Prime and Composite

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Answer Key & Explanations

Prime and Composite · Grade 4 · Worksheet 3

1. Emma is organizing her rock collection into display cases. She has 121 rocks and wants to arrange them into equal rows. If she tries to make 11 equal rows, will she have any rocks left over? Explain how you know whether 121 is a prime or composite number. Answer: No, because 121 is a composite number (11 × 11 = 121) Solution: To determine if a number is prime or composite, we check if it has factors other than 1 and itself. The number 17 is prime because its only factors are 1 and 17.
   Full step-by-step solution

   To determine if a number is prime or composite, we check if it has factors other than 1 and itself. For example, the number 15 is composite because it can be divided evenly by 3 and 5 (3 × 5 = 15). The number 17 is prime because its only factors are 1 and 17.

2. A rectangular garden is drawn on grid paper. The garden is 12 units long and 8 units wide. If each grid square represents 1 square meter, what is the area of the garden? Answer: 96 Solution: We are told the garden is a rectangle with length 12 units and width 8 units, and each grid square is 1 square meter. Recall the formula for the area of a rectangle.
   Full step-by-step solution

   We are told the garden is a rectangle with length 12 units and width 8 units, and each grid square is 1 square meter. Step 1: Recall the formula for the area of a rectangle. Area = length × width Step 2: Substitute the given values into the formula. Area = 12 × 8 Step 3: Multiply the numbers. 12 × 8 = 96 Step 4: Include the units. Since each grid square is 1 square meter, the area is 96 square meters. Final answer: 96

3. Is 91 a prime number or a composite number? Answer: composite Solution: A prime number has exactly two factors: 1 and itself. A composite number has more than two factors. Find the square root of 91.
   Full step-by-step solution

   Step 1: A prime number has exactly two factors: 1 and itself. A composite number has more than two factors. Step 2: Find the square root of 91. sqrt(91) is about 9.5, so we only need to test prime numbers less than or equal to 9: 2, 3, 5, and 7. Step 3: Test divisibility by 2. 91 is odd, so it is not divisible by 2. Step 4: Test divisibility by 3. Sum of digits: 9 + 1 = 10. 10 is not divisible by 3, so 91 is not divisible by 3. Step 5: Test divisibility by 5. The last digit of 91 is 1, not 0 or 5, so it is not divisible by 5. Step 6: Test divisibility by 7. 7 × 13 = 91. Since 91 ÷ 7 = 13 exactly, 91 is divisible by 7. Step 7: This means 91 has factors 1, 7, 13, and 91 — that is four factors. Step 8: Since 91 has more than two factors, it is a composite number. The answer is composite.

4. A rectangular garden is drawn with a length of 12 meters and a width of 8 meters. The gardener plants flowers in a square section that is 4 meters on each side, located in one corner of the garden. What is the area, in square meters, of the remaining part of the garden that is not planted with flowers? Answer: 80 Solution: Find the total area of the rectangular garden. The garden is a rectangle with length 12 m and width 8 m. Area of rectangle = length × width Total area = 12 × 8 = 96 square meters.
   Full step-by-step solution

   Step 1: Find the total area of the rectangular garden. The garden is a rectangle with length 12 m and width 8 m. Area of rectangle = length × width Total area = 12 × 8 = 96 square meters. Step 2: Find the area of the square section planted with flowers. The square has side length 4 m. Area of square = side × side Flower area = 4 × 4 = 16 square meters. Step 3: Subtract the flower area from the total garden area to find the remaining area. Remaining area = Total area − Flower area Remaining area = 96 − 16 = 80 square meters. Step 4: Conclusion. The area of the remaining part of the garden is 80 square meters.

5. Emma is organizing her sticker collection into equal rows for a display board. She has 121 stickers total. Can she arrange all her stickers into exactly 11 equal rows without any stickers left over? Explain why or why not. Answer: B. yes Solution: When we talk about arranging items into equal rows, we're really asking if one number divides evenly into another. A prime number can only be divided evenly by 1 and itself, while a composite number has other factors.
   Full step-by-step solution

   When we talk about arranging items into equal rows, we're really asking if one number divides evenly into another. A prime number can only be divided evenly by 1 and itself, while a composite number has other factors. For example, if you had 25 stickers and wanted to arrange them in 5 equal rows, that would work because 25 ÷ 5 = 5 with no remainder.