Fractions & Shapes Worksheet

Cheatsheet Content

### Fractions and Recurring Decimals 1. Convert $\frac{3}{8}$ to a decimal. 2. Convert $\frac{5}{11}$ to a recurring decimal. 3. Express $0.\overline{4}$ as a fraction in its simplest form. 4. Express $0.1\overline{6}$ as a fraction in its simplest form. 5. Convert $\frac{7}{20}$ to a decimal. 6. Convert $\frac{2}{9}$ to a recurring decimal. 7. Express $0.\overline{72}$ as a fraction in its simplest form. 8. Convert $0.375$ to a fraction in its simplest form. 9. Convert $\frac{1}{6}$ to a recurring decimal. 10. Express $0.\overline{123}$ as a fraction. 11. Convert $\frac{13}{25}$ to a decimal. 12. Convert $\frac{4}{7}$ to a recurring decimal, showing the first 6 decimal places. 13. Express $0.\overline{5}$ as a fraction. 14. Convert $0.8$ to a fraction in its simplest form. 15. Convert $\frac{9}{16}$ to a decimal. 16. Convert $\frac{1}{3}$ to a recurring decimal. 17. Express $0.2\overline{3}$ as a fraction. 18. Convert $\frac{17}{50}$ to a decimal. 19. Convert $\frac{5}{6}$ to a recurring decimal. 20. Express $0.\overline{09}$ as a fraction. 21. Convert $\frac{1}{8}$ to a decimal. 22. Convert $\frac{7}{11}$ to a recurring decimal. 23. Express $0.\overline{8}$ as a fraction in its simplest form. 24. Express $0.4\overline{2}$ as a fraction in its simplest form. 25. Convert $\frac{11}{20}$ to a decimal. 26. Convert $\frac{5}{9}$ to a recurring decimal. 27. Express $0.\overline{36}$ as a fraction in its simplest form. 28. Convert $0.625$ to a fraction in its simplest form. 29. Convert $\frac{1}{12}$ to a recurring decimal. 30. Express $0.\overline{01}$ as a fraction. ### Ordering Fractions 1. Order the following fractions from smallest to largest: $\frac{1}{2}, \frac{3}{5}, \frac{2}{3}$. 2. Order the following fractions from largest to smallest: $\frac{3}{4}, \frac{7}{10}, \frac{5}{8}$. 3. Which fraction is larger: $\frac{2}{7}$ or $\frac{3}{10}$? 4. Order the following fractions from smallest to largest: $\frac{5}{6}, \frac{7}{9}, \frac{11}{12}$. 5. Order the following fractions from largest to smallest: $\frac{1}{3}, \frac{2}{5}, \frac{3}{8}$. 6. Insert $ ,$ or $=$: $\frac{4}{9} \underline{\hspace{1cm}} \frac{5}{12}$. 7. Order the following fractions from smallest to largest: $\frac{1}{4}, \frac{2}{9}, \frac{3}{11}$. 8. Order the following fractions from largest to smallest: $\frac{9}{10}, \frac{11}{12}, \frac{14}{15}$. 9. Which fraction is smaller: $\frac{5}{14}$ or $\frac{3}{8}$? 10. Order the following fractions from smallest to largest: $\frac{2}{5}, \frac{1}{3}, \frac{3}{7}, \frac{4}{9}$. 11. Order the following fractions from largest to smallest: $\frac{7}{8}, \frac{4}{5}, \frac{9}{11}$. 12. Insert $ ,$ or $=$: $\frac{6}{7} \underline{\hspace{1cm}} \frac{18}{21}$. 13. Order the following fractions from smallest to largest: $\frac{3}{4}, \frac{7}{8}, \frac{5}{6}$. 14. Order the following fractions from largest to smallest: $\frac{1}{5}, \frac{2}{11}, \frac{3}{16}$. 15. Which fraction is larger: $\frac{7}{12}$ or $\frac{11}{18}$? 16. Order the following fractions from smallest to largest: $\frac{1}{2}, \frac{4}{7}, \frac{5}{9}$. 17. Order the following fractions from largest to smallest: $\frac{13}{15}, \frac{17}{20}, \frac{25}{30}$. 18. Insert $ ,$ or $=$: $\frac{2}{3} \underline{\hspace{1cm}} \frac{7}{10}$. 19. Order the following fractions from smallest to largest: $\frac{3}{10}, \frac{1}{4}, \frac{2}{7}$. 20. Order the following fractions from largest to smallest: $\frac{5}{9}, \frac{7}{12}, \frac{3}{5}$. 21. Order the following fractions from smallest to largest: $\frac{1}{3}, \frac{4}{10}, \frac{3}{8}$. 22. Order the following fractions from largest to smallest: $\frac{5}{7}, \frac{2}{3}, \frac{7}{9}$. 23. Which fraction is smaller: $\frac{6}{11}$ or $\frac{5}{9}$? 24. Order the following fractions from smallest to largest: $\frac{2}{6}, \frac{3}{10}, \frac{1}{5}$. 25. Order the following fractions from largest to smallest: $\frac{11}{13}, \frac{8}{9}, \frac{17}{19}$. 26. Insert $ ,$ or $=$: $\frac{5}{8} \underline{\hspace{1cm}} \frac{15}{24}$. 27. Order the following fractions from smallest to largest: $\frac{4}{5}, \frac{7}{10}, \frac{13}{15}$. 28. Order the following fractions from largest to smallest: $\frac{1}{6}, \frac{2}{13}, \frac{3}{19}$. 29. Which fraction is larger: $\frac{9}{14}$ or $\frac{13}{21}$? 30. Order the following fractions from smallest to largest: $\frac{1}{7}, \frac{2}{15}, \frac{3}{22}$. ### Subtracting Mixed Numbers 1. Calculate: $3\frac{1}{2} - 1\frac{1}{4}$. 2. Calculate: $5\frac{2}{3} - 2\frac{1}{6}$. 3. Calculate: $4\frac{1}{5} - 1\frac{3}{10}$. 4. Calculate: $6\frac{3}{4} - 2\frac{7}{8}$. 5. Calculate: $2\frac{1}{3} - 1\frac{4}{5}$. 6. Calculate: $7\frac{5}{6} - 3\frac{1}{2}$. 7. Calculate: $8\frac{1}{2} - 4\frac{2}{3}$. 8. Calculate: $5\frac{3}{8} - 2\frac{1}{4}$. 9. Calculate: $10\frac{2}{7} - 3\frac{1}{2}$. 10. Calculate: $9\frac{1}{4} - 5\frac{5}{6}$. 11. Calculate: $4\frac{1}{6} - 1\frac{2}{3}$. 12. Calculate: $6\frac{7}{10} - 2\frac{1}{5}$. 13. Calculate: $3\frac{2}{9} - 1\frac{1}{3}$. 14. Calculate: $7\frac{1}{8} - 2\frac{3}{4}$. 15. Calculate: $11\frac{1}{2} - 6\frac{4}{5}$. 16. Calculate: $5\frac{3}{4} - 1\frac{5}{6}$. 17. Calculate: $8\frac{1}{3} - 3\frac{7}{9}$. 18. Calculate: $9\frac{5}{12} - 4\frac{1}{3}$. 19. Calculate: $12\frac{1}{5} - 7\frac{1}{2}$. 20. Calculate: $6\frac{2}{3} - 2\frac{3}{4}$. 21. Calculate: $4\frac{1}{2} - 2\frac{3}{5}$. 22. Calculate: $7\frac{1}{4} - 3\frac{5}{8}$. 23. Calculate: $5\frac{5}{6} - 1\frac{1}{3}$. 24. Calculate: $10\frac{3}{10} - 4\frac{1}{2}$. 25. Calculate: $3\frac{1}{7} - 1\frac{2}{3}$. 26. Calculate: $8\frac{1}{6} - 2\frac{3}{4}$. 27. Calculate: $6\frac{2}{5} - 3\frac{7}{10}$. 28. Calculate: $11\frac{1}{3} - 5\frac{1}{2}$. 29. Calculate: $9\frac{7}{8} - 4\frac{1}{4}$. 30. Calculate: $7\frac{1}{5} - 2\frac{2}{3}$. ### Multiplying an Integer by a Mixed Number 1. Calculate: $3 \times 2\frac{1}{4}$. 2. Calculate: $5 \times 1\frac{2}{3}$. 3. Calculate: $4 \times 3\frac{1}{2}$. 4. Calculate: $6 \times 2\frac{5}{6}$. 5. Calculate: $2 \times 4\frac{3}{8}$. 6. Calculate: $7 \times 1\frac{1}{5}$. 7. Calculate: $8 \times 3\frac{1}{4}$. 8. Calculate: $10 \times 2\frac{2}{5}$. 9. Calculate: $9 \times 1\frac{1}{3}$. 10. Calculate: $12 \times 3\frac{1}{6}$. 11. Calculate: $11 \times 2\frac{3}{4}$. 12. Calculate: $15 \times 1\frac{2}{5}$. 13. Calculate: $4 \times 5\frac{1}{2}$. 14. Calculate: $7 \times 2\frac{3}{7}$. 15. Calculate: $6 \times 4\frac{1}{9}$. 16. Calculate: $8 \times 1\frac{7}{8}$. 17. Calculate: $10 \times 3\frac{3}{10}$. 18. Calculate: $9 \times 2\frac{5}{12}$. 19. Calculate: $3 \times 6\frac{2}{3}$. 20. Calculate: $5 \times 4\frac{1}{15}$. 21. Calculate: $4 \times 1\frac{3}{4}$. 22. Calculate: $6 \times 3\frac{1}{2}$. 23. Calculate: $7 \times 2\frac{2}{7}$. 24. Calculate: $9 \times 1\frac{5}{6}$. 25. Calculate: $10 \times 4\frac{1}{5}$. 26. Calculate: $12 \times 2\frac{1}{4}$. 27. Calculate: $5 \times 3\frac{2}{3}$. 28. Calculate: $8 \times 1\frac{3}{4}$. 29. Calculate: $11 \times 2\frac{1}{2}$. 30. Calculate: $14 \times 1\frac{3}{7}$. ### Dividing an Integer by a Fraction 1. Calculate: $6 \div \frac{1}{3}$. 2. Calculate: $10 \div \frac{2}{5}$. 3. Calculate: $4 \div \frac{1}{2}$. 4. Calculate: $9 \div \frac{3}{4}$. 5. Calculate: $5 \div \frac{1}{6}$. 6. Calculate: $8 \div \frac{2}{3}$. 7. Calculate: $12 \div \frac{4}{5}$. 8. Calculate: $7 \div \frac{1}{4}$. 9. Calculate: $15 \div \frac{5}{6}$. 10. Calculate: $11 \div \frac{1}{7}$. 11. Calculate: $20 \div \frac{2}{9}$. 12. Calculate: $3 \div \frac{3}{8}$. 13. Calculate: $14 \div \frac{7}{10}$. 14. Calculate: $18 \div \frac{9}{11}$. 15. Calculate: $5 \div \frac{2}{7}$. 16. Calculate: $13 \div \frac{1}{5}$. 17. Calculate: $16 \div \frac{4}{9}$. 18. Calculate: $2 \div \frac{5}{12}$. 19. Calculate: $25 \div \frac{1}{10}$. 20. Calculate: $1 \div \frac{3}{5}$. 21. Calculate: $10 \div \frac{1}{2}$. 22. Calculate: $12 \div \frac{3}{4}$. 23. Calculate: $6 \div \frac{2}{3}$. 24. Calculate: $14 \div \frac{7}{8}$. 25. Calculate: $9 \div \frac{1}{5}$. 26. Calculate: $24 \div \frac{4}{5}$. 27. Calculate: $8 \div \frac{1}{4}$. 28. Calculate: $18 \div \frac{2}{9}$. 29. Calculate: $7 \div \frac{3}{10}$. 30. Calculate: $21 \div \frac{7}{12}$. ### Making Fraction Calculations Easier 1. Evaluate: $\frac{1}{2} \times \frac{4}{5} \times \frac{10}{3}$. 2. Evaluate: $\frac{2}{3} \div \frac{4}{9} \times \frac{1}{2}$. 3. Evaluate: $(\frac{1}{4} + \frac{1}{2}) \times \frac{8}{9}$. 4. Evaluate: $\frac{5}{6} - \frac{1}{3} \times \frac{3}{4}$. 5. Evaluate: $\frac{3}{7} \times (2\frac{1}{3} + \frac{1}{7})$. 6. Evaluate: $\frac{9}{10} \div (\frac{3}{5} + \frac{1}{2})$. 7. Evaluate: $\frac{5}{8} + \frac{1}{4} - \frac{1}{2}$. 8. Evaluate: $(1\frac{1}{2} \div \frac{3}{4}) - \frac{2}{3}$. 9. Evaluate: $2\frac{1}{5} \times \frac{10}{11} \div \frac{1}{2}$. 10. Evaluate: $\frac{7}{12} + \frac{1}{3} \times \frac{9}{14}$. 11. Evaluate: $(\frac{2}{3} - \frac{1}{6}) \div \frac{5}{9}$. 12. Evaluate: $\frac{4}{5} \times (2\frac{1}{4} - \frac{1}{2})$. 13. Evaluate: $\frac{1}{8} + \frac{3}{4} \times \frac{2}{5}$. 14. Evaluate: $3\frac{1}{3} \div (2 \times \frac{5}{6})$. 15. Evaluate: $\frac{11}{15} - \frac{1}{3} \div \frac{5}{9}$. 16. Evaluate: $(2\frac{1}{2} + \frac{1}{4}) \times \frac{2}{11}$. 17. Evaluate: $\frac{6}{7} \times \frac{14}{15} \div \frac{4}{5}$. 18. Evaluate: $\frac{1}{2} + \frac{1}{3} + \frac{1}{6}$. 19. Evaluate: $4\frac{1}{2} \div 1\frac{1}{2} \times \frac{2}{3}$. 20. Evaluate: $(\frac{3}{4} - \frac{1}{2}) \div (\frac{1}{3} + \frac{1}{6})$. 21. Evaluate: $\frac{2}{5} \times \frac{3}{4} \div \frac{6}{7}$. 22. Evaluate: $(\frac{3}{5} + \frac{1}{10}) \times \frac{5}{7}$. 23. Evaluate: $1\frac{1}{4} + \frac{1}{2} \times \frac{2}{3}$. 24. Evaluate: $\frac{7}{9} \div \frac{14}{15} - \frac{1}{3}$. 25. Evaluate: $2\frac{1}{2} - \frac{3}{4} \div \frac{1}{2}$. 26. Evaluate: $(\frac{5}{8} - \frac{1}{4}) \times 1\frac{1}{3}$. 27. Evaluate: $\frac{1}{5} + \frac{2}{3} \times \frac{9}{10}$. 28. Evaluate: $3\frac{1}{4} \div (\frac{1}{2} + \frac{1}{4})$. 29. Evaluate: $\frac{4}{7} \times \frac{21}{24} + \frac{1}{2}$. 30. Evaluate: $(1\frac{1}{3} \times \frac{3}{4}) \div \frac{5}{6}$. ### Quadrilaterals and Polygons 1. Name a quadrilateral with exactly one pair of parallel sides. 2. What is the sum of interior angles of a pentagon? 3. A regular polygon has an exterior angle of $40^\circ$. How many sides does it have? 4. What is the name of a quadrilateral with four equal sides and four right angles? 5. If the sum of interior angles of a polygon is $1080^\circ$, how many sides does it have? 6. Is a square a rhombus? Explain why. 7. Find the measure of each interior angle of a regular octagon. 8. How many diagonals can be drawn from one vertex of a hexagon? 9. Define a trapezoid. 10. The interior angle of a regular polygon is $150^\circ$. How many sides does it have? 11. What is the sum of the exterior angles of any convex polygon? 12. Name a quadrilateral with two pairs of equal adjacent sides, but no parallel sides. 13. If a polygon has 10 sides, what is the sum of its interior angles? 14. Can a quadrilateral have exactly two right angles and no parallel sides? Sketch an example. 15. What type of quadrilateral has diagonals that bisect each other at right angles? 16. Find the measure of each exterior angle of a regular decagon. 17. A polygon has 8 sides. How many diagonals does it have in total? 18. Describe the properties of a parallelogram. 19. If one interior angle of a regular polygon is $144^\circ$, how many sides does it have? 20. True or False: All sides of a rectangle are equal in length. Explain your answer. 21. What is the sum of interior angles of a quadrilateral? 22. A regular polygon has an exterior angle of $60^\circ$. How many sides does it have? 23. What is the name of a quadrilateral with all sides equal but no right angles? 24. If the sum of interior angles of a polygon is $900^\circ$, how many sides does it have? 25. Find the measure of each interior angle of a regular hexagon. 26. How many diagonals does a pentagon have? 27. Define a kite. 28. The interior angle of a regular polygon is $162^\circ$. How many sides does it have? 29. What is the maximum number of obtuse angles a quadrilateral can have? 30. A polygon has 9 sides. What is the sum of its exterior angles? ### The Circumference of a Circle 1. Find the circumference of a circle with a radius of 7 cm. (Use $\pi \approx \frac{22}{7}$) 2. A circle has a diameter of 10 m. Calculate its circumference. (Use $\pi \approx 3.14$) 3. If the circumference of a circle is $44$ cm, what is its radius? (Use $\pi \approx \frac{22}{7}$) 4. A circular pond has a diameter of 8 meters. What is the distance around the pond? (Use $\pi \approx 3.14$) 5. Calculate the circumference of a circle with a radius of 3.5 cm. (Use $\pi \approx \frac{22}{7}$) 6. The circumference of a bicycle wheel is $157$ cm. What is its diameter? (Use $\pi \approx 3.14$) 7. A semi-circular arc has a length of $22$ cm. What is the radius of the full circle? (Use $\pi \approx \frac{22}{7}$) 8. Find the circumference of a circle if its radius is 14 mm. (Use $\pi \approx \frac{22}{7}$) 9. A circular table has a circumference of $25.12$ feet. What is its radius? (Use $\pi \approx 3.14$) 10. A running track is circular with a radius of 50 meters. How far does a runner travel in one lap? (Use $\pi \approx 3.14$) 11. If the diameter of a circle is 21 cm, find its circumference. (Use $\pi \approx \frac{22}{7}$) 12. The circumference of a pizza is $78.5$ cm. What is its diameter? (Use $\pi \approx 3.14$) 13. A car tyre has a radius of 30 cm. What is its circumference? (Use $\pi \approx 3.14$) 14. A circular garden has a circumference of $132$ meters. What is its radius? (Use $\pi \approx \frac{22}{7}$) 15. Find the perimeter of a semi-circle with a diameter of 14 cm. (Use $\pi \approx \frac{22}{7}$) 16. What is the circumference of a circle with a radius of 10.5 inches? (Use $\pi \approx \frac{22}{7}$) 17. A circular clock face has a circumference of $62.8$ cm. What is its diameter? (Use $\pi \approx 3.14$) 18. A hula hoop has a circumference of $220$ cm. What is its radius? (Use $\pi \approx \frac{22}{7}$) 19. If the radius of a circle is 2.8 meters, calculate its circumference. (Use $\pi \approx \frac{22}{7}$) 20. A circular emblem has a circumference of $31.4$ cm. What is its radius? (Use $\pi \approx 3.14$) 21. Find the circumference of a circle with a radius of 21 cm. (Use $\pi \approx \frac{22}{7}$) 22. A circle has a diameter of 14 m. Calculate its circumference. (Use $\pi \approx \frac{22}{7}$) 23. If the circumference of a circle is $188.4$ cm, what is its diameter? (Use $\pi \approx 3.14$) 24. A circular park has a radius of 25 meters. What is the distance around the park? (Use $\pi \approx 3.14$) 25. Calculate the circumference of a circle with a diameter of 7 cm. (Use $\pi \approx \frac{22}{7}$) 26. The circumference of a Ferris wheel is $314$ meters. What is its radius? (Use $\pi \approx 3.14$) 27. A semi-circular window frame has a diameter of 80 cm. What is the length of the curved part? (Use $\pi \approx 3.14$) 28. Find the circumference of a circle if its radius is 4.2 cm. (Use $\pi \approx \frac{22}{7}$) 29. A circular swimming pool has a circumference of $62.8$ meters. What is its diameter? (Use $\pi \approx 3.14$) 30. A satellite orbits Earth in a circular path with a radius of 6400 km. What is the length of one orbit? (Use $\pi \approx 3.14$) ### 3D Shapes 1. How many faces, edges, and vertices does a cube have? 2. A triangular prism has a base that is an equilateral triangle. How many faces does it have? 3. Describe the cross-section of a cylinder cut parallel to its base. 4. How many vertices does a square pyramid have? 5. What 3D shape can be formed by rotating a rectangle about one of its sides? 6. How many edges does a pentagonal prism have? 7. Describe the number of faces, edges, and vertices of a triangular pyramid (tetrahedron). 8. What is the name of a 3D shape with two circular bases and a curved surface? 9. A cuboid has dimensions 5 cm by 3 cm by 2 cm. How many faces does it have? 10. What shape is the cross-section of a cone cut perpendicular to its base, through the apex? 11. How many faces meet at a single vertex of a cube? 12. A hexagonal prism has how many vertices? 13. What 3D shape has only one curved face and one circular base? 14. How many edges does a rectangular prism have? 15. If you slice a sphere, what shape is the cross-section? 16. Describe the defining characteristics of a prism. 17. A dodecahedron has 12 faces. How many vertices does it have if it's a regular dodecahedron? (Euler's formula: F+V-E=2) 18. What is the difference between a pyramid and a prism? 19. How many faces, edges, and vertices does an octagonal pyramid have? 20. What 3D shape can be formed by rotating a semi-circle about its diameter? 21. How many faces, edges, and vertices does a triangular prism have? 22. What is the cross-section of a cube cut diagonally through opposite vertices? 23. A cone has how many faces, edges, and vertices? 24. How many faces does a hexagonal pyramid have? 25. What 3D shape has all its points equidistant from a central point? 26. How many edges does an octagonal prism have? 27. Describe the cross-section of a square pyramid cut parallel to its base. 28. What is the name of a 3D shape with a single base and triangular faces that meet at an apex? 29. A rectangular prism has how many vertices? 30. If you cut a cylinder parallel to its height, what shape is the cross-section?