PSHS NCE Percent Reviewer

TEACHER ABI PSHS NCE · QUANTITATIVE ABILITY

Percent

Turn fractions and decimals into percents, find a percent of a number, and solve simple increase, decrease, discount, and score problems.

Grade 6–7 friendlyFast percent tricksRegular practiceQuick Fire + Mastery

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Percent

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Percent means “out of 100”

25% = 25/100 = 1/4 = 0.25

These all describe the same amount.

Useful percent facts to know:
50% = half
25% = one fourth
75% = three fourths
10% = divide by 10
1% = divide by 100

DO IT FAST

Use FRIENDLY PERCENTS first

1. 10%: Move the decimal point one place left.
2. 5%: Find 10%, then take half.
3. 20%: Find 10%, then double it.
4. 25%: Find one fourth.
5. 50%: Find half.
6. Other percents: Convert to a decimal or fraction when that is easier.

WORKED EXAMPLES

Six patterns you should recognize

1. Fraction to percent

3/4 = ?%

3 ÷ 4 = 0.75 = 75%

75%

2. Decimal to percent

0.36 = ?%

0.36 × 100 = 36%

36%

3. Find a percent of a number

What is 20% of 80?

10% of 80 is 8. Double it.

16

4. Find the whole

15 is 25% of what number?

25% is one fourth. If one fourth is 15, the whole is 15 × 4.

60

5. Discount

A ₱500 item is 20% off.

20% of ₱500 = ₱100.

₱500 − ₱100 = ₱400

Sale price: ₱400

6. Percent score

A student got 18 out of 20 correct.

18/20 = 0.9 = 90%

90%

TRY WITH ME

Find 15% without a long formula

What is 15% of 200?

1. 10% of 200 = 20.
2. 5% is half of 10%, so 5% of 200 = 10.
3. 15% = 10% + 5%.

30

COMMON TRAPS

Watch out for these

Forgetting percent means out of 100.
35% = 35/100 = 0.35.

Finding the discount but not the sale price.
If the question asks what you pay, subtract the discount.

Moving the decimal the wrong way.
Decimal to percent: multiply by 100.

Using a long method when a friendly percent works.
For 25%, 50%, 10%, and 5%, mental math is often faster.

REGULAR PRACTICE

Build the skill

These mix conversions, percent of a number, finding the whole, discounts, and test scores.

QUICK FIRE

Can you see the friendly percent?

Five short questions. Use mental math whenever possible.

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.

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Percent Change and Successive Discounts UPCAT Reviewer: Lesson and Practice

TEACHER ABI UPCAT MATHEMATICS

Percent Change and Successive Discounts

Use multipliers to compare changes quickly and avoid adding successive percentages.

5-10 minute lesson27 original questionsAdaptive practiceSaves progress

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Percent Change and Successive Discounts

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Percent change acts on a base amount

Convert each percent change into a multiplier. An increase of r% uses 1+r; a decrease uses 1−r, with r written as a decimal. For successive changes, multiply the factors in the order they occur. To recover an original amount, divide the final amount by the combined multiplier.

New value

new = original × multiplier

Original value

original = new ÷ multiplier

DO IT FAST

See the multiplier shortcut in a real discount

Problem: A ₱1,000 bag is discounted by 20%, then by another 10%. What is the final price?

Recognize: Each discount acts on the price left after the previous discount.

Do it fast: 20% off means keep 80%, or ×0.80. Then 10% off means keep 90%, or ×0.90.

₱1,000 × 0.80 × 0.90 = ₱720.

The overall discount is ₱280, or 28%—not 30%.

Why it works

The second 10% is taken from ₱800, not from the original ₱1,000. That is why successive percentages must be multiplied.

WORKED EXAMPLES

Five forms you should recognize

1. Percent increase

A ₱750 fee increases by 12%.

₱750(1.12)=₱840

2. Single discount

A ₱1,600 item is 25% off, so the customer pays 75%.

₱1,600(0.75)=₱1,200

3. Successive discounts

Twenty percent off followed by 10% off leaves:

0.80(0.90)=0.72

The customer pays 72%, so the effective discount is 28%—not 30%.

4. Recover the original

A fee becomes ₱920 after a 15% increase.

original=₱9201.15=₱800

5. Equal increase and decrease

A 20% increase followed by a 20% decrease gives:

1.20(0.80)=0.96

The final value is 4% below the original because the two percentages use different bases.

COMMON TRAPS

Check before you commit

• Adding successive discounts
• Using the percent as the final multiplier
• Subtracting a percent from pesos
• Multiplying backward when finding the original
• Assuming equal increase and decrease cancel
• Rounding too early

FIVE-FORM SKILL CHECK

Do you need the lesson-or just practice?

One original question in each form recommends your next step. It does not yet verify mastery.

CHOOSE YOUR PRACTICE

Work at the level you need.

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

Ready to verify this competency?

A score of 5/5 verifies mastery. An unsuccessful attempt loads a different five-form bank.

QUICK ANSWERS

Percent Change and Successive Discounts FAQ

Why are there two mastery sets?

A different five-question set appears after an unsuccessful attempt so memorizing one set does not verify mastery.

Does 5/5 mean I never need this topic again?

It verifies this competency today; revisit it later through mixed practice.

RELATED COMPETENCIES

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