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Grade 7 · Maths · curriculum collection

Grade 7 Maths, Common Core domains

8 units for Grade 7 maths, organised by Common Core domain: Ratios and Proportional Relationships, The Number System, Expressions and Equations, Geometry, Statistics and Probability. Each unit has a short lesson, a practice worksheet and a review worksheet, both with answer keys.

8 units16 worksheets192 questions with answers
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Answer-checked and approved on 29 October 2026

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Aligned by StudyBrix at domain level. Not an official publication of, or endorsed by, the standards' authors. Framework: Common Core State Standards for Mathematics.

Units in teaching order

01

7.RP Ratios and Proportional Relationships

Percentages

Percent of a quantity, percent change, successive percent changes and finding the whole from a percent.

Short lesson: Find the original whole

Study guide for Grades 6 to 9: 2 worked examples and 2 practice questions. Divide by the percentage as a decimal, not by the whole-number percent.

whole = part ÷ (p/100)

Divide by the percentage as a decimal, not by the whole-number percent.

Worked example

40% of a number is 392. What is the number?

392 ÷ 0.4 = 980

Answer: 980

Read the full study guide

Worksheets

A practice worksheet and a review worksheet, 12 and 12 questions.

Worksheets (PDF)Answer keys (PDF)
Practice worksheet: 12 questions

  1. Find 56% of 300.

  2. A value increases from 140 to 191.8. What is the percentage increase?

  3. A quantity starts at 1600, increases by 50%, then decreases by 40%. Find the final quantity.

  4. 10% of a number is 14. What is the number?

  5. Find 69% of 680.

  6. A value increases from 610 to 695.4. What is the percentage increase?

  7. A quantity starts at 4200, increases by 50%, then decreases by 20%. Find the final quantity.

  8. 25% of a number is 290. What is the number?

  9. Find 12% of 760.

  10. A value increases from 640 to 665.6. What is the percentage increase?

  11. A quantity starts at 7500, increases by 20%, then decreases by 10%. Find the final quantity.

  12. 50% of a number is 550. What is the number?

Answer key
  1. 168 56/100 × 300 = 168
  2. 37 % (191.8 − 140) ÷ 140 × 100 = 37%
  3. 1440 1600 × 1.5 × 0.6 = 1440
  4. 140 14 ÷ 0.1 = 140
  5. 469.2 69/100 × 680 = 469.2
  6. 14 % (695.4 − 610) ÷ 610 × 100 = 14%
  7. 5040 4200 × 1.5 × 0.8 = 5040
  8. 1160 290 ÷ 0.25 = 1160
  9. 91.2 12/100 × 760 = 91.2
  10. 4 % (665.6 − 640) ÷ 640 × 100 = 4%
  11. 8100 7500 × 1.2 × 0.9 = 8100
  12. 1100 550 ÷ 0.5 = 1100
Review worksheet: 12 questions

  1. A quantity starts at 3500, increases by 10%, then decreases by 25%. Find the final quantity.

  2. Find 19% of 470.

  3. A value increases from 160 to 187.2. What is the percentage increase?

  4. 75% of a number is 795. What is the number?

  5. A quantity starts at 300, increases by 50%, then decreases by 40%. Find the final quantity.

  6. Find 26% of 430.

  7. A value increases from 780 to 959.4. What is the percentage increase?

  8. 50% of a number is 300. What is the number?

  9. A quantity starts at 1000, increases by 25%, then decreases by 10%. Find the final quantity.

  10. Find 15% of 350.

  11. A value increases from 680 to 863.6. What is the percentage increase?

  12. 10% of a number is 56. What is the number?

Answer key
  1. 2887.5 3500 × 1.1 × 0.75 = 2887.5
  2. 89.3 19/100 × 470 = 89.3
  3. 17 % (187.2 − 160) ÷ 160 × 100 = 17%
  4. 1060 795 ÷ 0.75 = 1060
  5. 270 300 × 1.5 × 0.6 = 270
  6. 111.8 26/100 × 430 = 111.8
  7. 23 % (959.4 − 780) ÷ 780 × 100 = 23%
  8. 600 300 ÷ 0.5 = 600
  9. 1125 1000 × 1.25 × 0.9 = 1125
  10. 52.5 15/100 × 350 = 52.5
  11. 27 % (863.6 − 680) ÷ 680 × 100 = 27%
  12. 560 56 ÷ 0.1 = 560

Related ready-made worksheets: Grade 7 Percentages worksheet

02

7.RP Ratios and Proportional Relationships

Ratio and proportion problems

Proportional relationships and sharing in a ratio.

Short lesson: Equations, expressions and equivalent steps

Study guide for Grades 6 to 9: 4 key ideas, including expression or equation, balance and distribute; 2 worked examples and 3 practice questions. Preserve equality and check a solution in the original equation.

  • Expression or equation. An expression represents a value; an equation asserts equality between two expressions.
  • Balance. Applying the same valid operation to both sides preserves an equation. Division by zero is never valid.
  • Distribute. a(b + c) = ab + ac. The multiplier acts on every term inside the brackets.
  • Check. Substitute a proposed solution into the original equation, not just a rearranged line.

Worked example

Which item is an equation?

The equals sign asserts that two expressions have equal values.

Answer: 3x + 2 = 11

Read the full study guide

Worksheets

A practice worksheet and a review worksheet, 12 and 12 questions.

Worksheets (PDF)Answer keys (PDF)
Practice worksheet: 12 questions

  1. Split 196 in the ratio 5:2. What is the first share?

  2. y = kx. When x = 22, y = 264. Find y when x = 57.

  3. Split 80 in the ratio 11:9. What is the first share?

  4. y = kx. When x = 26, y = 78. Find y when x = 59.

  5. Split 88 in the ratio 4:7. What is the first share?

  6. y = kx. When x = 28, y = 252. Find y when x = 73.

  7. Split 72 in the ratio 10:8. What is the first share?

  8. y = kx. When x = 14, y = 112. Find y when x = 50.

  9. Split 400 in the ratio 9:7. What is the first share?

  10. y = kx. When x = 14, y = 112. Find y when x = 55.

  11. Split 117 in the ratio 9:4. What is the first share?

  12. y = kx. When x = 2, y = 14. Find y when x = 58.

Answer key
  1. 140 196 ÷ (5 + 2) = 28; 5 × 28 = 140
  2. 684 k = 264/22 = 12; y = 12 × 57 = 684
  3. 44 80 ÷ (11 + 9) = 4; 11 × 4 = 44
  4. 177 k = 78/26 = 3; y = 3 × 59 = 177
  5. 32 88 ÷ (4 + 7) = 8; 4 × 8 = 32
  6. 657 k = 252/28 = 9; y = 9 × 73 = 657
  7. 40 72 ÷ (10 + 8) = 4; 10 × 4 = 40
  8. 400 k = 112/14 = 8; y = 8 × 50 = 400
  9. 225 400 ÷ (9 + 7) = 25; 9 × 25 = 225
  10. 440 k = 112/14 = 8; y = 8 × 55 = 440
  11. 81 117 ÷ (9 + 4) = 9; 9 × 9 = 81
  12. 406 k = 14/2 = 7; y = 7 × 58 = 406
Review worksheet: 12 questions

  1. y = kx. When x = 29, y = 435. Find y when x = 77.

  2. Split 56 in the ratio 6:2. What is the first share?

  3. y = kx. When x = 17, y = 221. Find y when x = 40.

  4. Split 204 in the ratio 8:9. What is the first share?

  5. y = kx. When x = 7, y = 91. Find y when x = 43.

  6. Split 176 in the ratio 7:9. What is the first share?

  7. y = kx. When x = 12, y = 144. Find y when x = 38.

  8. Split 95 in the ratio 12:7. What is the first share?

  9. y = kx. When x = 27, y = 243. Find y when x = 58.

  10. Split 500 in the ratio 8:12. What is the first share?

  11. y = kx. When x = 9, y = 45. Find y when x = 86.

  12. Split 234 in the ratio 2:7. What is the first share?

Answer key
  1. 1155 k = 435/29 = 15; y = 15 × 77 = 1155
  2. 42 56 ÷ (6 + 2) = 7; 6 × 7 = 42
  3. 520 k = 221/17 = 13; y = 13 × 40 = 520
  4. 96 204 ÷ (8 + 9) = 12; 8 × 12 = 96
  5. 559 k = 91/7 = 13; y = 13 × 43 = 559
  6. 77 176 ÷ (7 + 9) = 11; 7 × 11 = 77
  7. 456 k = 144/12 = 12; y = 12 × 38 = 456
  8. 60 95 ÷ (12 + 7) = 5; 12 × 5 = 60
  9. 522 k = 243/27 = 9; y = 9 × 58 = 522
  10. 200 500 ÷ (8 + 12) = 25; 8 × 25 = 200
  11. 430 k = 45/9 = 5; y = 5 × 86 = 430
  12. 52 234 ÷ (2 + 7) = 26; 2 × 26 = 52

Related ready-made worksheets: Grade 7 Algebra worksheet

03

7.NS The Number System

Integer operations

Adding integers, subtracting integers and multiplying integers.

Short lesson: Subtract signed integers

Study guide for Grades 6 to 8: 2 worked examples and 2 practice questions. Subtracting a negative is adding its opposite.

a − b = a + (−b)

Subtracting a negative is adding its opposite.

Worked example

(41) − (-53) = ?

(41) + (53) = 94

Answer: 94

Read the full study guide

Worksheets

A practice worksheet and a review worksheet, 12 and 12 questions.

Worksheets (PDF)Answer keys (PDF)
Practice worksheet: 12 questions

  1. (-145) + 21 = ?

  2. (-65) − (70) = ?

  3. (-24) × (-10) = ?

  4. (-39) + 44 = ?

  5. (-59) − (-92) = ?

  6. (-21) × (-3) = ?

  7. (-92) + 3 = ?

  8. (-38) − (59) = ?

  9. (-33) × (-6) = ?

  10. (-140) + 6 = ?

  11. (-56) − (32) = ?

  12. (-16) × (-32) = ?

Answer key
  1. -124 (-145) + 21 = -124
  2. -135 (-65) + (-70) = -135
  3. 240 (-24) × (-10) = 240
  4. 5 (-39) + 44 = 5
  5. 33 (-59) + (92) = 33
  6. 63 (-21) × (-3) = 63
  7. -89 (-92) + 3 = -89
  8. -97 (-38) + (-59) = -97
  9. 198 (-33) × (-6) = 198
  10. -134 (-140) + 6 = -134
  11. -88 (-56) + (-32) = -88
  12. 512 (-16) × (-32) = 512
Review worksheet: 12 questions

  1. (-41) − (-40) = ?

  2. (-27) + 106 = ?

  3. (-27) × (-19) = ?

  4. (-63) − (-10) = ?

  5. (-21) + 5 = ?

  6. (-15) × (-10) = ?

  7. (-97) − (21) = ?

  8. (-92) + 125 = ?

  9. (-35) × (-34) = ?

  10. (1) − (6) = ?

  11. (-141) + 143 = ?

  12. (-34) × (-32) = ?

Answer key
  1. -1 (-41) + (40) = -1
  2. 79 (-27) + 106 = 79
  3. 513 (-27) × (-19) = 513
  4. -53 (-63) + (10) = -53
  5. -16 (-21) + 5 = -16
  6. 150 (-15) × (-10) = 150
  7. -118 (-97) + (-21) = -118
  8. 33 (-92) + 125 = 33
  9. 1190 (-35) × (-34) = 1190
  10. -5 (1) + (-6) = -5
  11. 2 (-141) + 143 = 2
  12. 1088 (-34) × (-32) = 1088

Related ready-made worksheets: Grade 7 Arithmetic worksheet

04

7.NS The Number System

Dividing fractions

Dividing fractions.

Short lesson: Subtract mixed numbers

Study guide for Grades 4 to 7: 2 worked examples and 2 practice questions. Convert to improper fractions; then subtract with a common denominator.

w a/b = (wb + a)/b

Convert to improper fractions; then subtract with a common denominator.

Worked example

Calculate 7 1/4 − 5 2/4. Give a fraction in simplest form.

(29 − 22)/4 = 7/4

Answer: 7/4

Read the full study guide

Worksheets

A practice worksheet and a review worksheet, 12 and 12 questions.

Worksheets (PDF)Answer keys (PDF)
Practice worksheet: 12 questions

  1. 9/5 ÷ 5/12 = ?

  2. 10/20 ÷ 1/12 = ?

  3. 6/7 ÷ 2/11 = ?

  4. 9/17 ÷ 4/3 = ?

  5. 4/10 ÷ 5/3 = ?

  6. 11/18 ÷ 5/13 = ?

  7. 1/8 ÷ 10/2 = ?

  8. 2/17 ÷ 9/18 = ?

  9. 12/13 ÷ 4/5 = ?

  10. 9/8 ÷ 12/20 = ?

  11. 3/2 ÷ 4/17 = ?

  12. 1/17 ÷ 5/19 = ?

Answer key
  1. 108/25 9/5 × 12/5 = 108/25
  2. 6 10/20 × 12/1 = 6
  3. 33/7 6/7 × 11/2 = 33/7
  4. 27/68 9/17 × 3/4 = 27/68
  5. 6/25 4/10 × 3/5 = 6/25
  6. 143/90 11/18 × 13/5 = 143/90
  7. 1/40 1/8 × 2/10 = 1/40
  8. 4/17 2/17 × 18/9 = 4/17
  9. 15/13 12/13 × 5/4 = 15/13
  10. 15/8 9/8 × 20/12 = 15/8
  11. 51/8 3/2 × 17/4 = 51/8
  12. 19/85 1/17 × 19/5 = 19/85
Review worksheet: 12 questions

  1. 2/15 ÷ 6/10 = ?

  2. 12/11 ÷ 10/3 = ?

  3. 2/10 ÷ 7/9 = ?

  4. 6/17 ÷ 3/15 = ?

  5. 3/18 ÷ 12/7 = ?

  6. 11/19 ÷ 4/7 = ?

  7. 9/7 ÷ 12/7 = ?

  8. 9/15 ÷ 3/9 = ?

  9. 6/16 ÷ 4/19 = ?

  10. 12/17 ÷ 10/8 = ?

  11. 9/8 ÷ 12/13 = ?

  12. 7/17 ÷ 5/6 = ?

Answer key
  1. 2/9 2/15 × 10/6 = 2/9
  2. 18/55 12/11 × 3/10 = 18/55
  3. 9/35 2/10 × 9/7 = 9/35
  4. 30/17 6/17 × 15/3 = 30/17
  5. 7/72 3/18 × 7/12 = 7/72
  6. 77/76 11/19 × 7/4 = 77/76
  7. 3/4 9/7 × 7/12 = 3/4
  8. 9/5 9/15 × 9/3 = 9/5
  9. 57/32 6/16 × 19/4 = 57/32
  10. 48/85 12/17 × 8/10 = 48/85
  11. 39/32 9/8 × 13/12 = 39/32
  12. 42/85 7/17 × 6/5 = 42/85

Related ready-made worksheets: Grade 7 Fractions worksheet

05

7.EE Expressions and Equations

Algebra

Two-step equations, evaluating expressions, one-step equations and combining like terms.

Short lesson: Combine like terms

Study guide for Grades 6 to 9: 2 worked examples and 2 practice questions. Only terms with the same variable part can be combined this way.

ax + bx = (a + b)x

Only terms with the same variable part can be combined this way.

Worked example

Find the coefficient of x after simplifying 32x + 33x.

(32 + 33)x = 65x

Answer: 65

Read the full study guide

Worksheets

A practice worksheet and a review worksheet, 12 and 12 questions.

Worksheets (PDF)Answer keys (PDF)
Practice worksheet: 12 questions

  1. Solve for x: 10x + 5 = 285

  2. Find the coefficient of x after simplifying 12x + 37x.

  3. Evaluate 5x + 30 when x = 15.

  4. Solve for x: 3x = -81

  5. Solve for x: 20x + 80 = 20

  6. Find the coefficient of x after simplifying 6x + 9x.

  7. Evaluate 5x + 25 when x = -13.

  8. Solve for x: 30x = -90

  9. Solve for x: 3x + 38 = 89

  10. Find the coefficient of x after simplifying 17x + 30x.

  11. Evaluate 6x + 25 when x = -7.

  12. Solve for x: 26x = -494

Answer key
  1. 28 10x = 285 − 5 = 280; x = 28
  2. 49 (12 + 37)x = 49x
  3. 105 5 × (15) + 30 = 105
  4. -27 x = -81 ÷ 3 = -27
  5. -3 20x = 20 − 80 = -60; x = -3
  6. 15 (6 + 9)x = 15x
  7. -40 5 × (-13) + 25 = -40
  8. -3 x = -90 ÷ 30 = -3
  9. 17 3x = 89 − 38 = 51; x = 17
  10. 47 (17 + 30)x = 47x
  11. -17 6 × (-7) + 25 = -17
  12. -19 x = -494 ÷ 26 = -19
Review worksheet: 12 questions

  1. Solve for x: 6x + 28 = -44

  2. Evaluate 4x + 5 when x = 0.

  3. Find the coefficient of x after simplifying 5x + 33x.

  4. Solve for x: 26x = 910

  5. Solve for x: 5x + 47 = 82

  6. Evaluate 15x + 4 when x = 14.

  7. Find the coefficient of x after simplifying 25x + 4x.

  8. Solve for x: 17x = 680

  9. Solve for x: 9x + 49 = 103

  10. Evaluate 8x + 14 when x = 13.

  11. Find the coefficient of x after simplifying 16x + 20x.

  12. Solve for x: 8x = 40

Answer key
  1. -12 6x = -44 − 28 = -72; x = -12
  2. 5 4 × (0) + 5 = 5
  3. 38 (5 + 33)x = 38x
  4. 35 x = 910 ÷ 26 = 35
  5. 7 5x = 82 − 47 = 35; x = 7
  6. 214 15 × (14) + 4 = 214
  7. 29 (25 + 4)x = 29x
  8. 40 x = 680 ÷ 17 = 40
  9. 6 9x = 103 − 49 = 54; x = 6
  10. 118 8 × (13) + 14 = 118
  11. 36 (16 + 20)x = 36x
  12. 5 x = 40 ÷ 8 = 5

Related ready-made worksheets: Grade 7 Algebra worksheet

06

7.EE Expressions and Equations

Powers & roots

Whole-number exponents.

Short lesson: Evaluate powers

Study guide for Grades 6 to 9: 2 worked examples and 2 practice questions. The exponent counts factors, not additions.

aⁿ = a × a × … × a (n factors)

The exponent counts factors, not additions.

Worked example

9^5 = ?

9 × 9 × 9 × 9 × 9 = 59049

Answer: 59049

Read the full study guide

Worksheets

A practice worksheet and a review worksheet, 12 and 12 questions.

Worksheets (PDF)Answer keys (PDF)
Practice worksheet: 12 questions

  1. 10^5 = ?

  2. 8^4 = ?

  3. 7^3 = ?

  4. 9^2 = ?

  5. 9^3 = ?

  6. 8^2 = ?

  7. 5^2 = ?

  8. 7^2 = ?

  9. 2^3 = ?

  10. 10^3 = ?

  11. 3^2 = ?

  12. 12^3 = ?

Answer key
  1. 100000 10 × 10 × 10 × 10 × 10 = 100000
  2. 4096 8 × 8 × 8 × 8 = 4096
  3. 343 7 × 7 × 7 = 343
  4. 81 9 × 9 = 81
  5. 729 9 × 9 × 9 = 729
  6. 64 8 × 8 = 64
  7. 25 5 × 5 = 25
  8. 49 7 × 7 = 49
  9. 8 2 × 2 × 2 = 8
  10. 1000 10 × 10 × 10 = 1000
  11. 9 3 × 3 = 9
  12. 1728 12 × 12 × 12 = 1728
Review worksheet: 12 questions

  1. 11^2 = ?

  2. 6^3 = ?

  3. 12^4 = ?

  4. 6^4 = ?

  5. 4^2 = ?

  6. 11^5 = ?

  7. 11^4 = ?

  8. 12^2 = ?

  9. 9^5 = ?

  10. 3^5 = ?

  11. 4^5 = ?

  12. 5^4 = ?

Answer key
  1. 121 11 × 11 = 121
  2. 216 6 × 6 × 6 = 216
  3. 20736 12 × 12 × 12 × 12 = 20736
  4. 1296 6 × 6 × 6 × 6 = 1296
  5. 16 4 × 4 = 16
  6. 161051 11 × 11 × 11 × 11 × 11 = 161051
  7. 14641 11 × 11 × 11 × 11 = 14641
  8. 144 12 × 12 = 144
  9. 59049 9 × 9 × 9 × 9 × 9 = 59049
  10. 243 3 × 3 × 3 × 3 × 3 = 243
  11. 1024 4 × 4 × 4 × 4 × 4 = 1024
  12. 625 5 × 5 × 5 × 5 = 625
07

7.G Geometry

Geometry

Area of trapezoids, scale factors and area, circumference of circles and area of circles.

Short lesson: Scale factors and area

Study guide for Grades 7 to 10: 2 worked examples and 2 practice questions. A length scale factor k changes area by k squared.

new area = old area × k²

A length scale factor k changes area by k squared.

Worked example

A shape has area 64 cm². All lengths are multiplied by 2. Find the new area in cm².

64 × 2² = 256

Answer: 256 cm²

Read the full study guide

Worksheets

A practice worksheet and a review worksheet, 12 and 12 questions.

Worksheets (PDF)Answer keys (PDF)
Practice worksheet: 12 questions

  1. A trapezoid has parallel sides 20 cm and 3 cm and height 7 cm. Find its area in cm².

  2. A shape has area 7 cm². All lengths are multiplied by 9. Find the new area in cm².

  3. A circle has radius 51 cm. Its area is kπ cm². Find k.

  4. A circle has radius 71 cm. Its circumference is kπ cm. Find k.

  5. A trapezoid has parallel sides 30 cm and 2 cm and height 18 cm. Find its area in cm².

  6. A shape has area 24 cm². All lengths are multiplied by 3. Find the new area in cm².

  7. A circle has radius 64 cm. Its area is kπ cm². Find k.

  8. A circle has radius 25 cm. Its circumference is kπ cm. Find k.

  9. A trapezoid has parallel sides 17 cm and 13 cm and height 14 cm. Find its area in cm².

  10. A shape has area 26 cm². All lengths are multiplied by 7. Find the new area in cm².

  11. A circle has radius 43 cm. Its area is kπ cm². Find k.

  12. A circle has radius 73 cm. Its circumference is kπ cm. Find k.

Answer key
  1. 80.5 cm² (20 + 3) × 7 ÷ 2 = 80.5
  2. 567 cm² 7 × 9² = 567
  3. 2601 A = π × 51² = 2601π → k = 2601
  4. 142 C = 2 × π × 71 = 142π
  5. 288 cm² (30 + 2) × 18 ÷ 2 = 288
  6. 216 cm² 24 × 3² = 216
  7. 4096 A = π × 64² = 4096π → k = 4096
  8. 50 C = 2 × π × 25 = 50π
  9. 210 cm² (17 + 13) × 14 ÷ 2 = 210
  10. 1274 cm² 26 × 7² = 1274
  11. 1849 A = π × 43² = 1849π → k = 1849
  12. 146 C = 2 × π × 73 = 146π
Review worksheet: 12 questions

  1. A trapezoid has parallel sides 30 cm and 23 cm and height 7 cm. Find its area in cm².

  2. A shape has area 16 cm². All lengths are multiplied by 6. Find the new area in cm².

  3. A circle has radius 42 cm. Its area is kπ cm². Find k.

  4. A circle has radius 51 cm. Its circumference is kπ cm. Find k.

  5. A trapezoid has parallel sides 28 cm and 9 cm and height 19 cm. Find its area in cm².

  6. A shape has area 51 cm². All lengths are multiplied by 4. Find the new area in cm².

  7. A circle has radius 47 cm. Its area is kπ cm². Find k.

  8. A circle has radius 63 cm. Its circumference is kπ cm. Find k.

  9. A trapezoid has parallel sides 26 cm and 17 cm and height 18 cm. Find its area in cm².

  10. A shape has area 43 cm². All lengths are multiplied by 6. Find the new area in cm².

  11. A circle has radius 69 cm. Its area is kπ cm². Find k.

  12. A circle has radius 50 cm. Its circumference is kπ cm. Find k.

Answer key
  1. 185.5 cm² (30 + 23) × 7 ÷ 2 = 185.5
  2. 576 cm² 16 × 6² = 576
  3. 1764 A = π × 42² = 1764π → k = 1764
  4. 102 C = 2 × π × 51 = 102π
  5. 351.5 cm² (28 + 9) × 19 ÷ 2 = 351.5
  6. 816 cm² 51 × 4² = 816
  7. 2209 A = π × 47² = 2209π → k = 2209
  8. 126 C = 2 × π × 63 = 126π
  9. 387 cm² (26 + 17) × 18 ÷ 2 = 387
  10. 1548 cm² 43 × 6² = 1548
  11. 4761 A = π × 69² = 4761π → k = 4761
  12. 100 C = 2 × π × 50 = 100π

Related ready-made worksheets: Grade 7 Geometry worksheet

08

7.SP Statistics and Probability

Statistics & probability

Simple probability, probability of an event not happening and probability of two events.

Short lesson: Two draws with replacement

Study guide for Grades 7 to 10: 2 worked examples and 2 practice questions. Replacing the first item keeps the second probability unchanged.

P(A then A) = P(A)²; independent draws

Replacing the first item keeps the second probability unchanged.

Worked example

A bag has 5 red and 6 blue counters. Draw twice, replacing the first counter. What is the probability both are red? Give a simplified fraction.

5/11 × 5/11 = 25/121

Answer: 25/121

Read the full study guide

Worksheets

A practice worksheet and a review worksheet, 12 and 12 questions.

Worksheets (PDF)Answer keys (PDF)
Practice worksheet: 12 questions

  1. A bag has 8 red and 10 blue counters. Draw twice, replacing the first counter. What is the probability both are red? Give a simplified fraction.

  2. P(A) = 13/36. Find P(not A).

  3. A bag contains 7 red counters and 27 blue counters. One counter is drawn at random. What is the probability of red?

  4. A bag has 10 red and 14 blue counters. Draw twice, replacing the first counter. What is the probability both are red? Give a simplified fraction.

  5. P(A) = 2/6. Find P(not A).

  6. A bag contains 3 red counters and 13 blue counters. One counter is drawn at random. What is the probability of red?

  7. A bag has 8 red and 15 blue counters. Draw twice, replacing the first counter. What is the probability both are red? Give a simplified fraction.

  8. P(A) = 13/33. Find P(not A).

  9. A bag contains 29 red counters and 28 blue counters. One counter is drawn at random. What is the probability of red?

  10. A bag has 8 red and 4 blue counters. Draw twice, replacing the first counter. What is the probability both are red? Give a simplified fraction.

  11. P(A) = 26/29. Find P(not A).

  12. A bag contains 18 red counters and 14 blue counters. One counter is drawn at random. What is the probability of red?

Answer key
  1. 16/81 8/18 × 8/18 = 16/81
  2. 23/36 1 − 13/36 = 23/36
  3. 7/34 7/(7 + 27) = 7/34
  4. 25/144 10/24 × 10/24 = 25/144
  5. 2/3 1 − 2/6 = 2/3
  6. 3/16 3/(3 + 13) = 3/16
  7. 64/529 8/23 × 8/23 = 64/529
  8. 20/33 1 − 13/33 = 20/33
  9. 29/57 29/(29 + 28) = 29/57
  10. 4/9 8/12 × 8/12 = 4/9
  11. 3/29 1 − 26/29 = 3/29
  12. 9/16 18/(18 + 14) = 9/16
Review worksheet: 12 questions

  1. P(A) = 7/20. Find P(not A).

  2. A bag has 10 red and 1 blue counters. Draw twice, replacing the first counter. What is the probability both are red? Give a simplified fraction.

  3. A bag contains 8 red counters and 35 blue counters. One counter is drawn at random. What is the probability of red?

  4. P(A) = 10/15. Find P(not A).

  5. A bag has 2 red and 1 blue counters. Draw twice, replacing the first counter. What is the probability both are red? Give a simplified fraction.

  6. A bag contains 5 red counters and 11 blue counters. One counter is drawn at random. What is the probability of red?

  7. P(A) = 23/25. Find P(not A).

  8. A bag has 10 red and 2 blue counters. Draw twice, replacing the first counter. What is the probability both are red? Give a simplified fraction.

  9. A bag contains 16 red counters and 8 blue counters. One counter is drawn at random. What is the probability of red?

  10. P(A) = 17/32. Find P(not A).

  11. A bag has 11 red and 15 blue counters. Draw twice, replacing the first counter. What is the probability both are red? Give a simplified fraction.

  12. A bag contains 16 red counters and 20 blue counters. One counter is drawn at random. What is the probability of red?

Answer key
  1. 13/20 1 − 7/20 = 13/20
  2. 100/121 10/11 × 10/11 = 100/121
  3. 8/43 8/(8 + 35) = 8/43
  4. 1/3 1 − 10/15 = 1/3
  5. 4/9 2/3 × 2/3 = 4/9
  6. 5/16 5/(5 + 11) = 5/16
  7. 2/25 1 − 23/25 = 2/25
  8. 25/36 10/12 × 10/12 = 25/36
  9. 2/3 16/(16 + 8) = 2/3
  10. 15/32 1 − 17/32 = 15/32
  11. 121/676 11/26 × 11/26 = 121/676
  12. 4/9 16/(16 + 20) = 4/9

Related ready-made worksheets: Grade 7 Statistics & probability worksheet