MathematicsFreePrintable
Ratios, Expressions, and Geometry
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Ratios, Expressions, and Geometry
📊 Part 1: Ratios and Proportional Relationships
1. If the ratio of red to blue marbles is 3:5, how many red marbles are there if there are 20 blue marbles?
10 red marbles
12 red marbles
15 red marbles
18 red marbles
2. A recipe calls for 2 cups of flour for every 3 cups of sugar. If you use 9 cups of sugar, how many cups of flour do you need?
3. On a scale map, 1 inch represents 5 miles. If two cities are 3.5 inches apart on the map, what is the actual distance between them?
The actual distance is _____________ miles.
4. Which of the following represent proportional relationships? Check all that apply:
y = 3x
y = 2x + 5
y = -4x
y = x² + 1
✏️ Part 2: Expressions and Equations
5. You have twice as many apples as oranges. If oranges = x, write an expression for the number of apples.
Number of apples = _____________
6. Sarah has 3 more books than Jake. If Jake has b books, and together they have 27 books, write and solve an equation to find how many books Jake has.
7. A parking meter costs $0.25 for every 15 minutes. Write an expression for the cost of parking for h hours.
0.25h
h
4h
15h
8. Solve for x: 3x - 7 = 14
📐 Part 3: Geometry - Area of Composite Shapes
9. A composite shape is made of a rectangle (8 ft by 6 ft) with a right triangle (base 4 ft, height 3 ft) attached to one side. Find the total area.
10. Explain in your own words how you would find the area of a composite shape made from multiple rectangles and triangles.
11. A garden is shaped like a rectangle with a semicircle cut out from one corner. The rectangle is 12 ft by 8 ft, and the semicircle has a radius of 3 ft. What is the area of the garden? (Use π ≈ 3.14)
12. Real-World Connection: Describe one situation from your daily life where you might need to calculate the area of a composite shape.
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