverse proportion work problem with verification
Mixed Practice Problem 3: Map Scale
Map scale problems are direct proportion. The ratio between map distance and actual distance remains constant throughout the map.
Notes
Map problems often appear in UPCAT. Remind students to check that their answer makes sense - larger map distances should correspond to larger actual distances.
Topic
Practice Problems
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S13
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13
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flowchart TD A[Map: 3 cm represents 75 km<br/>Find: distance for 7 cm] --> B[Set up proportion] B --> C[3 cm / 75 km = 7 cm / x km] C --> D[Cross multiply] D --> E[3x = 75 × 7] E --> F[3x = 525] F --> G[x = 175 km] H[Alternative: Scale Factor] --> I[Scale = 75 km ÷ 3 cm = 25 km/cm] I --> J[7 cm × 25 km/cm = 175 km] G --> K[fa:fa-check Both methods give 175 km] J --> K L[Check Units] --> M[cm maps to km ✓] L --> N[Larger map distance → Larger actual distance ✓]
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mermaid_flowchart
Description
Map scale problem solved using both proportion and scale factor methods
Quick Problem-Solving Strategy
Having a systematic approach saves time and reduces errors in UPCAT. This strategy works for virtually all ratio and proportion problems you'll encounter.
Notes
This systematic approach should become automatic with practice. Emphasize that the few seconds spent on proper setup saves minutes on calculation and checking.
Topic
Problem-Solving Strategy
Slide Id
S14
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mermaid
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14
Mermaid Diagram
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flowchart TD A[Read Problem Completely] --> B[Identify Key Information] B --> C{Direct or Inverse?} C -->|Same Direction| D[Direct: y = kx<br/>Set up a/b = c/d] C -->|Opposite Direction| E[Inverse: xy = k<br/>Set up a×b = c×d] D --> F[Check Units Match] E --> F F -->|No| G[Convert Units] F -->|Yes| H[Cross Multiply & Solve] G --> H H --> I[Get Numerical Answer] I --> J[fa:fa-lightbulb Does Answer Make Sense?] J -->|No| K[Check Work for Errors] J -->|Yes| L[fa:fa-check Verify by Substitution] K --> H L --> M[Final Answer]
Type
mermaid_flowchart
Description
Comprehensive problem-solving strategy flowchart for all ratio and proportion problems
Summary and Key Takeaways
Ratio and proportion mastery opens doors to solving mixture problems, scale drawings, speed-time-distance, percentage problems, and much more. These concepts appear throughout the UPCAT Math section.
Notes
This summary ties everything together. Encourage students to practice problems from different contexts to build flexibility and confidence for the UPCAT.
Topic
Chapter Summary
Slide Id
S15
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mermaid
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15
Mermaid Diagram
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mindmap root((Ratio & Proportion Mastery)) Key Formulas Cross Product: ad = bc Direct: y = kx Inverse: xy = k Partitive: Total ÷ Sum of Parts Problem Types Cost and Quantity Workers and Time Speed Distance Time Recipe Scaling Map Scales Mixtures Success Strategies Identify Type First Check Units Always Cross Multiply Carefully Verify Answer Makes Sense Practice Different Contexts
Type
mermaid_mindmap
Description
Comprehensive mind map summarizing all key concepts, formulas, problem types, and success strategies
References
- UPCAT Math Review Materials - Ratio and Proportion Chapter
- Philippine Mathematics Curriculum Standards for Senior High School
- UPCAT Previous Years' Question Papers - Mathematics Section
- Mathematical Problem-Solving Strategies for Philippine College Entrance Exams
In summary
Ratio and proportion are fundamental mathematical skills that will serve you well beyond the UPCAT. They provide a logical framework for solving many real-world problems and appear in various forms throughout mathematics. By mastering the techniques of identifying problem types, setting up proportions correctly, and using cross-multiplication systematically, you'll be well-prepared for the wide variety of ratio and proportion questions that appear on the UPCAT. Remember: consistent practice with different problem contexts builds the recognition skills that make these problems quick and manageable on test day.
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