Fractions Equal Parts

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Answer Key & Explanations

Fractions Equal Parts · Grade 3 · Worksheet 1

1. A rectangular garden is divided into 8 equal sections. If 3 sections are planted with tomatoes and the rest with carrots, what fraction of the garden is planted with carrots? Answer: 5/8 Solution: The garden is divided into 8 equal sections. Determine how many sections are tomatoes. The problem says 3 sections are planted with tomatoes.
   Full step-by-step solution

   Step 1: Understand the problem. The garden is divided into 8 equal sections. So, the whole garden is represented as 8/8. Step 2: Determine how many sections are tomatoes. The problem says 3 sections are planted with tomatoes. Step 3: Find how many sections are carrots. Total sections = 8 Tomato sections = 3 Carrot sections = 8 - 3 = 5 Step 4: Write the fraction for carrots. Since there are 5 carrot sections out of 8 total sections, the fraction is 5/8. Step 5: Conclusion. The fraction of the garden planted with carrots is 5/8.

2. Liam is helping his teacher set up chairs for the school concert. He needs to arrange 72 chairs into 8 equal rows. How many chairs should Liam put in each row? Answer: 9 Solution: We are told that Liam has 72 chairs and must arrange them into 8 equal rows. To find how many chairs go in each row, we need to divide the total chairs by the number of rows. Write the division problem.
   Full step-by-step solution

   We are told that Liam has 72 chairs and must arrange them into 8 equal rows. To find how many chairs go in each row, we need to divide the total chairs by the number of rows. Step 1: Write the division problem. Total chairs = 72 Number of rows = 8 So, chairs per row = 72 ÷ 8. Step 2: Think about what 72 ÷ 8 means. We are splitting 72 into 8 equal groups. We can also think: 8 times what number equals 72? Step 3: Recall the multiplication fact for 8. 8 × 9 = 72. Since 8 × 9 = 72, then 72 ÷ 8 = 9. Step 4: Conclusion. Liam should put 9 chairs in each row. Final answer: 9

3. Liam is helping his teacher organize the classroom library. They have 72 books that need to be placed equally on 8 shelves. How many books should Liam put on each shelf? Answer: 9 Solution: We have 72 books total and 8 shelves. We want to split the books equally among the shelves. That means we need to divide 72 by 8.
   Full step-by-step solution

   We have 72 books total and 8 shelves. We want to split the books equally among the shelves. That means we need to divide 72 by 8. Step 1: Write the division problem. 72 ÷ 8 = ? Step 2: Think about multiplication — what number times 8 equals 72? 8 × 9 = 72. Step 3: So, 72 ÷ 8 = 9. Step 4: This means each shelf gets 9 books. Answer: Liam should put 9 books on each shelf.

4. Shade 1/6 of the rectangle. Answer: 1/6 Solution: The rectangle is divided into 6 equal parts. The denominator is 6, so the whole is split into 6 equal pieces. The numerator is 1, so we need to shade exactly 1 of those 6 equal parts.
   Full step-by-step solution

   Step 1: The rectangle is divided into 6 equal parts. The denominator is 6, so the whole is split into 6 equal pieces. Step 2: The numerator is 1, so we need to shade exactly 1 of those 6 equal parts. Step 3: Choose any one part and shade it completely. Step 4: The shaded part represents the fraction 1/6 of the whole rectangle. The answer is 1/6.

5. A rectangular garden is divided into 8 equal sections. If 3 sections are planted with carrots and 2 sections are planted with tomatoes, what fraction of the garden is planted with vegetables? Answer: 5/8 Solution: The garden is divided into 8 equal sections. This means the whole garden can be represented by the fraction 8/8. Identify the planted sections.
   Full step-by-step solution

   Step 1: Understand the problem. The garden is divided into 8 equal sections. This means the whole garden can be represented by the fraction 8/8. Step 2: Identify the planted sections. Carrots are planted in 3 sections. Tomatoes are planted in 2 sections. Step 3: Find the total number of sections planted with vegetables. Add the carrot sections and the tomato sections: 3 + 2 = 5. Step 4: Write this as a fraction of the whole garden. Since there are 8 equal sections in total, 5 sections out of 8 is written as the fraction 5/8. Step 5: State the final answer. Therefore, the fraction of the garden planted with vegetables is 5/8.

6. Shade 9/11 of the rectangle. Answer: 9/11 Solution: The rectangle is divided into 11 equal parts. The denominator is 11, which tells us the total number of equal parts. Step 2: The numerator is 9, which tells us how many parts to shade.
   Full step-by-step solution

   Step 1: The rectangle is divided into 11 equal parts. The denominator is 11, which tells us the total number of equal parts. Step 2: The numerator is 9, which tells us how many parts to shade. Step 3: Shade 9 of the 11 equal parts. Step 4: The shaded fraction is 9/11. The answer is 9/11.

7. Hana shades 2/3 of a rectangle that is divided into 12 equal parts. How many parts does she shade? Answer: 8 Solution: The rectangle is divided into 12 equal parts. The fraction 2/3 means 2 out of every 3 equal parts are shaded. To find how many parts that is, divide the total number of parts (12) by the denominator (3): 12 ÷ 3 = 4.
   Full step-by-step solution

   Step 1: The rectangle is divided into 12 equal parts. The fraction 2/3 means 2 out of every 3 equal parts are shaded. Step 2: To find how many parts that is, divide the total number of parts (12) by the denominator (3): 12 ÷ 3 = 4. This tells us each 'third' has 4 parts. Step 3: Since the numerator is 2, we take 2 groups of 4: 2 × 4 = 8. Step 4: Hana shades 8 parts of the rectangle. The answer is 8.

8. A rectangular garden is divided into 15 equal square sections. The gardener plants flowers in 8 sections and vegetables in 4 sections. The remaining sections are left for herbs. What fraction of the garden is planted with flowers? Answer: 8/15 Solution: The garden is divided into 15 equal sections, so the whole garden is represented by 15/15. Flowers are planted in 8 sections, so the fraction for flowers is 8 out of 15 total sections. Write this as a fraction: 8/15.
   Full step-by-step solution

   Step 1: The garden is divided into 15 equal sections, so the whole garden is represented by 15/15. Step 2: Flowers are planted in 8 sections, so the fraction for flowers is 8 out of 15 total sections. Step 3: Write this as a fraction: 8/15. The answer is 8/15.

9. Emma is helping her teacher organize the school art supplies. They have 64 colored pencils that need to be divided equally among 8 art boxes. How many colored pencils should Emma put in each art box? Answer: 8 Solution: Identify the total number of colored pencils: 64 Identify the number of art boxes: 8 Divide the total pencils by the number of boxes: 64 ÷ 8 Calculate: 64 ÷ 8 = 8 Check: 8 boxes × 8 pencils per box = 64 pencils total Emma should put 8 colored pencils in each art box.
   Full step-by-step solution

   Step 1: Identify the total number of colored pencils: 64 Step 2: Identify the number of art boxes: 8 Step 3: Divide the total pencils by the number of boxes: 64 ÷ 8 Step 4: Calculate: 64 ÷ 8 = 8 Step 5: Check: 8 boxes × 8 pencils per box = 64 pencils total Emma should put 8 colored pencils in each art box.