PSHS NCE Ratios and Proportions Reviewer

TEACHER ABI PSHS NCE · QUANTITATIVE ABILITY

Ratios and Proportions

Compare quantities, build equivalent ratios, and solve proportion problems without guessing.

Grade 6–7 friendlyEquivalent ratiosRegular practiceQuick Fire + Mastery

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Ratios and Proportions

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A ratio compares two quantities

A basket has 6 red balls and 9 blue balls.

red : blue = 6 : 9 = 2 : 3

The ratio simplifies just like a fraction.

Order matters. Red to blue is 2:3. Blue to red is 3:2.

DO IT FAST

Use MATCH → SCALE → CHECK

1. MATCH: Keep the quantities in the same order.
2. SCALE: Multiply or divide both parts by the same number.
3. CHECK: Make sure both sides of the proportion changed by the same factor.

Example: 3:5 = 6:10 because both parts were multiplied by 2.

WORKED EXAMPLES

Six patterns you should recognize

1. Simplify a ratio

12 : 18

Divide both by 6.

2 : 3

2. Build an equivalent ratio

4:7 = ? : 21

7 became 21, so multiply by 3.

4 × 3 = 12

12 : 21

3. Find a missing term

5:8 = 15:x

5 became 15, so multiply by 3. Then 8 × 3 = 24.

x = 24

4. Part-to-whole

A class has 8 boys and 12 girls. What is the ratio of boys to all students?

8 : 20 = 2 : 5

2 : 5

5. Rate as a ratio

A car travels 180 km in 3 hours.

180 ÷ 3 = 60 km/h

60 km per hour

6. Use a proportion in context

3 notebooks cost ₱75. At the same rate, how much do 5 notebooks cost?

One notebook costs ₱25, so 5 cost ₱125.

₱125

TRY WITH ME

Find the missing number

4 : 6 = 10 : x

1. 4 became 10. That is ×2.5.
2. Do the same to 6.
3. 6 × 2.5 = 15.

x = 15

COMMON TRAPS

Watch out for these

Switching the order.
If the question asks cats to dogs, do not answer dogs to cats.

Changing only one part.
Equivalent ratios must scale both parts by the same factor.

Confusing part-to-part with part-to-whole.
Read what the ratio is actually comparing.

Cross-multiplying too soon.
If the scale factor is obvious, use it. It is often faster.

REGULAR PRACTICE

Build the skill

These mix simplifying ratios, equivalent ratios, missing terms, rates, and short word problems.

QUICK FIRE

Can you scale it fast?

Five short questions. Use the easiest scale factor you can see.

Question 1 of 5

FRESH MASTERY CHECK

Can you do it without hints?

Score 5/5 to verify this competency. If you miss one, a fresh set will be ready.

NEED HELP?

Ratios still getting mixed up?

Send Teacher Abi the problem that confused you and your result. I can help you spot the easiest scale factor.

Message Teacher Abi

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