Digital SAT · Math · Unit 3 · Problem Solving & Data

Lesson 3.1 · Percent, Ratio & Proportion

On the test: 2–4 questions a test — easy marks if every percent becomes a multiplier

Big idea. “Percent” means “per 100”, so p% is just the number p/100. Turn every percent into a MULTIPLIER and the words become arithmetic: “30% of x” is 0.30x, “increased by 20%” is ×1.20, “decreased by 25%” is ×0.75. A ratio a : b says the two amounts are a parts and b parts of the same size.

🧑‍🏫 Rule 1 · part = (p/100) × wholestep 1 of 4

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📋 The question · SAT · March US 2023 · Math 800 Book Q2
What is 90% of 80?
1. A)10
2. B)72
3. C)88
4. D)152
percent of
$90% of 80 = 0.9 \times 80 = 72$
March US 2023. “of” means multiply.

🧑‍🏫 Rule 2 · Percent of a percentstep 1 of 5

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📋 The question · SAT · May 2024 · Math 800 Book Q18
52% nonfiction; of the fiction, 75% westerns and the rest romance. 933 romance. Total books?
(type the answer)
the question
$52% nonfiction; fiction 75% westerns$
May 2024: 933 romance books. Total?

🎛 Move it · change after change

August US 2023: increase by 20%, then decrease by 25%. Slide the two changes and watch the multipliers MULTIPLY.

change 1+20% → ×1.20change 2-25% → ×0.75

start

100

× 1.20

120

× 0.75

Overall multiplier 1.20 × 0.75 = 0.9000 → net change -10.00%, NOT -5%. The second change is a percent of the NEW amount.

🧑‍🏫 Rule 3 · One change = one multiplierstep 1 of 5

1
increase
$+ 20% \Rightarrow \times 1.20$
Keep the 100% and add 20%.

Trap · adding percents

+20% then −25% is NOT −5%. And “270% of” the price is ×2.7, while “increased by 270%” would be ×3.7.

🧑‍🏫 Rule 4 · One sentence → one multiplicationstep 1 of 5

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📋 The question · SAT · March 2024 · Math 800 Book Q12
Speed A is 7,900% of speed C, and C is 0.008% of B. Which represents $a + b$ in terms of $c$ ?
1. A) $12, 579 c$
2. B) $8, 025 c$
3. C) $7, 908 c$
4. D) $2, 040 c$
the question
$a = 7900% of c, c = 0.008% of b$
March 2024: $a + b$ in terms of $c$ .

🧑‍🏫 Rule 5 · Two percents of the same thingstep 1 of 3

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📋 The question · SAT · June 2024 · Math 800 Book Q31
Mass A is 483% of B and 0.069% of C. If C is $p %$ of B, what is $\frac{p}{1000}$ ?
(type the answer)
the question
$A = 4.83 B = 0.00069 C$
June 2024: $C$ is $p %$ of $B$ ; find $\frac{p}{1000}$ .

🧑‍🏫 Rule 6 · Ratio = equal-sized partsstep 1 of 5

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📋 The question · SAT · June 2023 · Math 800 Book Q4
Green : blue tiles is 5 : 2. With 16 blue tiles, how many green?
(type the answer)
the question
$green : blue = 5 : 2, 16 blue$
June 2023.

🧑‍🏫 Rule 7 · Proportional = same multiplierstep 1 of 5

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📋 The question · SAT · June 2024 · Math 800 Book Q22
$p$ is proportional to $t$ ; $p = 2340$ when $t = 3120$ . $p$ when $t = 2496$ ?
1. A)1,716
2. B)1,872
3. C)3,276
4. D)3,328
the question
$p = 2340 at t = 3120$
June 2024: $p$ when $t = 2496$ ?

Real question 1SAT · December 2024 · Math 800 Book Q44type the answer

On a plot of land, 52.0% of the square footage is farmland and the rest is pasture. Buildings are on 21.5% of the farmland and 14.0% of the pasture. If buildings are on $p %$ of the plot, what is $p$ ?

🧑‍🏫 Rule · Percent change = (new − old) ÷ oldstep 1 of 3

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📋 The question · Gen Z Study
A price rose from $40 to $52. By what percent did it increase?
(type the answer)
change
$52 - 40 = 12$

🧑‍🏫 Rule · Reverse percent: divide by the multiplierstep 1 of 2

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📋 The question · Gen Z Study
After a 25% discount, a jacket costs $60. What was the original price?
(type the answer)
multiplier
$price \times 0.75 = 60$

Take with you

▸p% = p/100. “of” means multiply.
▸Part ÷ whole × 100 = percent; part ÷ (p/100) = whole.
▸Increase r% → ×(1 + r); decrease r% → ×(1 − r); successive changes MULTIPLY.
▸“is p% of” chains: write one equation per sentence, then substitute.
▸Ratios: find one part; proportions: find the constant multiplier.

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