Improper Fractions

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Answer Key & Explanations

Improper Fractions · Grade 3 · Worksheet 1

1. Liam is making fruit smoothies for his soccer team. He has 17/4 cups of strawberries to use. How many whole cups of strawberries does Liam have, and how many extra fourths of a cup are left over? Answer: 4 whole cups and 1 extra fourth Solution: Start with 17/4 cups of strawberries Since 4/4 = 1 whole cup, divide 17 by 4 17 ÷ 4 = 4 with remainder 1 This means 17/4 = 4 whole cups and 1/4 cup left over So Liam has 4 whole cups and 1 extra fourth of a cup
   Full step-by-step solution

   Step 1: Start with 17/4 cups of strawberries Step 2: Since 4/4 = 1 whole cup, divide 17 by 4 Step 3: 17 ÷ 4 = 4 with remainder 1 Step 4: This means 17/4 = 4 whole cups and 1/4 cup left over Step 5: So Liam has 4 whole cups and 1 extra fourth of a cup

2. 7/3 + 2/3 = ? Answer: 3 Solution: Add the numerators: 7 + 2 = 9 Keep the denominator the same: 9/3 Simplify the fraction: 9 ÷ 3 = 3 The answer is 3.
   Full step-by-step solution

   Step 1: Add the numerators: 7 + 2 = 9 Step 2: Keep the denominator the same: 9/3 Step 3: Simplify the fraction: 9 ÷ 3 = 3 The answer is 3.

3. Noah is making fruit punch for a school party. He has 17/4 cups of orange juice. How many whole cups of orange juice does Noah have, and how many extra fourths of a cup are left over? Answer: 4 whole cups and 1 extra fourth Solution: An improper fraction has a numerator that is larger than its denominator. To understand it, we can see how many whole units we can make from the parts.
   Full step-by-step solution

   An improper fraction has a numerator that is larger than its denominator. To understand it, we can see how many whole units we can make from the parts. For example, if you have 7/2 of a pizza, you can see how many whole pizzas that is and how many slices are left.

4. Convert 17/4 to a mixed number. Answer: 4 1/4 Solution: Divide the numerator (17) by the denominator (4). 17 ÷ 4 = 4 with a remainder of 1. The whole number part of the mixed number is the quotient, which is 4.
   Full step-by-step solution

   Step 1: Divide the numerator (17) by the denominator (4). Step 2: 17 ÷ 4 = 4 with a remainder of 1. Step 3: The whole number part of the mixed number is the quotient, which is 4. Step 4: The fractional part is the remainder (1) over the original denominator (4), which is 1/4. Step 5: Combine the whole number and the fraction: 4 + 1/4 = 4 1/4. The answer is 4 1/4.

5. Convert 17/5 to a mixed number. Answer: 3 2/5 Solution: Divide the numerator (17) by the denominator (5). 17 ÷ 5 = 3 with a remainder of 2. The quotient (3) becomes the whole number part of the mixed number.
   Full step-by-step solution

   Step 1: Divide the numerator (17) by the denominator (5). Step 2: 17 ÷ 5 = 3 with a remainder of 2. Step 3: The quotient (3) becomes the whole number part of the mixed number. Step 4: The remainder (2) becomes the numerator of the fraction part. Step 5: The denominator (5) stays the same. Step 6: Combine the whole number and the fraction: 3 2/5. The answer is 3 2/5.

6. A rectangular garden is divided into 8 equal square plots. If the gardener plants vegetables in 7 of these plots, what improper fraction represents the part of the garden with vegetables? Then convert this improper fraction to a mixed number. Answer: 7/8, 7/8 is already a proper fraction Solution: The garden is divided into 8 equal plots, so the whole garden is represented by 8/8. Vegetables are planted in 7 plots, so the fraction is 7/8. Check if this is an improper fraction.
   Full step-by-step solution

   Step 1: The garden is divided into 8 equal plots, so the whole garden is represented by 8/8. Step 2: Vegetables are planted in 7 plots, so the fraction is 7/8. Step 3: Check if this is an improper fraction. An improper fraction has a numerator larger than the denominator. Here, 7 is less than 8, so 7/8 is actually a proper fraction. Step 4: Since it's already a proper fraction, it doesn't need to be converted to a mixed number. The answer is 7/8, which is already a proper fraction.

7. Lily baked 24 cookies for her class party. She wants to put them into goodie bags, with each bag holding exactly 5 cookies. How many full goodie bags can Lily make, and how many cookies will be left over? Answer: 4 full bags with 4 cookies left over Solution: Lily has 24 cookies. Each bag holds 5 cookies. We need to find how many full bags she can make and how many cookies will be left over.
   Full step-by-step solution

   Let's solve this step by step. Step 1: Understand the problem. Lily has 24 cookies. Each bag holds 5 cookies. We need to find how many full bags she can make and how many cookies will be left over. Step 2: Find how many full bags. To find the number of full bags, we divide the total cookies by the number of cookies per bag, but only take the whole number part. 24 ÷ 5 = 4 remainder something, because 5 × 4 = 20, and 5 × 5 = 25 (too many). Step 3: Calculate the remainder. If 4 full bags use 5 × 4 = 20 cookies, then the leftover cookies are: 24 − 20 = 4 cookies. Step 4: Conclusion. Lily can make 4 full goodie bags, and there will be 4 cookies left over. Final answer: 4 full bags with 4 cookies left over.

8. A rectangular garden is divided into 8 equal sections. If 5 sections are planted with tomatoes, what improper fraction represents the tomato sections? Then convert this improper fraction to a mixed number. Answer: 5/8 and 5/8 is already a proper fraction Solution: The garden is divided into 8 equal sections, so the total number of sections is 8. 5 sections are planted with tomatoes. Write the fraction representing tomato sections.
   Full step-by-step solution

   Step 1: Understand the problem. The garden is divided into 8 equal sections, so the total number of sections is 8. 5 sections are planted with tomatoes. Step 2: Write the fraction representing tomato sections. The fraction is: number of tomato sections / total sections = 5/8. Step 3: Check if 5/8 is an improper fraction. An improper fraction has a numerator larger than or equal to the denominator. Here, numerator = 5, denominator = 8. Since 5 is less than 8, 5/8 is a proper fraction, not an improper fraction. Step 4: Since it is already a proper fraction, it does not need to be converted to a mixed number. A mixed number is used when an improper fraction is greater than or equal to 1, but 5/8 is less than 1. Step 5: Final answer. The fraction for tomato sections is 5/8, and it is already a proper fraction.

9. Liam is baking cookies for his class party. He has 17/4 cups of chocolate chips to use. How many whole cups of chocolate chips does Liam have? Answer: 4 1/4 Solution: We are told Liam has 17/4 cups of chocolate chips. Understand what 17/4 means. 17/4 means 17 divided by 4.
   Full step-by-step solution

   Let's work through the problem step-by-step. We are told Liam has 17/4 cups of chocolate chips. Step 1: Understand what 17/4 means. 17/4 means 17 divided by 4. Step 2: Divide 17 by 4. 4 goes into 17 four times because 4 × 4 = 16. Step 3: Find the remainder. 17 − 16 = 1. Step 4: Write as a mixed number. Since 17/4 = 4 with remainder 1, we can write it as: 4 whole cups and 1/4 of a cup. Step 5: Final answer. So, 17/4 cups = 4 1/4 cups. Liam has 4 whole cups and 1/4 cup of chocolate chips.