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MathematicsGrade 7en

⚖️ Proportions and Scaling

Master the fundamentals of proportional reasoning in Grade 7 mathematics. Learn to identify equivalent ratios, set up and solve proportions using cross-multiplication, and apply scale factors to enlarge or reduce figures and create accurate scale drawings. These skills form the foundation for geometry, measurement, and real-world problem-solving. **What you'll learn:** - Identify and verify equivalent ratios - Set up and solve proportions using cross-multiplication - Apply scale factors to similar figures and drawings - Distinguish between direct proportional relationships and non-proportional situations - Solve multi-step problems involving scaling and proportional reasoning

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  1. Question 1

    Which of the following ratios is equivalent to 3:53:5?

  2. Question 2

    A recipe uses flour and sugar in the ratio 4:24:2. If you want to use 8 cups of flour, how many cups of sugar do you need?

  3. Question 3

    A proportion is an equation that states two ratios are equal.

  4. Question 4

    Solve for xx in the proportion: 59=x18\frac{5}{9} = \frac{x}{18}

  5. Question 5

    A map has a scale of 1 cm:50 km1 \text{ cm} : 50 \text{ km}. If two cities are 5 cm apart on the map, how far apart are they in real life?

  6. Question 6

    What is the scale factor if a model car has a length of 15 cm and the actual car has a length of 450 cm?

  7. Question 7

    If a rectangle is enlarged by a scale factor of 2, its area will also increase by a scale factor of 2.

  8. Question 8

    Two figures are similar with a scale factor of 3:53:5. If the smaller figure has a side length of 9 cm, what is the corresponding side length of the larger figure?

  9. Question 9

    Which pair of ratios does NOT form a proportion?

  10. Question 10

    A recipe makes 12 cookies and uses 2 cups of flour. How much flour is needed to make 30 cookies?

  11. Question 11

    On a scale drawing, 2 inches represents 50 miles. If two locations are 350 miles apart, how many inches apart should they be on the drawing?

  12. Question 12

    All similar figures have sides that are proportional to each other.

  13. Question 13

    Solve for yy in the proportion: 4y=1215\frac{4}{y} = \frac{12}{15}

  14. Question 14

    A garden is drawn to a scale of 1 cm:2 m1 \text{ cm} : 2 \text{ m}. If the drawing shows the garden is 8 cm long, what is the actual length of the garden?

  15. Question 15

    Which of the following scenarios represents a proportional relationship?

  16. Question 16

    If the scale factor from Figure A to Figure B is 2:12:1, then Figure B is twice as large as Figure A.