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Order Rationals

Grade 6 · Ratios · Worksheet 2

  1. Liam is tracking the temperature changes in his city over a week. On Monday morning, the temperature was -3°C. By noon, it had risen by 8 degrees. Overnight, it dropped by 5 degrees. On Tuesday, it rose another 4 degrees. What was the final temperature on Tuesday? Answer: ______________
  2. A rectangular garden is drawn on a coordinate plane with corners at (2, 1), (8, 1), (8, 5), and (2, 5). A circular fountain is placed in the center of the garden with a radius that is exactly one-third the length of the garden. What is the area of the fountain? (Use π = 3.14) Answer: ______________
  3. Order: -7/3, 3.5, -1, 9/4, -2.75 Answer: ______________
  4. Noah is helping his science class plot the daily high temperatures (in degrees Celsius) from a week of a winter experiment. The recorded temperatures are: -2.5, 1/6, -3, 0.5, -1 1/6. Noah needs to order these temperatures from coldest to warmest to correctly place them on a classroom number line. What is the correct order? Answer: ______________
  5. Order: -3.5, 7/3, -1.75, 0.6, -2.25 Answer: ______________
  6. Order: -3/4, 1.25, -1.5, 0.5, -2.25 Answer: ______________
  7. Isabella is helping her science class create a giant number line on the classroom floor to show the freezing points of different liquids. She needs to mark the following temperatures (in degrees Celsius) from least to greatest: -9.5, 15/2, -4 1/3, 6.75, -8.2, and 1/4. What is the correct order from least to greatest? Answer: ______________
  8. (-3.25) + 2.75 - (-1.5) = ? Answer: ______________
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Answer Key & Explanations

Order Rationals · Grade 6 · Worksheet 2

  1. Liam is tracking the temperature changes in his city over a week. On Monday morning, the temperature was -3°C. By noon, it had risen by 8 degrees. Overnight, it dropped by 5 degrees. On Tuesday, it rose another 4 degrees. What was the final temperature on Tuesday? Answer: 4°C Solution: Monday morning: -3°C It rose by 8 degrees. -3 + 8 = 5°C So, Monday noon temperature: 5°C It dropped by 5 degrees from Monday noon. 5 - 5 = 0°C So, Tuesday morning temperature: 0°C It rose by 4 degrees.
    Full step-by-step solution

    Let's go step by step. **Step 1: Start with Monday morning temperature** Monday morning: -3°C **Step 2: Temperature change by Monday noon** It rose by 8 degrees. Calculation: -3 + 8 = 5°C So, Monday noon temperature: 5°C **Step 3: Overnight temperature drop** It dropped by 5 degrees from Monday noon. Calculation: 5 - 5 = 0°C So, Tuesday morning temperature: 0°C **Step 4: Temperature change on Tuesday** It rose by 4 degrees. Calculation: 0 + 4 = 4°C **Final Answer:** The temperature on Tuesday after the rise is 4°C.

  2. A rectangular garden is drawn on a coordinate plane with corners at (2, 1), (8, 1), (8, 5), and (2, 5). A circular fountain is placed in the center of the garden with a radius that is exactly one-third the length of the garden. What is the area of the fountain? (Use π = 3.14) Answer: 12.56 Solution: Find the length and width of the rectangular garden. The corners are at (2, 1), (8, 1), (8, 5), and (2, 5). The length along the x-axis: from x = 2 to x = 8 → 8 − 2 = 6.
    Full step-by-step solution

    Step 1: Find the length and width of the rectangular garden. The corners are at (2, 1), (8, 1), (8, 5), and (2, 5). The length along the x-axis: from x = 2 to x = 8 → 8 − 2 = 6. The width along the y-axis: from y = 1 to y = 5 → 5 − 1 = 4. So the garden is 6 units long and 4 units wide. Step 2: Determine which side is the "length" for the problem. The problem says: "radius is exactly one-third the length of the garden." In a rectangle, "length" usually means the longer side, so length = 6. Step 3: Calculate the radius of the fountain. Radius = (1/3) × length = (1/3) × 6 = 2. Step 4: Calculate the area of the circular fountain. Area of a circle = π × radius². Using π = 3.14 and radius = 2: Area = 3.14 × (2²) = 3.14 × 4 = 12.56. Step 5: Final answer. The area of the fountain is 12.56.

  3. Order: -7/3, 3.5, -1, 9/4, -2.75 Answer: -2.75, -7/3, -1, 9/4, 3.5 Solution: Convert all numbers to decimals. -7/3 = -2.333... Compare negatives first: -2.75 < -2.333...
    Full step-by-step solution

    Step 1: Convert all numbers to decimals. -7/3 = -2.333... 3.5 = 3.5 -1 = -1 9/4 = 2.25 -2.75 = -2.75 Step 2: Order from least to greatest (left to right on number line). Compare negatives first: -2.75 < -2.333... < -1 Then positives: 2.25 < 3.5 Step 3: Write the ordered list: -2.75, -7/3, -1, 9/4, 3.5 The answer is -2.75, -7/3, -1, 9/4, 3.5.

  4. Noah is helping his science class plot the daily high temperatures (in degrees Celsius) from a week of a winter experiment. The recorded temperatures are: -2.5, 1/6, -3, 0.5, -1 1/6. Noah needs to order these temperatures from coldest to warmest to correctly place them on a classroom number line. What is the correct order? Answer: -3, -2.5, -1 1/6, 1/6, 0.5 Solution: Convert all numbers to decimal form for easy comparison. - -2.5 is already a decimal. - 1/6 = 0.1666...
    Full step-by-step solution

    Step 1: Convert all numbers to decimal form for easy comparison. - -2.5 is already a decimal. - 1/6 = 0.1666... (approximately 0.167) - -3 is already an integer. - 0.5 is already a decimal. - -1 1/6 = -(1 + 1/6) = -1.1666... (approximately -1.167) Step 2: List the numbers in decimal form: -2.5, 0.167, -3, 0.5, -1.167. Step 3: Order from coldest (smallest) to warmest (largest) on a number line: - The smallest is -3. - Next is -2.5. - Next is -1.167. - Next is 0.167. - The largest is 0.5. Step 4: Write the order using the original forms: -3, -2.5, -1 1/6, 1/6, 0.5. Final answer: -3, -2.5, -1 1/6, 1/6, 0.5.

  5. Order: -3.5, 7/3, -1.75, 0.6, -2.25 Answer: -3.5, -2.25, -1.75, 0.6, 7/3 Solution: Convert all numbers to decimals for easy comparison. -3.5 is already a decimal. 7/3 = 2.333...
    Full step-by-step solution

    Step 1: Convert all numbers to decimals for easy comparison. -3.5 is already a decimal. 7/3 = 2.333... (repeating) -1.75 is already a decimal. 0.6 is already a decimal. -2.25 is already a decimal. Step 2: List the numbers in decimal form: -3.5, 2.333..., -1.75, 0.6, -2.25 Step 3: Order from least to greatest (most negative to most positive). On a number line, the smallest number is the one farthest to the left. -3.5 is the smallest (most negative). Next is -2.25. Then -1.75. Then 0.6 (positive but less than 2.333...). Finally, 7/3 = 2.333... is the largest. Step 4: Write the ordered list: -3.5, -2.25, -1.75, 0.6, 7/3 The answer is -3.5, -2.25, -1.75, 0.6, 7/3.

  6. Order: -3/4, 1.25, -1.5, 0.5, -2.25 Answer: -2.25, -1.5, -3/4, 0.5, 1.25 Solution: Convert all numbers to decimals for easy comparison: -3/4 = -0.75, 1.25 stays 1.25, -1.5 stays -1.5, 0.5 stays 0.5, -2.25 stays -2.25. Write the ordered list: -2.25, -1.5, -3/4, 0.5, 1.25.
    Full step-by-step solution

    Step 1: Convert all numbers to decimals for easy comparison: -3/4 = -0.75, 1.25 stays 1.25, -1.5 stays -1.5, 0.5 stays 0.5, -2.25 stays -2.25. Step 2: List the numbers from least to greatest (left to right on the number line): Start with the most negative: -2.25, then -1.5, then -0.75 (-3/4), then 0.5, then 1.25. Step 3: Write the ordered list: -2.25, -1.5, -3/4, 0.5, 1.25. The answer is -2.25, -1.5, -3/4, 0.5, 1.25.

  7. Isabella is helping her science class create a giant number line on the classroom floor to show the freezing points of different liquids. She needs to mark the following temperatures (in degrees Celsius) from least to greatest: -9.5, 15/2, -4 1/3, 6.75, -8.2, and 1/4. What is the correct order from least to greatest? Answer: -9.5, -8.2, -4 1/3, 1/4, 15/2, 6.75 Solution: Convert all numbers to decimals for easy comparison. -9.5 is already a decimal. 15/2 = 7.5 -4 1/3 = -(4 + 1/3) = -(4 + 0.3333...) = -4.3333...
    Full step-by-step solution

    Step 1: Convert all numbers to decimals for easy comparison. -9.5 is already a decimal. 15/2 = 7.5 -4 1/3 = -(4 + 1/3) = -(4 + 0.3333...) = -4.3333... (approximately -4.333) 6.75 is already a decimal. -8.2 is already a decimal. 1/4 = 0.25 Step 2: List all decimals: -9.5, 7.5, -4.333, 6.75, -8.2, 0.25 Step 3: Order from least to greatest (most negative to most positive): -9.5 is the smallest (most negative). Next is -8.2, since -8.2 is more negative than -4.333. Then -4.333 (which is -4 1/3). Now for positives: 0.25 (which is 1/4), then 6.75, then 7.5 (which is 15/2). Step 4: Write the ordered list using the original forms: -9.5, -8.2, -4 1/3, 1/4, 15/2, 6.75. The answer is -9.5, -8.2, -4 1/3, 1/4, 15/2, 6.75.

  8. (-3.25) + 2.75 - (-1.5) = ? Answer: 1 Solution: Start with the expression: (-3.25) + 2.75 - (-1.5) Subtracting a negative becomes addition: (-3.25) + 2.75 + 1.5 Add the first two numbers: -3.25 + 2.75 = -0.5 Add the result to the last number: -0.5 + 1.5 = 1.0 The final answer is 1.
    Full step-by-step solution

    Step 1: Start with the expression: (-3.25) + 2.75 - (-1.5) Step 2: Subtracting a negative becomes addition: (-3.25) + 2.75 + 1.5 Step 3: Add the first two numbers: -3.25 + 2.75 = -0.5 Step 4: Add the result to the last number: -0.5 + 1.5 = 1.0 Step 5: The final answer is 1.