Whole as Fractions

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Answer Key & Explanations

Whole as Fractions · Grade 3 · Worksheet 2

1. Liam is organizing his baseball card collection. He has 120 cards and wants to put them equally into 8 different albums. How many cards will be in each album? Answer: 15 Solution: We are told Liam has 120 cards and wants to put them equally into 8 albums. This means we need to divide the total number of cards by the number of albums. Write the division problem.
   Full step-by-step solution

   We are told Liam has 120 cards and wants to put them equally into 8 albums. This means we need to divide the total number of cards by the number of albums. Step 1: Write the division problem. Total cards = 120 Number of albums = 8 So we calculate: 120 ÷ 8 Step 2: Perform the division. We can think of it as: how many times does 8 go into 120? 8 × 10 = 80 120 − 80 = 40 8 × 5 = 40 40 − 40 = 0 So, 10 + 5 = 15. Step 3: Check the result. If each album gets 15 cards, then 8 albums would have: 8 × 15 = 120 cards. This matches the total number of cards. Step 4: Conclusion. Each album will have 15 cards. ANSWER: 15

2. Liam is organizing his baseball card collection. He has 120 cards total and wants to put them into albums. Each album page holds 8 cards. How many complete pages will Liam fill with his baseball cards? Answer: 15 Solution: Liam has 120 baseball cards total. Each album page holds 8 cards. We need to find how many complete pages he can fill.
   Full step-by-step solution

   Step 1: Understand the problem. Liam has 120 baseball cards total. Each album page holds 8 cards. We need to find how many complete pages he can fill. Step 2: Set up the division. To find the number of pages, divide the total number of cards by the number of cards per page: 120 ÷ 8 Step 3: Perform the division. 120 divided by 8 equals 15. We can check: 8 × 15 = 120. Step 4: Interpret the result. Since 120 divided by 8 is exactly 15, there is no remainder. This means all cards fit perfectly into 15 pages, with no leftover cards. Step 5: Final answer. Liam will fill 15 complete pages with his baseball cards.

3. 5/1 + 3/1 = ? Answer: 8 Solution: We are adding two fractions: 5/1 + 3/1. Recognize that both fractions have the same denominator, which is 1. When denominators are the same, we can add the numerators directly.
   Full step-by-step solution

   We are adding two fractions: 5/1 + 3/1. Step 1: Recognize that both fractions have the same denominator, which is 1. When denominators are the same, we can add the numerators directly. Step 2: Add the numerators: 5 + 3 = 8. Step 3: Keep the denominator the same: 8/1. Step 4: Simplify 8/1. Any number divided by 1 is itself, so 8/1 = 8. Final answer: 8

4. 27/3 = ? Answer: 9 Solution: The fraction is 27/3. This means 27 divided by 3. 27 ÷ 3 = 9.
   Full step-by-step solution

   Step 1: The fraction is 27/3. This means 27 divided by 3. Step 2: 27 ÷ 3 = 9. Step 3: So 27/3 equals the whole number 9. The answer is 9.

5. A rectangular garden is divided into 8 equal sections. If 3 sections are planted with carrots, what fraction of the garden has carrots? Write your answer as a fraction. Answer: 3/8 Solution: The garden is divided into 8 equal sections. Identify how many sections have carrots. The problem says 3 sections are planted with carrots.
   Full step-by-step solution

   Step 1: Understand the problem. The garden is divided into 8 equal sections. So, the whole garden is represented by 8 sections. Step 2: Identify how many sections have carrots. The problem says 3 sections are planted with carrots. Step 3: Write the fraction. A fraction is: (number of parts we are interested in) / (total number of equal parts). Here, that is 3 sections with carrots out of 8 total sections. Step 4: Form the fraction. So, the fraction of the garden with carrots is 3/8. Step 5: Check if it can be simplified. 3 and 8 have no common factors other than 1, so 3/8 is already in simplest form. Final answer: 3/8

6. Liam is helping his teacher organize books for the school library. He has 240 books that need to be placed equally on 8 empty shelves. How many books should Liam put on each shelf? Answer: 30 Solution: We are told that Liam has 240 books and needs to place them equally on 8 empty shelves. This means we need to divide the total number of books by the number of shelves. Write the division problem.
   Full step-by-step solution

   We are told that Liam has 240 books and needs to place them equally on 8 empty shelves. This means we need to divide the total number of books by the number of shelves. Step 1: Write the division problem. Total books = 240 Number of shelves = 8 So we calculate: 240 ÷ 8 Step 2: Perform the division. One way to think about it: 8 times what number equals 240? We can break 240 into 24 × 10. We know 8 × 3 = 24, so 8 × 30 = 240. Step 3: Check the reasoning. If 8 × 30 = 240, then 240 ÷ 8 = 30. This means each shelf gets 30 books. Step 4: Verify the answer. If there are 8 shelves and each has 30 books, total books = 8 × 30 = 240, which matches the problem. Therefore, Liam should put 30 books on each shelf.

7. Lucas is packing 8 cookies into boxes. Each box holds 8 cookies. How many full boxes can Lucas pack? Write your answer as a whole number. Answer: 1 Solution: Lucas has 8 cookies and each box holds 8 cookies. Step 2: Divide the total cookies by the box size: 8 ÷ 8 = 1. Step 3: This means Lucas can fill 1 boxes completely.
   Full step-by-step solution

   Step 1: Lucas has 8 cookies and each box holds 8 cookies. Step 2: Divide the total cookies by the box size: 8 ÷ 8 = 1. Step 3: This means Lucas can fill 1 boxes completely. The answer is 1.

8. Emma is making a batch of her favorite granola bars. The recipe calls for 3 whole cups of oats. Emma only has a 1/3 cup measuring scoop. How many scoops of oats does Emma need to use to get the 3 whole cups? Answer: 9 Solution: Emma needs 3 whole cups of oats. She is using a 1/3 cup scoop. This means each scoop is one part out of three equal parts that make one whole cup.
   Full step-by-step solution

   Step 1: Emma needs 3 whole cups of oats. Step 2: She is using a 1/3 cup scoop. This means each scoop is one part out of three equal parts that make one whole cup. Step 3: To make one whole cup, she needs 3 scoops (because 3 scoops of 1/3 cup each = 3/3 = 1 whole cup). Step 4: Since she needs 3 whole cups, multiply the number of scoops per cup by the number of cups: 3 scoops per cup × 3 cups = 9 scoops. Step 5: Check: 9 scoops of 1/3 cup each equals 9/3, which simplifies to 3 whole cups. The answer is 9 scoops.

9. 7/1 + 5/1 = ? Answer: 12 Solution: Write the whole numbers as fractions: 7 = 7/1 and 5 = 5/1. Since the denominators are the same (both are 1), add the numerators: 7 + 5 = 12. Write the result as a fraction: 12/1.
   Full step-by-step solution

   Step 1: Write the whole numbers as fractions: 7 = 7/1 and 5 = 5/1. Step 2: Since the denominators are the same (both are 1), add the numerators: 7 + 5 = 12. Step 3: Write the result as a fraction: 12/1. Step 4: Simplify 12/1 to get the whole number 12. The answer is 12.