Estimate sums and differences: word problems

Key notes :

🎁1. Importance of Estimation in Word Problems

  • Estimation: Helps quickly determine if an answer is reasonable without needing the exact calculation.
  • Usefulness: Particularly helpful when making quick decisions, budgeting, or planning in real-life situations where an exact number isn’t necessary.

🎄2. Steps to Solve Word Problems with Estimation

  1. Read the Problem Carefully:
    • Identify what is being asked: Is it asking for a sum, a difference, or both?
    • Look for clues that suggest estimation is appropriate, such as words like “about,” “approximately,” or “around.”
  2. Round the Numbers:
    • Round the numbers in the problem to a nearby place value (nearest ten, hundred, or thousand) that makes the math simpler.
    • Example: If the problem involves 347 and 589, you might round these to 350 and 600.
  3. Estimate the Sum or Difference:
    • Addition: Add the rounded numbers to get an estimated sum.
      • Example: 350+600=950
    • Subtraction: Subtract the rounded numbers to get an estimated difference.
      • Example: 600−350=250
  4. Check the Reasonableness of the Estimate:
    • After estimating, consider whether the estimate makes sense in the context of the problem.
    • Optionally, calculate the exact sum or difference to compare with the estimate.

🎨3. Common Types of Word Problems

  1. Shopping Scenarios:
    • Example: “If you buy items priced at $47, $53, and $29, estimate the total cost.”
    • Estimation: Round to 50+50+30=130
  2. Distance or Travel Problems:
    • Example: “Estimate the total distance if you drive 423 miles to one place and 275 miles to another.”
    • Estimation: Round to 400+300=700 miles.
  3. Budgeting Problems:
    • Example: “You have $950. If you spend $234 and $319, estimate how much money you have left.”
    • Estimation: Round to 950−(230+320), which simplifies to 950−550=400.

🎍4. Estimation Techniques

  1. Front-End Estimation:
    • Focus on the largest place value (e.g., hundreds) for a quick estimate.
    • Example: 562+437→ Estimate using 500+400=900.
  2. Rounding:
    • Round each number to the nearest ten, hundred, or thousand before performing the operation.
    • Example: 723+487 → Round to 720+490
  3. Compatible Numbers:
    • Adjust numbers slightly to make mental math easier.
    • Example: For 399+502, round to 400+500 for an estimate.

🎀5. Practice Problems

  1. Word Problem Example 1:
    • Problem: “Sarah buys 3 books for $24 each and a notebook for $8. Estimate her total spending.”
    • Estimation: Round to 25×3+10=75+10=85
  2. Word Problem Example 2:
    • Problem: “A truck carries 1,276 pounds of cargo to one city and 843 pounds to another. Estimate the total cargo weight.”
    • Estimation: Round to 1,300+800=2,100 pounds.
  3. Word Problem Example 3:
    • Problem: “You had $500 and spent $178 on groceries and $145 on clothes. Estimate how much money you have left.”
    • Estimation: Round to 500−(180+150)=500−330=170

🎃6. Tips for Estimating in Word Problems

  • Choose Appropriate Place Values: Decide whether to round to the nearest ten, hundred, or thousand based on the problem’s context.
  • Use Estimation to Verify: After solving the exact problem, use estimation to check if your answer is reasonable.
  • Practice Estimating Quickly: The more you practice, the quicker and more accurate your estimations will become.

Learn with an example

🗼 A total of 6,00,085 students took a standardized test last year. 2,34,122 students scored above average scores.

About how many students scored at or below average on the test? Choose the better estimate.

Subtract the number of students who received above average scores from the total number of students.

6,00,085 − 2,34,122 = ?

Round each number to the nearest hundred thousand.

6,00,085 – 2,34,122 = ?
6,00,0002,00,000 = 4,00,000

4,00,000 is the better estimate.

🗼 A treasure hunter discovered a buried treasure chest. He opened it up and discovered that it contained 1,804 diamonds and 6,543 rubies.

About how many gems were in the chest? Choose the better estimate.

Add the number of diamonds and the number of rubies.

1,804 + 6,543 = ?

Round each number to the nearest thousand.

1,804 + 6,543 = ?
2,000 + 7,000 = 9,000

9,000 is the better estimate.

🗼 A petri dish originally contained 38,035 bacteria. A scientist let the bacteria grow and now there are 98,667 of them.

About how many more bacteria are there now? Choose the better estimate.

  • 60,000
  • 90,000

Subtract the original number of bacteria from the number of bacteria now .

98,667 – 38,035 = ?

Round each number to the nearest ten thousand.

60,000 is the better estimate.

Let’s practice!