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Order Rationals

Grade 6 · Ratios · Worksheet 1

  1. Emma is tracking her bank account balance. On Monday, she had $1,250. On Tuesday, she deposited her paycheck of $850. On Wednesday, she paid her rent of $1,100 and then bought groceries for $95. On Thursday, she received a refund of $45. What was her final account balance on Thursday? Answer: ______________
  2. Mason is organizing a set of rational numbers for his math project. He needs to order the following numbers from least to greatest and then plot them on a number line: -2.7, 1/2, -1 2/7, 0.8, -1.2, 3/4. Help Mason order these numbers correctly. Answer: ______________
  3. Order: -8.5, 11/2, -9, 4.75, -7/4 Answer: ______________
  4. Order: -3/5, 1.75, -2, 0.5, -1.25 Answer: ______________
  5. (-2.75) + 4.5 - (-1.25) = ? Answer: ______________
  6. Emma is preparing a science fair display about the melting points of different substances. She recorded the following temperatures (in degrees Celsius) for five materials: -5.75, 7/2, -2 1/3, 0.4, and -1.5. Emma needs to order these temperatures from least to greatest to correctly place them on a number line for her display. What is the correct order? Answer: ______________
  7. Order: -2.5, 3/4, -1.25, 1.5, -1/2 Answer: ______________
  8. Liam is drawing a number line from -10 to 10. He needs to plot the following numbers in order from least to greatest: -7.5, 15/2, -5, 2.5, -3 1/2, 0, -10/5. Help Liam arrange them in order from least to greatest. Answer: ______________
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Answer Key & Explanations

Order Rationals · Grade 6 · Worksheet 1

  1. Emma is tracking her bank account balance. On Monday, she had $1,250. On Tuesday, she deposited her paycheck of $850. On Wednesday, she paid her rent of $1,100 and then bought groceries for $95. On Thursday, she received a refund of $45. What was her final account balance on Thursday? Answer: $950 Solution: Start with Monday's balance: $1,250 Add Tuesday's paycheck: $1,250 + $850 = $2,100 Subtract Wednesday's rent: $2,100 - $1,100 = $1,000 Subtract Wednesday's groceries: $1,000 - $95 = $905 Add Thursday's refund: $905 + $45 = $950 Emma's final account balance on Thursday was $950.
    Full step-by-step solution

    Step 1: Start with Monday's balance: $1,250 Step 2: Add Tuesday's paycheck: $1,250 + $850 = $2,100 Step 3: Subtract Wednesday's rent: $2,100 - $1,100 = $1,000 Step 4: Subtract Wednesday's groceries: $1,000 - $95 = $905 Step 5: Add Thursday's refund: $905 + $45 = $950 Emma's final account balance on Thursday was $950.

  2. Mason is organizing a set of rational numbers for his math project. He needs to order the following numbers from least to greatest and then plot them on a number line: -2.7, 1/2, -1 2/7, 0.8, -1.2, 3/4. Help Mason order these numbers correctly. Answer: -2.7, -1 2/7, -1.2, 1/2, 3/4, 0.8 Solution: Convert all numbers to decimals for easy comparison. -2.7 is already a decimal. 1/2 = 0.5 -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. 1/2 = 0.5 -1 2/7 = -(1 + 2/7) = -(1 + 0.2857...) = -1.2857... which rounds to -1.2857 0.8 is already a decimal. -1.2 is already a decimal. 3/4 = 0.75 Step 2: List all decimals: -2.7, 0.5, -1.2857, 0.8, -1.2, 0.75 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: 0.5, 0.75, 0.8. Order: 0.5, 0.75, 0.8. Step 4: Write the ordered list using the original forms: -2.7, -1 2/7, -1.2, 1/2, 3/4, 0.8. The answer is -2.7, -1 2/7, -1.2, 1/2, 3/4, 0.8.

  3. Order: -8.5, 11/2, -9, 4.75, -7/4 Answer: -9, -8.5, -7/4, 4.75, 11/2 Solution: Convert all numbers to decimals. Negative numbers: -9, -8.5, -1.75 Positive numbers: 4.75, 5.5 -9 < -8.5 < -1.75 < 4.75 < 5.5 -9, -8.5, -7/4, 4.75, 11/2
    Full step-by-step solution

    Step 1: Convert all numbers to decimals. 11/2 = 5.5 -7/4 = -1.75 So the set is: -8.5, 5.5, -9, 4.75, -1.75 Step 2: Order from least to greatest (left to right on number line). Negative numbers: -9, -8.5, -1.75 Positive numbers: 4.75, 5.5 Step 3: Arrange in increasing order: -9 < -8.5 < -1.75 < 4.75 < 5.5 Step 4: Write the answer using the original forms: -9, -8.5, -7/4, 4.75, 11/2

  4. Order: -3/5, 1.75, -2, 0.5, -1.25 Answer: -2, -1.25, -3/5, 0.5, 1.75 Solution: Convert all numbers to decimals for easy comparison: -3/5 = -0.6, 1.75 stays 1.75, -2 stays -2, 0.5 stays 0.5, -1.25 stays -1.25. Write the final order: -2, -1.25, -3/5, 0.5, 1.75.
    Full step-by-step solution

    Step 1: Convert all numbers to decimals for easy comparison: -3/5 = -0.6, 1.75 stays 1.75, -2 stays -2, 0.5 stays 0.5, -1.25 stays -1.25. Step 2: Order from least to greatest (left to right on number line): Start with the most negative: -2, then -1.25, then -0.6 (which is -3/5), then 0.5, then 1.75. Step 3: Write the final order: -2, -1.25, -3/5, 0.5, 1.75. The answer is -2, -1.25, -3/5, 0.5, 1.75.

  5. (-2.75) + 4.5 - (-1.25) = ? Answer: 3 Solution: Start with the expression: (-2.75) + 4.5 - (-1.25) Simplify the subtraction of a negative: -(-1.25) becomes +1.25 Rewrite the expression: (-2.75) + 4.5 + 1.25 Add the positive numbers first: 4.5 + 1.25 = 5.75 Now add the negative number: 5.75 + (-2.75) = 5.75 - 2.75 Calculate: 5.75 - 2.75 = 3…
    Full step-by-step solution

    Step 1: Start with the expression: (-2.75) + 4.5 - (-1.25) Step 2: Simplify the subtraction of a negative: -(-1.25) becomes +1.25 Step 3: Rewrite the expression: (-2.75) + 4.5 + 1.25 Step 4: Add the positive numbers first: 4.5 + 1.25 = 5.75 Step 5: Now add the negative number: 5.75 + (-2.75) = 5.75 - 2.75 Step 6: Calculate: 5.75 - 2.75 = 3 The answer is 3.

  6. Emma is preparing a science fair display about the melting points of different substances. She recorded the following temperatures (in degrees Celsius) for five materials: -5.75, 7/2, -2 1/3, 0.4, and -1.5. Emma needs to order these temperatures from least to greatest to correctly place them on a number line for her display. What is the correct order? Answer: -5.75, -2 1/3, -1.5, 0.4, 7/2 Solution: Convert all numbers to decimals for easy comparison. -5.75 is already a decimal. 7/2 = 3.5.
    Full step-by-step solution

    Step 1: Convert all numbers to decimals for easy comparison. -5.75 is already a decimal. 7/2 = 3.5. -2 1/3 = -(2 + 1/3) = -(2 + 0.333...) = -2.333... (repeating). 0.4 is already a decimal. -1.5 is already a decimal. Step 2: List all decimals: -5.75, 3.5, -2.333..., 0.4, -1.5. Step 3: Order from least to greatest (most negative to most positive): -5.75 is the smallest (most negative). Next, compare -2.333... and -1.5. Since -2.333... is more negative than -1.5, it comes next. Then -1.5. Now for positives: 0.4 and 3.5. 0.4 is less than 3.5. So the order is: -5.75, -2.333..., -1.5, 0.4, 3.5. Step 4: Write the ordered list using the original forms: -5.75, -2 1/3, -1.5, 0.4, 7/2. The answer is -5.75, -2 1/3, -1.5, 0.4, 7/2.

  7. 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.

  8. Liam is drawing a number line from -10 to 10. He needs to plot the following numbers in order from least to greatest: -7.5, 15/2, -5, 2.5, -3 1/2, 0, -10/5. Help Liam arrange them in order from least to greatest. Answer: -7.5, -5, -10/5, -3 1/2, 0, 2.5, 15/2 Solution: Convert all numbers to decimals. 15/2 = 7.5, -3 1/2 = -3.5, -10/5 = -2. Identify negatives: -7.5, -5, -3.5, -2.
    Full step-by-step solution

    Step 1: Convert all numbers to decimals. 15/2 = 7.5, -3 1/2 = -3.5, -10/5 = -2. So the list is: -7.5, 7.5, -5, 2.5, -3.5, 0, -2. Step 2: Identify negatives: -7.5, -5, -3.5, -2. Order them from least to greatest (most negative first): -7.5, -5, -3.5, -2. Step 3: Identify positives: 0, 2.5, 7.5. Order from least to greatest: 0, 2.5, 7.5. Step 4: Combine the ordered lists: -7.5, -5, -3.5, -2, 0, 2.5, 7.5. Step 5: Convert back to original forms: -7.5 stays -7.5, -5 stays -5, -3.5 becomes -3 1/2, -2 becomes -10/5, 0 stays 0, 2.5 stays 2.5, 7.5 becomes 15/2. The final order from least to greatest is: -7.5, -5, -10/5, -3 1/2, 0, 2.5, 15/2.