Improper Fractions

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Answer Key & Explanations

Improper Fractions · Grade 3 · Worksheet 2

1. Emma is drawing a rectangular banner that is divided into 5 equal sections. She colors 8 of these sections for a school project. What improper fraction represents the sections she colored? Then convert that improper fraction to a mixed number. Answer: 8/5 and 1 3/5 Solution: The banner is divided into 5 equal sections, so each whole banner is 5/5. Step 2: Emma colors 8 sections, so the improper fraction is 8/5. Step 3: To convert 8/5 to a mixed number, divide 8 by 5.
   Full step-by-step solution

   Step 1: The banner is divided into 5 equal sections, so each whole banner is 5/5. Step 2: Emma colors 8 sections, so the improper fraction is 8/5. Step 3: To convert 8/5 to a mixed number, divide 8 by 5. 8 divided by 5 is 1 with a remainder of 3. Step 4: The whole number part is 1, and the remainder becomes the numerator over the same denominator (5). So the mixed number is 1 3/5. The answer is 8/5 and 1 3/5.

2. 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.

3. 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.

4. Sophia is organizing a field day for her class. She has 29/6 gallons of water to fill water bottles. How many whole gallons of water does Sophia have, and how many extra sixths of a gallon are left over? Answer: 4 whole gallons and 5 extra sixths Solution: Start with the improper fraction 29/6. A whole gallon is 6/6. So we need to find how many groups of 6/6 are in 29/6.
   Full step-by-step solution

   Step 1: Start with the improper fraction 29/6. Step 2: A whole gallon is 6/6. So we need to find how many groups of 6/6 are in 29/6. Step 3: Divide 29 by 6: 29 ÷ 6 = 4 with a remainder of 5. Step 4: This means we have 4 whole gallons (4 × 6/6 = 24/6) and 5 extra sixths (29/6 − 24/6 = 5/6). Step 5: So Sophia has 4 whole gallons and 5 extra sixths of a gallon of water.

5. Matiu is making a big batch of homemade granola bars for his soccer team. The recipe calls for 31/8 cups of oats. How many whole cups of oats does Matiu need, and how many extra eighths of a cup are left over? Answer: 3 whole cups and 7 extra eighths Solution: We start with 31/8 cups of oats. This means 31 eighths. Since 8/8 = 1 whole cup, we need to find how many groups of 8 are in 31.
   Full step-by-step solution

   Step 1: We start with 31/8 cups of oats. This means 31 eighths. Step 2: Since 8/8 = 1 whole cup, we need to find how many groups of 8 are in 31. Step 3: Divide 31 by 8: 31 ÷ 8 = 3 with a remainder of 7. Step 4: This means we can make 3 whole cups (3 × 8/8 = 24/8) and we have 7 eighths left over (31/8 - 24/8 = 7/8). Step 5: So Matiu needs 3 whole cups of oats and 7 extra eighths of a cup. The answer is 3 whole cups and 7 extra eighths.

6. A rectangular swimming pool is divided into 8 equal lanes for a swim meet. If swimmers use 7 of these lanes for racing, what improper fraction represents the lanes being used? Then convert this improper fraction to a mixed number. Answer: 7/8, 7/8 Solution: The pool is divided into 8 equal lanes, so the whole pool represents 8/8. Swimmers use 7 lanes, so the fraction of lanes being used is 7/8.
   Full step-by-step solution

   Step 1: The pool is divided into 8 equal lanes, so the whole pool represents 8/8. Step 2: Swimmers use 7 lanes, so the fraction of lanes being used is 7/8. Step 3: Since 7/8 is a proper fraction (numerator is less than denominator), it cannot be converted to a mixed number with a whole number part. Step 4: The fraction 7/8 is already in simplest form. The improper fraction is 7/8, and as a mixed number it remains 7/8.

7. Noah is baking mini pizzas for his class party. He has 17/4 cups of pizza sauce to spread evenly on the pizzas. How many whole cups of pizza sauce does Noah 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 pizza sauce. Know that 4/4 equals 1 whole cup. Divide 17 by 4 to see how many whole cups there are: 17 ÷ 4 = 4 with a remainder of 1.
   Full step-by-step solution

   Step 1: Start with 17/4 cups of pizza sauce. Step 2: Know that 4/4 equals 1 whole cup. Step 3: Divide 17 by 4 to see how many whole cups there are: 17 ÷ 4 = 4 with a remainder of 1. Step 4: This means there are 4 whole cups (which is 16/4) and 1/4 cup left over. Step 5: So, Noah has 4 whole cups and 1 extra fourth of a cup of pizza sauce.

8. 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.

9. Liam is baking a large batch of cookies for the school fair. He needs to measure out 17/4 cups of flour for the recipe. How many whole cups of flour does Liam need, and how many extra fourths of a cup are left over? Answer: 4 whole cups and 1 extra fourth Solution: Start with the improper fraction 17/4. Divide the numerator (17) by the denominator (4) to find how many whole cups: 17 ÷ 4 = 4 with a remainder. Calculate the remainder: 4 × 4 = 16, so 17 - 16 = 1.
   Full step-by-step solution

   Step 1: Start with the improper fraction 17/4. Step 2: Divide the numerator (17) by the denominator (4) to find how many whole cups: 17 ÷ 4 = 4 with a remainder. Step 3: Calculate the remainder: 4 × 4 = 16, so 17 - 16 = 1. Step 4: This means there are 4 whole cups and 1/4 cup left over. Liam needs 4 whole cups of flour and has 1 extra fourth of a cup.