P4: Percent — Concepts, Formulas, and Practice

Big idea: Every percent problem fits one of three patterns based on “Part = Rate × Base,” where the rate is the percent written as a decimal.

1. What is r% of B? Part = (r% as decimal) × B
2. P is what percent of B? Rate = P ÷ B, then convert to percent by multiplying by 100%
3. P is r% of what number? Solve P = (r% as decimal) × B for B → B = P ÷ (r% as decimal)

Guided Examples

1) What is 35% of 390?

1. 35% as a decimal is 0.35.
2. Part = 0.35 × 390 = 136.5

Answer: 136.5

2) 200 is what percent of 460? (one decimal place)

1. Rate = 200 ÷ 460 ≈ 0.43478
2. Percent = 0.43478 × 100% = 43.478%
3. Rounded to one decimal place: 43.5%

Answer: 43.5%

3) 230 is 55% of what number? (one decimal place)

1. 230 = 0.55 × B
2. B = 230 ÷ 0.55 ≈ 418.1818…
3. Rounded to one decimal place: 418.2

Answer: 418.2

4) A restaurant bill is $60. A 17% tip = ?

1. 17% as a decimal is 0.17.
2. Tip = 0.17 × 60 = 10.2

Answer: $10.20

5) A shirt costs $25 with 30% off. Sale price = ? (before tax)

1. Discount = 0.30 × 25 = 7.5
2. Sale price = 25 − 7.5 = 17.5

Answer: $17.50

6) Joyce paid $150, which was 65% of the original price. Original price = ?

1. 150 = 0.65 × Original
2. Original = 150 ÷ 0.65 ≈ 230.76923
3. Nearest cent: $230.77

Answer: $230.77

7) Tracey paid $200 for an item originally $610. What percent of the original price did Tracey pay? (one decimal place)

1. Rate = 200 ÷ 610 ≈ 0.32786885
2. Percent = 0.32786885 × 100% ≈ 32.786885%
3. Rounded to one decimal place: 32.8%

Answer: 32.8%

8) What percent of 130 is 91?

1. Rate = 91 ÷ 130 = 0.7
2. Percent = 0.7 × 100% = 70%

Answer: 70%

9) What number is 20% of 140?

1. 20% as a decimal is 0.20.
2. Part = 0.20 × 140 = 28

Answer: 28

10) 96 is 80% of what number?

1. 96 = 0.80 × N
2. N = 96 ÷ 0.80 = 120

Answer: 120

11) 20% of 130 is what number?

1. 20% as a decimal is 0.20.
2. 0.20 × 130 = 26

Answer: 26

Percent in Context: Discounts & Markups

• Discount price: Sale = Original × (1 − rate). Example: 25 × (1 − 0.30) = 17.5
• Markup price: New = Original × (1 + rate)
• Percent change: (new − old) ÷ old × 100%

Fraction–Percent Bridge (minimal LaTeX only)

When fractions appear with percents, convert one form to the other and proceed.

Example A: Use fractions; give a reduced fraction.

[latex]\frac{7}{8}[/latex] + 0.8 → convert 0.8 to a fraction: [latex]\frac{8}{10} = \frac{4}{5}[/latex].

Add: [latex]\frac{7}{8} + \frac{4}{5} = \frac{35}{40} + \frac{32}{40} = \frac{67}{40}[/latex].

Answer: [latex]\frac{67}{40}[/latex]

Example B: Multiply; give a decimal to the nearest hundredth.

[latex]\frac{7}{8}[/latex] · 1.1 → write 1.1 as a fraction: [latex]\frac{11}{10}[/latex].

Multiply: [latex]\frac{7}{8} \cdot \frac{11}{10} = \frac{77}{80}[/latex] = 0.9625 ≈ 0.96

Answer: 0.96

Quick Checklist

• Convert the percent to a decimal before multiplying (r% → r ÷ 100).
• Label the Part and the Base (the “of” number) before you compute.
• For “what percent,” do Part ÷ Base, then multiply by 100%.
• Round only at the end to the place value requested.