Ratio and Proportion UPCAT Reviewer: Lesson and Practice

TEACHER ABI UPCAT MATHEMATICS

Ratio and Proportion

Identify what stays constant before building the proportion.

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Ratio and Proportion

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A proportion says two ratios describe the same relationship

A ratio compares quantities in the same order. A proportion states that two ratios are equal.

ab = cd → ad = bc

In direct variation, both quantities change by the same factor. In inverse variation, one increases while the other decreases so their product stays constant.

Respect the order

If the ratio is boys:girls, keep boys in the first position throughout.

Find one part

For sharing problems, add the ratio terms, divide the total by that sum, then multiply by the required number of parts.

DO IT FAST

Name the relationship before using a formula

Direct: more servings require more ingredients, so use the same scale factor. Inverse: more workers require less time for the same job, so keep workers×time constant.

Why it works

The calculation depends on whether the quantities grow together, move oppositely, or represent parts of one fixed total.

WORKED EXAMPLES

Five forms you should recognize

1. Sharing

Problem: Divide ₱1,260 in the ratio 3:4. Find the smaller share.

1,260(3 + 4) = 180; 3(180) = ₱540

Why: The total is divided into seven equal ratio parts.

2. Recipe scale

Problem: Three cups serve 8 people. How many cups serve 20 at the same rate?

3(208) = 7.5 cups

Why: Servings and ingredients vary directly.

3. Map scale

Problem: At 1 cm:250,000 cm, what does 7.2 cm represent?

7.2(250,000) = 1,800,000 cm = 18 km

Why: Apply the map scale, then convert the resulting units.

4. Inverse variation

Problem: Eight workers need 15 days. How long would 12 workers need at the same rate?

8(15) = 12t → t = 10 days

Why: The fixed job requires the same number of worker-days.

5. Changing ratio

Problem: Boys:girls = 3:5. After 6 boys join, the ratio is 3:4. Find the original total.

(3k + 6)(5k) = 34 → k = 8 → total = 64

Why: Adding students changes one part of the ratio but not the original number of girls.

COMMON TRAPS

Check before you commit

• Reversing the order of a ratio
• Treating a part-to-part ratio as a fraction of the whole
• Cross-multiplying quantities with mismatched units
• Using direct proportion when there is a fixed starting charge
• Assuming every worker problem is perfectly proportional
• Using the side-length scale factor for area without squaring it

FIVE-FORM SKILL CHECK

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Foundations

Build the core procedure with immediate explanations.

Core Practice

Use mixed forms with less scaffolding.

UPCAT-Style Transfer

Apply the competency in unfamiliar representations.

FRESH MASTERY CHECK

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QUICK ANSWERS

Ratio and Proportion FAQ

How do I know whether to add ratio terms?

Add them when the quantities are parts of one stated total.

When is a relationship directly proportional?

When it has the form y = kx and passes through the origin.

Why are workers and time usually inverse?

For one fixed job at equal productivity, increasing workers reduces the required time while worker-hours stay constant.

RELATED COMPETENCIES

Continue your mathematics review.

Fractions and DecimalsPercentSimilar TrianglesWork-Rate Problems

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