Unit Fractions

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Unit Fractions · Grade 3 · Worksheet 2

1. Liam is building a rectangular garden bed that is 8 feet long and 5 feet wide. He wants to divide the garden into equal square sections to plant different vegetables. If he makes sections that are each 1 square foot, how many sections will his garden have? Answer: 40 Solution: We have a rectangular garden bed with a length of 8 feet and a width of 5 feet. We want to divide it into equal square sections, each with an area of 1 square foot. We need to find the total number of such sections.
   Full step-by-step solution

   Step 1: Understand the problem. We have a rectangular garden bed with a length of 8 feet and a width of 5 feet. We want to divide it into equal square sections, each with an area of 1 square foot. We need to find the total number of such sections. Step 2: Find the total area of the garden bed. The area of a rectangle is length multiplied by width. So, Area = length × width = 8 feet × 5 feet. Step 3: Calculate the area. 8 × 5 = 40. So, the total area is 40 square feet. Step 4: Relate the area to the number of sections. Each section is 1 square foot. So, the number of sections = total area ÷ area of one section. That is: 40 square feet ÷ 1 square foot per section = 40 sections. Step 5: Final answer. Liam’s garden will have 40 sections.

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

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

3. Noah has a large rectangular cake that is divided into 7 equal rectangular slices, arranged in a single row. If the total area of the cake is 875 square centimeters, what is the area of each slice? Answer: 125 Solution: The cake is divided into 7 equal slices. The total area of the cake is 875 square centimeters. To find the area of one slice, divide the total area by the number of slices: 875 divided by 7.
   Full step-by-step solution

   Step 1: The cake is divided into 7 equal slices. Step 2: The total area of the cake is 875 square centimeters. Step 3: To find the area of one slice, divide the total area by the number of slices: 875 divided by 7. Step 4: 875 divided by 7 equals 125. Step 5: Each slice has an area of 125 square centimeters. The answer is 125.

4. Emma is helping her teacher divide a large 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 they create? Answer: 24 Solution: The bulletin board is 6 feet long and 4 feet wide. Each section is a square that is 1 foot by 1 foot. Along the length, 6 sections will fit because 6 ÷ 1 = 6.
   Full step-by-step solution

   Step 1: The bulletin board is 6 feet long and 4 feet wide. Step 2: Each section is a square that is 1 foot by 1 foot. Step 3: Along the length, 6 sections will fit because 6 ÷ 1 = 6. Step 4: Along the width, 4 sections will fit because 4 ÷ 1 = 4. Step 5: To find the total number of sections, multiply the number of sections along the length by the number of sections along the width: 6 × 4 = 24. The answer is 24 sections.

5. 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.