Whole as Fractions

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Answer Key & Explanations

Whole as Fractions · Grade 3 · Worksheet 1

1. 3/1 + 4/1 = ? Answer: 7 Solution: We are adding two fractions: 3/1 and 4/1. Both fractions have the same denominator, which is 1. When adding fractions with the same denominator, we keep the denominator the same and add the numerators.
   Full step-by-step solution

   Step 1: We are adding two fractions: 3/1 and 4/1. Step 2: Both fractions have the same denominator, which is 1. When adding fractions with the same denominator, we keep the denominator the same and add the numerators. Step 3: Add the numerators: 3 + 4 = 7. Step 4: Write the result as a fraction with the common denominator: 7/1. Step 5: Simplify the fraction. Any number divided by 1 is equal to itself. So, 7/1 = 7. Therefore, 3/1 + 4/1 = 7.

2. Lily is helping her teacher organize the classroom library. They have 96 books to put on shelves. If each shelf can hold 12 books, how many shelves will they need for all the books? Answer: 8 Solution: Lily has 96 books total Each shelf can hold 12 books To find how many shelves are needed, divide the total books by the books per shelf: 96 ÷ 12 12 × 8 = 96 Therefore, 96 ÷ 12 = 8 They will need 8 shelves to hold all the books.
   Full step-by-step solution

   Step 1: Lily has 96 books total Step 2: Each shelf can hold 12 books Step 3: To find how many shelves are needed, divide the total books by the books per shelf: 96 ÷ 12 Step 4: 12 × 8 = 96 Step 5: Therefore, 96 ÷ 12 = 8 They will need 8 shelves to hold all the books.

3. A rectangular garden is divided into 8 equal sections. If 3 sections are planted with tomatoes, what fraction of the garden has tomatoes? Write your answer as a fraction. Answer: 3/8 Solution: The garden is divided into 8 equal sections. This means the whole garden is represented by 8 sections. Identify the part in question.
   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 the part in question. We are told that 3 of these sections are planted with tomatoes. Step 3: Write the fraction. A fraction is written as (number of parts we have) / (total number of equal parts). So, the fraction of the garden with tomatoes is (number of tomato sections) / (total sections). Step 4: Substitute the numbers. Number of tomato sections = 3 Total sections = 8 Therefore, the fraction is 3/8. Step 5: State the answer. The fraction of the garden that has tomatoes is 3/8.

4. A rectangular classroom floor is covered with square tiles. The floor is 8 tiles long and 6 tiles wide. If 12 of these tiles are a different color to mark the reading area, what fraction of the total floor tiles are the different color? Write your answer as a fraction in simplest form. Answer: 1/4 Solution: 8 tiles long × 6 tiles wide = 48 total tiles The problem states 12 tiles are a different color 12/48 Both 12 and 48 can be divided by 12 12 ÷ 12 = 1 48 ÷ 12 = 4 So 12/48 = 1/4 The answer is 1/4.
   Full step-by-step solution

   Step 1: Find the total number of tiles on the floor 8 tiles long × 6 tiles wide = 48 total tiles Step 2: Identify how many tiles are the different color The problem states 12 tiles are a different color Step 3: Write the fraction of different colored tiles 12/48 Step 4: Simplify the fraction Both 12 and 48 can be divided by 12 12 ÷ 12 = 1 48 ÷ 12 = 4 So 12/48 = 1/4 The answer is 1/4.

5. Liam is organizing his baseball card collection. He has 120 cards in total and wants to put them equally into 8 different albums. How many cards should Liam put in each album? Answer: 15 Solution: 1. He wants to split them equally into 8 albums. We need to find how many cards go into each album.
   Full step-by-step solution

   Let's go step by step. 1. Understand the problem: Liam has 120 baseball cards in total. He wants to split them equally into 8 albums. We need to find how many cards go into each album. 2. Set up the math: To split equally, we divide the total number of cards by the number of albums. So, we calculate: 120 ÷ 8 3. Perform the division: 8 × 15 = 120 So, 120 ÷ 8 = 15 4. Interpret the result: This means each album gets 15 cards. 5. Check: 8 albums × 15 cards per album = 120 cards total. This matches the total number of cards Liam has. Final answer: 15

6. 16/1 = ? Answer: 16 Solution: The fraction is 16/1. Step 2: Any whole number can be written as itself over 1. Step 3: 16/1 means 16 divided by 1, which equals 16.
   Full step-by-step solution

   Step 1: The fraction is 16/1. Step 2: Any whole number can be written as itself over 1. Step 3: 16/1 means 16 divided by 1, which equals 16. The answer is 16.

7. 72/8 + 54/9 = ? Answer: 15 Solution: Simplify 72/8 by dividing 72 by 8. 72 ÷ 8 = 9 Simplify 54/9 by dividing 54 by 9. 54 ÷ 9 = 6 Add the results: 9 + 6 = 15 The answer is 15.
   Full step-by-step solution

   Step 1: Simplify 72/8 by dividing 72 by 8. 72 ÷ 8 = 9 Step 2: Simplify 54/9 by dividing 54 by 9. 54 ÷ 9 = 6 Step 3: Add the results: 9 + 6 = 15 The answer is 15.

8. Lily is organizing her sticker collection into a new sticker book. She has 84 stickers total and wants to put 6 stickers on each page. How many pages will Lily fill completely with her stickers? Answer: 14 Solution: Lily has 84 stickers total. She wants to put 6 stickers on each page.
   Full step-by-step solution

   Step 1: Lily has 84 stickers total. Step 2: She wants to put 6 stickers on each page. Step 3: To find how many pages she can fill, divide the total stickers by stickers per page: 84 ÷ 6 Step 4: 84 ÷ 6 = 14 Step 5: Check: 14 pages × 6 stickers per page = 84 stickers The answer is 14 pages.

9. Liam is helping his teacher organize the classroom library. They have 72 books to put on shelves. If each shelf can hold 8 books, how many shelves will they need for all the books? Answer: 9 Solution: We are told there are 72 books and each shelf holds 8 books. We want to find how many shelves are needed for all the books. Set up the division.
   Full step-by-step solution

   We are told there are 72 books and each shelf holds 8 books. We want to find how many shelves are needed for all the books. Step 1: Set up the division. We divide the total number of books by the number of books per shelf: 72 ÷ 8 Step 2: Perform the division. 8 × 9 = 72, so 72 ÷ 8 = 9. Step 3: Interpret the result. Since 72 divided by 8 equals 9, that means we need 9 shelves to hold all the books. Step 4: Check for remainder. There is no remainder because 72 is exactly divisible by 8, so no extra shelf is needed beyond the 9. Final answer: 9 shelves.