Compare Multi-Digit

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Answer Key & Explanations

Compare Multi-Digit · Grade 4 · Worksheet 3

1. A rectangular garden is drawn with a length of 24 meters and a width of 18 meters. A circular fountain with a diameter of 6 meters is placed in the center of the garden. What is the area of the garden that is NOT covered by the fountain? (Use π = 3.14) Answer: B. 379.74 m² Solution: Area of rectangle = length × width = 24 m × 18 m = 432 m² Radius = diameter ÷ 2 = 6 m ÷ 2 = 3 m Area of circle = π × radius² = 3.14 × (3 m)² = 3.14 × 9 m² = 28.26 m² Area not covered = area of rectangle - area of circle = 432 m² - 28.26 m² = 379.74 m² The correct answer is 379.74 m².
   Full step-by-step solution

   Step 1: Calculate the area of the rectangular garden Area of rectangle = length × width = 24 m × 18 m = 432 m² Step 2: Calculate the radius of the circular fountain Radius = diameter ÷ 2 = 6 m ÷ 2 = 3 m Step 3: Calculate the area of the circular fountain Area of circle = π × radius² = 3.14 × (3 m)² = 3.14 × 9 m² = 28.26 m² Step 4: Calculate the area NOT covered by the fountain Area not covered = area of rectangle - area of circle = 432 m² - 28.26 m² = 379.74 m² The correct answer is 379.74 m².

2. Aroha is collecting data on the number of books in two school libraries. The North School library has 135,729 books, and the South School library has 135,792 books. Which school library has more books? Answer: South School Solution: Write the two numbers: 135,729 and 135,792. Compare the hundred-thousands place: both have 1, so they are equal. Compare the ten-thousands place: both have 3, so they are still equal.
   Full step-by-step solution

   Step 1: Write the two numbers: 135,729 and 135,792. Step 2: Compare the hundred-thousands place: both have 1, so they are equal. Step 3: Compare the ten-thousands place: both have 3, so they are still equal. Step 4: Compare the thousands place: both have 5, so they are still equal. Step 5: Compare the hundreds place: both have 7, so they are still equal. Step 6: Compare the tens place: North School has 2, South School has 9. Step 7: Since 2 is less than 9, 135,729 is less than 135,792. Step 8: Therefore, South School library has more books. Final answer: South School

3. 4,321 > 4,123 = ? Answer: A. true Solution: Compare the thousands place. Both numbers have 4 in the thousands place. 4,321 → thousands digit = 4 4,123 → thousands digit = 4 So far, they are equal.
   Full step-by-step solution

   Let's compare the two numbers step by step. Step 1: Compare the thousands place. Both numbers have 4 in the thousands place. 4,321 → thousands digit = 4 4,123 → thousands digit = 4 So far, they are equal. Step 2: Compare the hundreds place. 4,321 → hundreds digit = 3 4,123 → hundreds digit = 1 Since 3 > 1, the number 4,321 is greater than 4,123. Step 3: Conclusion. We don't need to check the tens or ones digits because the hundreds place already decides the comparison. Therefore, 4,321 > 4,123 is true.

4. Charlotte is comparing the distances of two hiking trails in a national park. The Eagle Trail is 23,947 feet long, and the Bear Trail is 23,794 feet long. Which trail is longer? Answer: Eagle Trail Solution: Write both numbers: 23,947 and 23,794. Step 2: Compare the ten-thousands place: both have 2. Step 3: Compare the thousands place: both have 3.
   Full step-by-step solution

   Step 1: Write both numbers: 23,947 and 23,794. Step 2: Compare the ten-thousands place: both have 2. Step 3: Compare the thousands place: both have 3. Step 4: Compare the hundreds place: 9 (Eagle) vs. 7 (Bear). Since 9 is greater than 7, 23,947 is greater than 23,794. Step 5: Therefore, the Eagle Trail is longer. The answer is Eagle Trail.

5. Isabella is comparing the populations of two towns for her social studies project. The population of Oakville is 4,372, and the population of Lakewood is 4,327. Which town has a larger population? Answer: Oakville Solution: Write both numbers aligned by place value: 4,372 and 4,327. Compare the thousands place: both have 4, so they are the same. Compare the hundreds place: both have 3, so they are the same.
   Full step-by-step solution

   Step 1: Write both numbers aligned by place value: 4,372 and 4,327. Step 2: Compare the thousands place: both have 4, so they are the same. Step 3: Compare the hundreds place: both have 3, so they are the same. Step 4: Compare the tens place: Oakville has 7, Lakewood has 2. Since 7 is greater than 2, Oakville's number is larger. Step 5: Therefore, Oakville has the larger population. Answer: Oakville

6. Charlotte is comparing the number of steps she walked in two different months for her fitness challenge. In March, she walked 572,917 steps. In April, she walked 572,971 steps. In which month did Charlotte walk more steps? Answer: April Solution: Write the two numbers: 572,917 and 572,971. Both numbers have 6 digits. Compare the hundred-thousands place: both have 5, so they are equal.
   Full step-by-step solution

   Step 1: Write the two numbers: 572,917 and 572,971. Both numbers have 6 digits. Step 2: Compare the hundred-thousands place: both have 5, so they are equal. Step 3: Compare the ten-thousands place: both have 7, so they are equal. Step 4: Compare the thousands place: both have 2, so they are equal. Step 5: Compare the hundreds place: both have 9, so they are equal. Step 6: Compare the tens place: March has 1, April has 7. Since 1 is less than 7, 572,917 is less than 572,971. Step 7: Therefore, April has more steps. Final answer: April