Unit Fractions

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Unit Fractions · Grade 3 · Worksheet 1

1. A rectangular vegetable garden is divided into 6 equal square sections. The total area of the garden is 1,200 square feet. What is the area of each square section? Answer: 200 Solution: The total area of the garden is 1,200 square feet. The garden is divided into 6 equal sections.
   Full step-by-step solution

   Step 1: The total area of the garden is 1,200 square feet. Step 2: The garden is divided into 6 equal sections. Step 3: To find the area of one section, divide the total area by the number of sections: 1,200 ÷ 6 Step 4: Calculate: 1,200 ÷ 6 = 200 Step 5: Each square section has an area of 200 square feet.

2. 1/5 + 1/5 + 1/5 + 1/5 + 1/5 = ? Answer: 1 Solution: All fractions have the same denominator (5). Add the numerators: 1 + 1 + 1 + 1 + 1 = 5. Write the sum over the common denominator: 5/5.
   Full step-by-step solution

   Step 1: All fractions have the same denominator (5). Step 2: Add the numerators: 1 + 1 + 1 + 1 + 1 = 5. Step 3: Write the sum over the common denominator: 5/5. Step 4: Simplify: 5/5 = 1 whole. The answer is 1.

3. Emma is helping her teacher divide a rectangular bulletin board into equal sections for a class project. The bulletin board is 6 feet long and 4 feet wide. If they divide it into square sections that are each 1 foot by 1 foot, how many sections will the bulletin board have? Answer: 24 Solution: The bulletin board is a rectangle that is 6 feet long and 4 feet wide. To find the total number of 1-foot by 1-foot square sections, we need to find the area of the rectangle.
   Full step-by-step solution

   Step 1: The bulletin board is a rectangle that is 6 feet long and 4 feet wide. Step 2: To find the total number of 1-foot by 1-foot square sections, we need to find the area of the rectangle. Step 3: The area of a rectangle is found by multiplying length times width. Step 4: Area = 6 feet × 4 feet = 24 square feet. Step 5: Since each section is 1 square foot, the number of sections equals the area in square feet. The answer is 24 sections.

4. 1/6 + 1/6 + 1/6 = ? Answer: 1/2 Solution: All fractions have the same denominator (6). Add the numerators: 1 + 1 + 1 = 3. Write the sum over the common denominator: 3/6.
   Full step-by-step solution

   Step 1: All fractions have the same denominator (6). Step 2: Add the numerators: 1 + 1 + 1 = 3. Step 3: Write the sum over the common denominator: 3/6. Step 4: Simplify the fraction: 3/6 = 1/2. The answer is 1/2.

5. 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 = ? Answer: 1 Solution: All fractions have the same denominator (8). Count the number of unit fractions being added: there are 8 of them. Add the numerators: 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 8.
   Full step-by-step solution

   Step 1: All fractions have the same denominator (8). Step 2: Count the number of unit fractions being added: there are 8 of them. Step 3: Add the numerators: 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 8. Step 4: Write the sum over the common denominator: 8/8. Step 5: Simplify: 8/8 = 1 (any fraction where numerator equals denominator equals 1 whole). The answer is 1.

6. A rectangular garden is divided into 8 equal sections. If 3 sections are planted with tomatoes, what fraction of the garden has tomatoes? Answer: 3/8 Solution: The garden is 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 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 3 sections are planted with tomatoes. Step 3: Determine the fraction. A fraction is formed by: (Number of parts we are interested in) / (Total number of equal parts). Here, that is 3 sections out of 8 total sections. Step 4: Write the fraction. The fraction is 3/8. Step 5: Interpret the result. 3/8 of the garden has tomatoes. This fraction is already in simplest form since 3 and 8 have no common factors other than 1. Final Answer: 3/8

7. Liam is helping his teacher set up for a class party. He needs to divide a large rectangular sheet cake into equal pieces for all 24 students in his class. If he cuts the cake into rows and columns to make equal-sized square pieces, what fraction of the whole cake will each student get? Answer: 1/24 Solution: 1. The cake is a large rectangle. Liam cuts it into rows and columns to make equal-sized square pieces.
   Full step-by-step solution

   Let's think through the problem step by step. 1. The cake is a large rectangle. Liam cuts it into rows and columns to make equal-sized square pieces. 2. If there are R rows and C columns, the total number of pieces is R × C. 3. The problem says there are 24 students, and each student gets one piece, so the total number of pieces must be 24. So: R × C = 24. 4. Each piece is the same size and shape (a square), so each piece has the same area. 5. The fraction of the whole cake that one piece represents is: Fraction = 1 / (total number of pieces) 6. Since total pieces = 24, each piece is 1/24 of the whole cake. 7. Therefore, each student gets 1/24 of the cake. The number of rows and columns doesn't change the fraction as long as the total number of pieces is 24 and they are equal in size. Final answer: 1/24