Prime and Composite

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Answer Key & Explanations

Prime and Composite · Grade 4 · Worksheet 1

1. A rectangular garden is drawn with a length of 15 meters and a width of 12 meters. A triangular flower bed is placed in one corner of the garden, with its right angle at the corner. The triangle has legs measuring 5 meters and 6 meters. What is the area of the garden that is NOT covered by the flower bed? Answer: 165 Solution: Calculate the area of the rectangular garden. Area of rectangle = length × width = 15 × 12 = 180 square meters Calculate the area of the triangular flower bed.
   Full step-by-step solution

   Step 1: Calculate the area of the rectangular garden. Area of rectangle = length × width = 15 × 12 = 180 square meters Step 2: Calculate the area of the triangular flower bed. Area of triangle = (base × height) ÷ 2 = (5 × 6) ÷ 2 = 30 ÷ 2 = 15 square meters Step 3: Subtract the triangle's area from the rectangle's area to find the remaining garden area. Remaining area = 180 - 15 = 165 square meters The answer is 165.

2. 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 measures 4 meters on each side in one corner. What is the area of the garden that is NOT covered by the flower section? Answer: 80 Solution: Find the total area of the rectangular garden. The formula for the area of a rectangle is length × width. Length = 12 meters, width = 8 meters.
   Full step-by-step solution

   Step 1: Find the total area of the rectangular garden. The formula for the area of a rectangle is length × width. Length = 12 meters, width = 8 meters. Total area = 12 × 8 = 96 square meters. Step 2: Find the area of the square flower section. The formula for the area of a square is side × side. Side = 4 meters. Flower area = 4 × 4 = 16 square meters. Step 3: Find the area not covered by flowers. This is the total garden area minus the flower area. Area not covered = 96 − 16 = 80 square meters. Final answer: 80

3. Liam is organizing his rock collection into display cases. He has 127 rocks and wants to put the same number of rocks in each case. If he uses 7 cases, will there be any rocks left over? Explain how you know. Answer: Yes, there will be 1 rock left over Solution: Liam has 127 rocks and wants to divide them equally among 7 cases. Divide 127 by 7 to see if it divides evenly. 127 ÷ 7 = 18 with a remainder of 1 (because 7 × 18 = 126, and 127 - 126 = 1).
   Full step-by-step solution

   Step 1: Liam has 127 rocks and wants to divide them equally among 7 cases. Step 2: Divide 127 by 7 to see if it divides evenly. Step 3: 127 ÷ 7 = 18 with a remainder of 1 (because 7 × 18 = 126, and 127 - 126 = 1). Step 4: Since there is a remainder of 1, there will be 1 rock left over after putting 18 rocks in each of the 7 cases. The answer is: Yes, there will be 1 rock left over.

4. Noah is organizing his baseball card collection into albums. He has 127 cards and wants to put the same number of cards on each page. If he uses 7 pages, will he be able to place all cards equally with none left over? Explain why or why not. Answer: A. no Solution: We need to determine if 127 can be divided equally by 7 with no remainder. Calculate 127 ÷ 7 using long division. 7 × 18 = 126 127 - 126 = 1 Since there is a remainder of 1, 127 cannot be divided equally by 7.
   Full step-by-step solution

   Step 1: We need to determine if 127 can be divided equally by 7 with no remainder. Step 2: Calculate 127 ÷ 7 using long division. Step 3: 7 × 18 = 126 Step 4: 127 - 126 = 1 Step 5: Since there is a remainder of 1, 127 cannot be divided equally by 7. Step 6: Therefore, Noah cannot place all 127 cards equally on 7 pages with none left over.