Unit Fractions

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Unit Fractions · Grade 3 · Worksheet 1

1. A rectangular garden is divided into 8 equal sections. If 5 sections are planted with tomatoes, what fraction of the garden has tomatoes? Answer: 5/8 Solution: The garden is a rectangle divided into 8 equal sections. This means the whole garden is represented by 8 sections. Identify how many sections have tomatoes.
   Full step-by-step solution

   Step 1: Understand the problem. The garden is a rectangle divided into 8 equal sections. This means the whole garden is represented by 8 sections. Step 2: Identify how many sections have tomatoes. The problem says 5 sections are planted with tomatoes. Step 3: Determine the fraction. A fraction is formed by: (Number of parts with tomatoes) / (Total number of equal parts). So, fraction with tomatoes = 5 / 8. Step 4: Conclusion. Since 5 out of 8 equal sections have tomatoes, the fraction of the garden with tomatoes is 5/8.

2. Isabella is making a large rectangular pan of lasagna for a family dinner. The lasagna is 9 inches long and 6 inches wide. She wants to cut the entire pan into equal square servings, each 1 inch by 1 inch. Each serving will be one piece. How many equal square pieces will Isabella have in total? Answer: 54 Solution: The lasagna is 9 inches long. Each square piece is 1 inch long, so 9 ÷ 1 = 9 pieces fit along the length. The lasagna is 6 inches wide.
   Full step-by-step solution

   Step 1: The lasagna is 9 inches long. Each square piece is 1 inch long, so 9 ÷ 1 = 9 pieces fit along the length. Step 2: The lasagna is 6 inches wide. Each square piece is 1 inch wide, so 6 ÷ 1 = 6 pieces fit along the width. Step 3: To find the total number of square pieces, multiply the number along the length by the number along the width: 9 × 6 = 54. The answer is 54.

3. A farmer divides a rectangular field into 12 equal sections. If 7 sections are planted with corn, what fraction of the field is planted with corn? Answer: 7/12 Solution: The field is divided into 12 equal sections, so the total number of parts is 12. 7 sections are planted with corn, so 7 out of 12 parts have corn.
   Full step-by-step solution

   Step 1: The field is divided into 12 equal sections, so the total number of parts is 12. Step 2: 7 sections are planted with corn, so 7 out of 12 parts have corn. Step 3: The fraction is written as the number of planted sections over the total sections: 7/12. The answer is 7/12.

4. A farmer divides a rectangular field into 12 equal sections. If 7 sections are planted with corn, what fraction of the field has corn? Answer: 7/12 Solution: The field is divided into 12 equal sections, so the whole field represents 12/12. 7 sections are planted with corn, so the fraction with corn is 7 out of 12. Write this as a fraction: 7/12.
   Full step-by-step solution

   Step 1: The field is divided into 12 equal sections, so the whole field represents 12/12. Step 2: 7 sections are planted with corn, so the fraction with corn is 7 out of 12. Step 3: Write this as a fraction: 7/12. The answer is 7/12.

5. Hana is making a large rectangular garden for her vegetables. The garden is 8 feet long and 6 feet wide. She wants to divide the entire garden into equal square plots that are each 2 feet by 2 feet. How many square plots will she have? Answer: 12 Solution: Find how many 2-foot squares fit along the length. The garden is 8 feet long. Each square is 2 feet long.
   Full step-by-step solution

   Step 1: Find how many 2-foot squares fit along the length. The garden is 8 feet long. Each square is 2 feet long. 8 ÷ 2 = 4 squares fit along the length. Step 2: Find how many 2-foot squares fit along the width. The garden is 6 feet wide. Each square is 2 feet wide. 6 ÷ 2 = 3 squares fit along the width. Step 3: Multiply the number of squares along the length by the number along the width to get the total: 4 × 3 = 12. The answer is 12.