Order Rationals

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Order Rationals · Grade 6 · Worksheet 3

1. Charlotte is helping her science class prepare a number line display showing the elevation of different locations in a national park. She needs to order the following elevations (in meters) from least to greatest to place them correctly on the number line: -2.7, 3/5, -1 2/7, 0.2, -1.2, 7/8. Help Charlotte order these elevations from least to greatest. Answer: -2.7, -1 2/7, -1.2, 0.2, 3/5, 7/8 Solution: Convert all numbers to decimals for easy comparison. -2.7 is already a decimal. 3/5 = 0.6 -1 2/7 = -(1 + 2/7) = -(1 + 0.2857...) = -1.2857...
   Full step-by-step solution

   Step 1: Convert all numbers to decimals for easy comparison. -2.7 is already a decimal. 3/5 = 0.6 -1 2/7 = -(1 + 2/7) = -(1 + 0.2857...) = -1.2857... which rounds to -1.2857 0.2 is already a decimal. -1.2 is already a decimal. 7/8 = 0.875 Step 2: List all decimals: -2.7, 0.6, -1.2857, 0.2, -1.2, 0.875 Step 3: Order from least to greatest (most negative to most positive): -2.7 is the smallest (most negative). Next, compare -1.2857 and -1.2. Since -1.2857 is more negative than -1.2, it comes next. Then -1.2. Now for positives: 0.2, 0.6, 0.875. Order: 0.2, 0.6, 0.875. Step 4: Write the ordered list using the original forms: -2.7, -1 2/7, -1.2, 0.2, 3/5, 7/8. The answer is -2.7, -1 2/7, -1.2, 0.2, 3/5, 7/8.

2. (-2.5) + 3.75 - (-1.25) = ? Answer: 2.5 Solution: (-2.5) + 3.75 - (-1.25) Subtracting a negative number is the same as adding its positive: - (-1.25) = + 1.25 (-2.5) + 3.75 + 1.25 3.75 + 1.25 = 5.00 5.00 + (-2.5) = 5.00 - 2.50 = 2.50 2.5 Therefore, (-2.5) + 3.75 - (-1.25) = 2.5
   Full step-by-step solution

   Let's solve step-by-step: Step 1: Write the original problem (-2.5) + 3.75 - (-1.25) Step 2: Interpret the subtraction of a negative number Subtracting a negative number is the same as adding its positive: - (-1.25) = + 1.25 So the expression becomes: (-2.5) + 3.75 + 1.25 Step 3: Add the positive numbers first 3.75 + 1.25 = 5.00 Step 4: Now add the negative number to the result 5.00 + (-2.5) = 5.00 - 2.50 = 2.50 Step 5: Final answer 2.5 Therefore, (-2.5) + 3.75 - (-1.25) = 2.5

3. Order: -2.5, 3/4, -1.25, 1.5, -1/2 Answer: -2.5, -1.25, -1/2, 3/4, 1.5 Solution: Convert all numbers to decimals for easy comparison. 3/4 = 0.75, -1/2 = -0.5. The set is: -2.5, 0.75, -1.25, 1.5, -0.5.
   Full step-by-step solution

   Step 1: Convert all numbers to decimals for easy comparison. 3/4 = 0.75, -1/2 = -0.5. The set is: -2.5, 0.75, -1.25, 1.5, -0.5. Step 2: Order from least to greatest. Negative numbers are smaller than positive numbers. Among negatives: -2.5 < -1.25 < -0.5. Among positives: 0.75 < 1.5. Step 3: Combine: -2.5, -1.25, -0.5, 0.75, 1.5. Step 4: Convert back to original forms: -2.5, -1.25, -1/2, 3/4, 1.5. The answer is -2.5, -1.25, -1/2, 3/4, 1.5.

4. Liam is tracking the stock price of his favorite tech company over four days. On Monday, the stock was at $152.75. On Tuesday, it dropped by $12.50. On Wednesday, it gained $8.25. On Thursday, it dropped again by $5.75. What was the final stock price on Thursday? Answer: $142.75 Solution: Start with Monday's price: $152.75 Subtract Tuesday's drop: $152.75 - $12.50 = $140.25 Add Wednesday's gain: $140.25 + $8.25 = $148.50 Subtract Thursday's drop: $148.50 - $5.75 = $142.75 The final stock price on Thursday was $142.75.
   Full step-by-step solution

   Step 1: Start with Monday's price: $152.75 Step 2: Subtract Tuesday's drop: $152.75 - $12.50 = $140.25 Step 3: Add Wednesday's gain: $140.25 + $8.25 = $148.50 Step 4: Subtract Thursday's drop: $148.50 - $5.75 = $142.75 Step 5: The final stock price on Thursday was $142.75.

5. Order: -8.2, 13/4, -5, 6.75, -11/2 Answer: -8.2, -11/2, -5, 13/4, 6.75 Solution: Convert all numbers to decimals for easy comparison. 13/4 = 3.25 -11/2 = -5.5 So the set is: -8.2, 3.25, -5, 6.75, -5.5 Identify the negative numbers: -8.2, -5, -5.5 Order the negatives from least to greatest (most negative first): -8.2 is less than -5.5, and -5.5 is less than -5.
   Full step-by-step solution

   Step 1: Convert all numbers to decimals for easy comparison. 13/4 = 3.25 -11/2 = -5.5 So the set is: -8.2, 3.25, -5, 6.75, -5.5 Step 2: Identify the negative numbers: -8.2, -5, -5.5 Order the negatives from least to greatest (most negative first): -8.2 is less than -5.5, and -5.5 is less than -5. So negatives in order: -8.2, -5.5, -5 Step 3: Identify the positive numbers: 3.25, 6.75 Order the positives from least to greatest: 3.25, 6.75 Step 4: Combine the ordered negatives and positives: -8.2, -5.5, -5, 3.25, 6.75 Step 5: Write the final answer using the original forms: -8.2, -11/2, -5, 13/4, 6.75

6. Matiu is helping his class create a giant number line for the school hallway. He needs to plot the following elevations (in meters) from a geography field trip: -4.5, 2 3/4, -1.2, 3/2, and -3.25. Help Matiu order these elevations from least to greatest so he can place them correctly on the number line. Answer: -4.5, -3.25, -1.2, 3/2, 2 3/4 Solution: Convert all numbers to decimals for easy comparison. -4.5 is already a decimal. 2 3/4 = 2 + 3/4 = 2 + 0.75 = 2.75.
   Full step-by-step solution

   Step 1: Convert all numbers to decimals for easy comparison. -4.5 is already a decimal. 2 3/4 = 2 + 3/4 = 2 + 0.75 = 2.75. -1.2 is already a decimal. 3/2 = 1.5. -3.25 is already a decimal. Step 2: List all decimals: -4.5, 2.75, -1.2, 1.5, -3.25 Step 3: Order from least to greatest (most negative to most positive): -4.5 is the smallest (most negative). Next, compare -3.25 and -1.2. Since -3.25 is more negative than -1.2, it comes next. Then -1.2. Now for positives: 1.5, then 2.75. Step 4: Write the ordered list using the original forms: -4.5, -3.25, -1.2, 3/2, 2 3/4. The answer is -4.5, -3.25, -1.2, 3/2, 2 3/4.

7. Liam is tracking the stock prices of three tech companies over a week. TechCorp started at $125.50, dropped by $18.75, then rose by $12.25. DataSystems began at $98.80, rose by $15.40, then dropped by $8.60. CloudNet started at $142.20, dropped by $22.10, then rose by $9.85. What were the final stock prices for each company, and which one had the highest price at the end of the week? Answer: TechCorp: $119.00, DataSystems: $105.60, CloudNet: $129.95; CloudNet had the highest price Solution: Starting price: $125.50 After drop: $125.50 - $18.75 = $106.75 After rise: $106.75 + $12.25 = $119.00 Starting price: $98.80 After rise: $98.80 + $15.40 = $114.20 After drop: $114.20 - $8.60 = $105.60 Starting price: $142.20 After drop: $142.20 - $22.10 = $120.10 After rise: $120.10 + $9.85 =…
   Full step-by-step solution

   Step 1: Calculate TechCorp's final price Starting price: $125.50 After drop: $125.50 - $18.75 = $106.75 After rise: $106.75 + $12.25 = $119.00 Step 2: Calculate DataSystems' final price Starting price: $98.80 After rise: $98.80 + $15.40 = $114.20 After drop: $114.20 - $8.60 = $105.60 Step 3: Calculate CloudNet's final price Starting price: $142.20 After drop: $142.20 - $22.10 = $120.10 After rise: $120.10 + $9.85 = $129.95 Step 4: Compare the final prices TechCorp: $119.00 DataSystems: $105.60 CloudNet: $129.95 The highest price is CloudNet at $129.95.

8. Emma is tracking her bank account balance. She started with $1,250. She then deposited her paycheck of $875. Later, she paid her rent of $1,100 and bought groceries for $87.50. Finally, she transferred $200 to her savings account. What is her final bank account balance? Answer: 737.50 Solution: Start with the initial balance: $1,250 Add the paycheck deposit: $1,250 + $875 = $2,125 Subtract the rent payment: $2,125 - $1,100 = $1,025 Subtract the grocery payment: $1,025 - $87.50 = $937.50 Subtract the savings transfer: $937.50 - $200 = $737.50 The final balance is $737.50.
   Full step-by-step solution

   Step 1: Start with the initial balance: $1,250 Step 2: Add the paycheck deposit: $1,250 + $875 = $2,125 Step 3: Subtract the rent payment: $2,125 - $1,100 = $1,025 Step 4: Subtract the grocery payment: $1,025 - $87.50 = $937.50 Step 5: Subtract the savings transfer: $937.50 - $200 = $737.50 The final balance is $737.50.