Improper Fractions

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Answer Key & Explanations

Improper Fractions · Grade 3 · Worksheet 2

1. 7/4 + 5/4 = ? Answer: 3 Solution: Add the numerators: 7 + 5 = 12 Keep the denominator the same: 12/4 Simplify the fraction: 12 ÷ 4 = 3 The answer is 3.
   Full step-by-step solution

   Step 1: Add the numerators: 7 + 5 = 12 Step 2: Keep the denominator the same: 12/4 Step 3: Simplify the fraction: 12 ÷ 4 = 3 Step 4: The answer is 3.

2. Liam is making fruit smoothies for his class party. He has 17/4 cups of blueberries to use. How many whole cups of blueberries 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 blueberries. Since 4/4 equals 1 whole cup, divide 17 by 4 to find how many whole cups. 17 ÷ 4 = 4 with a remainder of 1.
   Full step-by-step solution

   Step 1: Start with 17/4 cups of blueberries. Step 2: Since 4/4 equals 1 whole cup, divide 17 by 4 to find how many whole cups. Step 3: 17 ÷ 4 = 4 with a remainder of 1. Step 4: This means there are 4 whole cups (4 × 4/4 = 16/4). Step 5: The remaining 1/4 cup is the extra fourth. Step 6: So Liam has 4 whole cups and 1 extra fourth of a cup of blueberries.

3. Lily is baking cupcakes for her school bake sale. She has 17/4 cups of flour to use for the recipe. How many whole cups of flour does Lily 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 flour Each whole cup equals 4/4, so divide 17 by 4 17 ÷ 4 = 4 with remainder 1 This means 17/4 = 4 whole cups and 1/4 cup left over So Lily has 4 whole cups and 1 extra fourth of a cup The answer is 4 whole cups and 1 extra fourth.
   Full step-by-step solution

   Step 1: Start with 17/4 cups of flour Step 2: Each whole cup equals 4/4, so 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 Lily has 4 whole cups and 1 extra fourth of a cup The answer is 4 whole cups and 1 extra fourth.

4. Lily baked 17 cookies for her class party. She wants to put them equally into 4 goodie bags. How many cookies will be in each bag, and how many will be left over? Answer: 4 cookies in each bag with 1 left over Solution: We know Lily has 17 cookies and wants to put them equally into 4 bags. We need to divide 17 cookies into 4 equal groups. This means we will use division: 17 ÷ 4.
   Full step-by-step solution

   Let's solve this step by step. We know Lily has 17 cookies and wants to put them equally into 4 bags. Step 1: Understand the problem We need to divide 17 cookies into 4 equal groups. This means we will use division: 17 ÷ 4. Step 2: Perform the division 4 × 4 = 16 17 − 16 = 1 So, 17 ÷ 4 = 4 remainder 1. Step 3: Interpret the result The quotient (4) tells us how many cookies go into each bag. The remainder (1) tells us how many cookies are left over. Step 4: Conclusion Each bag gets 4 cookies, and 1 cookie will be left over.

5. Liam is baking cookies for his class party. The recipe calls for 3/4 cups of sugar. He needs to triple the recipe to make enough cookies for everyone. How many cups of sugar does Liam need in total? Write your answer as a mixed number. Answer: 2 1/4 Solution: First, the recipe calls for 3/4 cups of sugar. Liam needs to triple the recipe, so we multiply 3/4 by 3. Write the multiplication.
   Full step-by-step solution

   First, the recipe calls for 3/4 cups of sugar. Liam needs to triple the recipe, so we multiply 3/4 by 3. Step 1: Write the multiplication. 3/4 * 3 Step 2: Write 3 as a fraction to make multiplication easier. 3/4 * 3/1 Step 3: Multiply the numerators: 3 * 3 = 9 Multiply the denominators: 4 * 1 = 4 So we have 9/4. Step 4: Convert 9/4 to a mixed number. 4 goes into 9 two whole times (because 4 * 2 = 8), with a remainder of 1. So 9/4 = 2 and 1/4. Step 5: Final answer: Liam needs 2 1/4 cups of sugar in total.

6. A rectangular swimming pool is divided into 8 equal lanes for a swim meet. If swimmers are using 5 of these lanes, what improper fraction represents the lanes being used? Then convert this improper fraction to a mixed number. Answer: 5/8 and 5/8 Solution: The pool is divided into 8 equal lanes, so the denominator is 8. Swimmers are using 5 lanes, so the numerator is 5. The improper fraction is 5/8.
   Full step-by-step solution

   Step 1: The pool is divided into 8 equal lanes, so the denominator is 8. Step 2: Swimmers are using 5 lanes, so the numerator is 5. Step 3: The improper fraction is 5/8. Step 4: Since 5 is less than 8, this fraction is already in proper form and cannot be converted to a mixed number with a whole number part. Step 5: The mixed number is also 5/8. The improper fraction is 5/8 and the mixed number is 5/8.

7. 5/4 + 3/4 = ? Answer: 2 Solution: We are adding: 5/4 + 3/4 Identify that both fractions have the same denominator (4). When fractions have the same denominator, we can add the numerators together and keep the denominator the same.
   Full step-by-step solution

   Step-by-step solution: We are adding: 5/4 + 3/4 Step 1: Identify that both fractions have the same denominator (4). When fractions have the same denominator, we can add the numerators together and keep the denominator the same. Step 2: Add the numerators: 5 + 3 = 8 So, 5/4 + 3/4 = 8/4 Step 3: Simplify the fraction 8/4. 8 divided by 4 equals 2. So, 8/4 = 2 Final answer: 2

8. Liam is making fruit punch for a school party. The recipe calls for 7/3 cups of orange juice. How many whole cups of orange juice does Liam need, and how many extra thirds of a cup are left over? Answer: 2 whole cups and 1 extra third Solution: Start with the improper fraction 7/3 Divide 7 by 3 to find how many whole cups: 7 ÷ 3 = 2 with a remainder of 1 This means we have 2 whole cups and 1/3 cup left over So Liam needs 2 whole cups of orange juice with 1 extra third of a cup The answer is 2 whole cups and 1 extra third.
   Full step-by-step solution

   Step 1: Start with the improper fraction 7/3 Step 2: Divide 7 by 3 to find how many whole cups: 7 ÷ 3 = 2 with a remainder of 1 Step 3: This means we have 2 whole cups and 1/3 cup left over Step 4: So Liam needs 2 whole cups of orange juice with 1 extra third of a cup The answer is 2 whole cups and 1 extra third.

9. Liam is making fruit punch for a school party. The recipe calls for 11/4 cups of orange juice. How many whole cups of orange juice does Liam need, and how many extra fourths of a cup are left over? Answer: 2 whole cups and 3 extra fourths Solution: Start with the improper fraction 11/4 Divide 11 by 4 to find how many whole cups: 11 ÷ 4 = 2 with remainder 3 The quotient 2 represents the whole cups The remainder 3 represents the extra fourths of a cup So Liam needs 2 whole cups and 3 extra fourths of a cup The answer is 2 whole cups and 3…
   Full step-by-step solution

   Step 1: Start with the improper fraction 11/4 Step 2: Divide 11 by 4 to find how many whole cups: 11 ÷ 4 = 2 with remainder 3 Step 3: The quotient 2 represents the whole cups Step 4: The remainder 3 represents the extra fourths of a cup Step 5: So Liam needs 2 whole cups and 3 extra fourths of a cup The answer is 2 whole cups and 3 extra fourths.