Math Studio — Grade 7

UNIT 01

Percent Problems

Percents describe parts of 100. Grade 7 applies them to real-life: discounts, tax, tips, and percent change.

Discount: Sale price = Original − (% × Original) · Tax/Tip: Total = Original + (% × Original) · % Change: (New − Old) ÷ Old × 100

$80 jacket, 20% off → 0.20 × 80 = $16 off → Sale price = $64

Q 01

A pair of sneakers costs $120. They are on sale for 25% off. What is the sale price?

Discount = 0.25 × 120 = $30. Sale price = 120 − 30.

Q 02

A meal costs $45. The sales tax is 8%. What is the total price with tax? (round to 2 decimal places)

Tax = 0.08 × 45 = $3.60. Total = 45 + 3.60.

Q 03

A book's price went from $25 to $30. What is the percent increase?

% Change = (30 − 25) ÷ 25 × 100 = 5/25 × 100.

UNIT 02

Operations with Rational Numbers

Rational numbers include all integers, fractions, and decimals — positive and negative. The rules for multiplying and dividing negatives are crucial.

Adding negatives: −3 + (−5) = −8 (same sign → add, keep sign).
Signs when multiplying: negative × negative = positive. negative × positive = negative.
Remember: Two negatives multiplied always make a positive.

(−4) × (−7) → +28 | (−6) × 3 → −18

Q 04

What is −8 + (−5)?

Q 05

What is (−9) × (−4)?

Q 06

Evaluate: (−5) × 3 + (−2)

Multiply first: (−5)×3 = −15. Then −15 + (−2) = −17.

UNIT 03

Multi-Step Equations

Grade 7 equations take two or more steps to solve. The distributive property and combining like terms are your main tools.

Two-step equation: Undo addition/subtraction first, then multiplication/division.
Distributive property: a(b + c) = ab + ac. Distribute before combining.

2(x + 3) = 14 → 2x + 6 = 14 → 2x = 8 → x = 4

Q 07

Solve for x: 2x + 5 = 17

Q 08

Solve for x: 3(x − 4) = 15

Divide both sides by 3 first: x − 4 = 5. Then add 4 to both sides.

Q 09

Solve for x: −2x + 10 = 4

Subtract 10: −2x = −6. Divide by −2 (remember: neg ÷ neg = pos).

UNIT 04

Circles & Angles

Circumference and area of circles use π (pi). Supplementary angles add to 180°. Complementary angles add to 90°.

Circumference = 2πr · Area of circle = πr² · Use π ≈ 3.14
Supplementary angles sum to 180° · Complementary angles sum to 90°

C = 2πr A = πr² π ≈ 3.14

Q 10

A circle has a radius of 7 cm. What is its circumference? Use π = 3.14. Round to 2 decimal places.

C = 2 × 3.14 × 7 = 6.28 × 7 = 43.96 cm

Q 11

A circle has a diameter of 10 inches. What is its area? Use π = 3.14.

Diameter = 10, so radius = 5. Area = 3.14 × 5² = 3.14 × 25.

Q 12

Two angles are supplementary. One angle measures 47°. What is the measure of the other angle?

UNIT 05

Probability

Probability measures how likely an event is. Theoretical probability is what math predicts. Experimental probability is what you actually observe in trials.

Theoretical P(event) = favorable outcomes ÷ total outcomes
Experimental P(event) = times event occurred ÷ total trials
Probability is always between 0 (impossible) and 1 (certain).

Bag: 2 red, 3 blue, 5 green → P(red) = 2/10 → = 1/5

Q 13

A bag holds 4 red marbles, 3 blue marbles, and 3 green marbles. What is the probability of picking a red marble? (enter as a fraction like a/b)

Total marbles = 4+3+3 = 10. P(red) = 4/10 (also accepted: 2/5).

Q 14

You roll a standard 6-sided die 60 times and get a 3 exactly 12 times. What is the experimental probability of rolling a 3? (as a fraction)

Experimental P = times it happened ÷ total rolls = 12/60 (also 1/5).

Q 15

The spinner above has 4 equal sections. If you spin it 200 times, how many times would you theoretically expect to land on Purple?

P(Purple) = 1/4. Expected = 1/4 × 200 = 50 times.