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Equivalent Ratio Tables

Grade 6 · Ratios · Worksheet 3

  1. If 2/5 = x/45, then x = ? Answer: ______________
  2. If 7:9 = x:45, then x = ? Answer: ______________
  3. If 7:9 = 42:x, then x = ? Answer: ______________
  4. A rectangular garden is drawn on a coordinate plane with corners at (2, 1), (8, 1), (8, 5), and (2, 5). A path is created by drawing a line from the midpoint of the top side to the midpoint of the bottom side, and another line from the midpoint of the left side to the midpoint of the right side. What is the ratio of the area of the smaller rectangle formed at the center where the paths cross to the area of the entire garden? Answer: ______________
  5. A rectangular solar panel array is drawn on a coordinate plane with corners at (0, 0), (1800, 0), (1800, 1200), and (0, 1200). The array is divided into three equal vertical sections by lines parallel to the y-axis. If each section contains solar panels arranged in a grid with 15 rows and 20 columns, what is the ratio of the area of one solar panel to the area of one vertical section? Answer: ______________
  6. A rectangular garden is drawn on a coordinate plane with corners at (2, 1), (8, 1), (8, 5), and (2, 5). If the gardener plants one rose bush for every 2 square units of area, how many rose bushes can be planted in the entire garden? Answer: ______________
  7. If 4/7 = 16/x, then x = ? Answer: ______________
  8. If 7:9 = 56:x, then x = ? Answer: ______________
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Answer Key & Explanations

Equivalent Ratio Tables · Grade 6 · Worksheet 3

  1. If 2/5 = x/45, then x = ? Answer: 18 Solution: Set up the equation: 2/5 = x/45 Cross-multiply: 2 × 45 = 5 × x Calculate: 90 = 5x Divide both sides by 5: 90 ÷ 5 = x Calculate: 18 = x The answer is 18.
    Full step-by-step solution

    Step 1: Set up the equation: 2/5 = x/45 Step 2: Cross-multiply: 2 × 45 = 5 × x Step 3: Calculate: 90 = 5x Step 4: Divide both sides by 5: 90 ÷ 5 = x Step 5: Calculate: 18 = x The answer is 18.

  2. If 7:9 = x:45, then x = ? Answer: 35 Solution: Write the proportion as equivalent fractions: 7/9 = x/45 Cross-multiply: 7 × 45 = 9 × x Calculate: 315 = 9x Divide both sides by 9: x = 315 ÷ 9 Calculate: x = 35 The answer is 35.
    Full step-by-step solution

    Step 1: Write the proportion as equivalent fractions: 7/9 = x/45 Step 2: Cross-multiply: 7 × 45 = 9 × x Step 3: Calculate: 315 = 9x Step 4: Divide both sides by 9: x = 315 ÷ 9 Step 5: Calculate: x = 35 The answer is 35.

  3. If 7:9 = 42:x, then x = ? Answer: 54 Solution: Write the proportion: 7/9 = 42/x Cross-multiply: 7 × x = 9 × 42 Calculate the right side: 9 × 42 = 378 The equation becomes: 7x = 378 Divide both sides by 7: x = 378 ÷ 7 Calculate: 378 ÷ 7 = 54 Therefore, x = 54
    Full step-by-step solution

    Step 1: Write the proportion: 7/9 = 42/x Step 2: Cross-multiply: 7 × x = 9 × 42 Step 3: Calculate the right side: 9 × 42 = 378 Step 4: The equation becomes: 7x = 378 Step 5: Divide both sides by 7: x = 378 ÷ 7 Step 6: Calculate: 378 ÷ 7 = 54 Step 7: Therefore, x = 54

  4. A rectangular garden is drawn on a coordinate plane with corners at (2, 1), (8, 1), (8, 5), and (2, 5). A path is created by drawing a line from the midpoint of the top side to the midpoint of the bottom side, and another line from the midpoint of the left side to the midpoint of the right side. What is the ratio of the area of the smaller rectangle formed at the center where the paths cross to the area of the entire garden? Answer: 1:4 Solution: When you connect the midpoints of opposite sides in a rectangle, you create four smaller rectangles of equal area.
    Full step-by-step solution

    When you connect the midpoints of opposite sides in a rectangle, you create four smaller rectangles of equal area. The intersection forms a central rectangle whose dimensions are exactly half the length and half the width of the original rectangle.

  5. A rectangular solar panel array is drawn on a coordinate plane with corners at (0, 0), (1800, 0), (1800, 1200), and (0, 1200). The array is divided into three equal vertical sections by lines parallel to the y-axis. If each section contains solar panels arranged in a grid with 15 rows and 20 columns, what is the ratio of the area of one solar panel to the area of one vertical section? Answer: 1:600 Solution: Length = 1800 units, Width = 1200 units Area = 1800 × 1200 = 2,160,000 square units The array is divided into 3 equal vertical sections Area of one section = 2,160,000 ÷ 3 = 720,000 square units Each section has 15 rows and 20 columns of panels Total panels per section = 15 × 20 = 300 panels…
    Full step-by-step solution

    Step 1: Find the area of the entire solar panel array Length = 1800 units, Width = 1200 units Area = 1800 × 1200 = 2,160,000 square units Step 2: Find the area of one vertical section The array is divided into 3 equal vertical sections Area of one section = 2,160,000 ÷ 3 = 720,000 square units Step 3: Find the area of one solar panel Each section has 15 rows and 20 columns of panels Total panels per section = 15 × 20 = 300 panels Area of one panel = 720,000 ÷ 300 = 2,400 square units Step 4: Find the ratio of panel area to section area Panel area : Section area = 2,400 : 720,000 Simplify by dividing both sides by 2,400: 1 : 300 The ratio is 1:300.

  6. A rectangular garden is drawn on a coordinate plane with corners at (2, 1), (8, 1), (8, 5), and (2, 5). If the gardener plants one rose bush for every 2 square units of area, how many rose bushes can be planted in the entire garden? Answer: 12 Solution: The garden is a rectangle with corners at (2, 1), (8, 1), (8, 5), and (2, 5). The bottom side is from (2, 1) to (8, 1). The length = 8 - 2 = 6 units.
    Full step-by-step solution

    Step 1: Identify the coordinates and shape The garden is a rectangle with corners at (2, 1), (8, 1), (8, 5), and (2, 5). Step 2: Find the length and width The bottom side is from (2, 1) to (8, 1). The length = 8 - 2 = 6 units. The left side is from (2, 1) to (2, 5). The width = 5 - 1 = 4 units. Step 3: Calculate the area Area of rectangle = length × width = 6 × 4 = 24 square units. Step 4: Determine rose bushes planted One rose bush is planted for every 2 square units. Number of rose bushes = Total area ÷ Area per bush = 24 ÷ 2 = 12. Step 5: Final answer The gardener can plant 12 rose bushes in the entire garden.

  7. If 4/7 = 16/x, then x = ? Answer: 28 Solution: 4/7 = 16/x Recognize that this is a proportion (two equal fractions). 4 * x = 7 * 16 4 * x = 112 Solve for x by dividing both sides by 4: x = 112 / 4 x = 28 Thus, the value of x is 28.
    Full step-by-step solution

    We start with the equation: 4/7 = 16/x Step 1: Recognize that this is a proportion (two equal fractions). We can solve for x by cross-multiplying. Step 2: Cross-multiply: 4 * x = 7 * 16 Step 3: Perform the multiplication on the right side: 4 * x = 112 Step 4: Solve for x by dividing both sides by 4: x = 112 / 4 Step 5: Perform the division: x = 28 Thus, the value of x is 28.

  8. If 7:9 = 56:x, then x = ? Answer: 72 Solution: Write the proportion as equivalent fractions: 7/9 = 56/x Cross-multiply: 7 * x = 9 * 56 Calculate the right side: 9 * 56 = 504 So the equation becomes: 7x = 504 Divide both sides by 7: x = 504 ÷ 7 Calculate: 504 ÷ 7 = 72 Therefore, x = 72
    Full step-by-step solution

    Step 1: Write the proportion as equivalent fractions: 7/9 = 56/x Step 2: Cross-multiply: 7 * x = 9 * 56 Step 3: Calculate the right side: 9 * 56 = 504 Step 4: So the equation becomes: 7x = 504 Step 5: Divide both sides by 7: x = 504 ÷ 7 Step 6: Calculate: 504 ÷ 7 = 72 Step 7: Therefore, x = 72