Fractions Number Line

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Answer Key & Explanations

Fractions Number Line · Grade 3 · Worksheet 1

1. Tane is helping his grandmother bake bread. The recipe calls for 1 and 1/3 cups of water, but Tane's measuring cup only shows fractions up to 1 cup. He draws a number line from 0 to 2 to help him find where 1 and 1/3 is. On a number line from 0 to 2, between which two whole numbers does 1 and 1/3 lie? Answer: 1 and 2 Solution: The whole numbers on it are 0, 1, and 2. The fraction 1 and 1/3 means 1 whole plus 1/3 of another whole. Since 1 and 1/3 is greater than 1 (because it has a whole and a part), it cannot be between 0 and 1.
   Full step-by-step solution

   Step 1: Look at the number line from 0 to 2. The whole numbers on it are 0, 1, and 2. Step 2: The fraction 1 and 1/3 means 1 whole plus 1/3 of another whole. Step 3: Since 1 and 1/3 is greater than 1 (because it has a whole and a part), it cannot be between 0 and 1. Step 4: Since 1 and 1/3 is less than 2 (because 1 + 1/3 = 1.33, and 2 is 2.00), it cannot be between 1 and 2. Step 5: Therefore, 1 and 1/3 lies between 1 and 2 on the number line. The answer is 1 and 2.

2. A number line is marked from 0 to 1 and divided into 8 equal parts. A point is placed on the mark that is 5 parts from 0. What fraction represents the location of this point? Answer: 5/8 Solution: That means each part represents 1/8 of the whole length. Identify the location of the point. The point is placed on the mark that is 5 parts from 0.
   Full step-by-step solution

   Step 1: Understand the problem. The number line goes from 0 to 1 and is divided into 8 equal parts. That means each part represents 1/8 of the whole length. Step 2: Identify the location of the point. The point is placed on the mark that is 5 parts from 0. Since each part is 1/8, 5 parts from 0 means 5 × (1/8). Step 3: Calculate the fraction. 5 × (1/8) = 5/8. Step 4: Interpret the result. The fraction 5/8 means the point is five-eighths of the way from 0 to 1. Final Answer: 5/8

3. Tane is helping his grandmother make a long garland for a party. The garland needs to be 12 feet long. They have a measuring tape that goes from 0 to 12 feet. Tane needs to attach a decoration at the point that represents 5/6 of the total length on the measuring tape. How many feet from the start should Tane attach the decoration? Answer: 10 Solution: The total length of the garland is 12 feet. We need to find 5/6 of 12 feet. Step 2: The denominator 6 means the whole length is divided into 6 equal parts.
   Full step-by-step solution

   Step 1: The total length of the garland is 12 feet. We need to find 5/6 of 12 feet. Step 2: The denominator 6 means the whole length is divided into 6 equal parts. Step 3: Divide the total length by the denominator: 12 divided by 6 equals 2. So each part is 2 feet long. Step 4: The numerator 5 means we need 5 of those equal parts. Multiply: 5 times 2 equals 10. Step 5: So 5/6 of 12 feet is 10 feet. The answer is 10.

4. A baker is making a long loaf of bread that measures 84 centimeters from end to end. She needs to cut the loaf into 7 equal pieces. What fraction of the whole loaf is each piece? Answer: 1/7 Solution: The baker has a loaf that is 84 cm long and needs to cut it into 7 equal pieces. We are asked what fraction of the whole loaf each piece is. Think about what "7 equal pieces" means.
   Full step-by-step solution

   Step 1: Understand the problem. The baker has a loaf that is 84 cm long and needs to cut it into 7 equal pieces. We are asked what fraction of the whole loaf each piece is. Step 2: Think about what "7 equal pieces" means. If you divide something into 7 equal parts, each part is 1 out of the 7 parts of the whole. Step 3: Write the fraction. Since the whole loaf is 1 (as a whole), and it is divided into 7 equal pieces, each piece is 1/7 of the whole loaf. Step 4: Note that the length 84 cm is extra information. We don't actually need the length to find the fraction, because the fraction is determined only by the number of equal pieces. If we did use the length: each piece length = 84 cm ÷ 7 = 12 cm. Fraction = (12 cm) / (84 cm) = 12/84 = 1/7 after simplifying. Step 5: Conclusion. Each piece is 1/7 of the whole loaf.

5. Carlos is walking on a nature trail that is 16 kilometers long. He stops to rest at a bench that is marked at the 3/4 point on the trail map's number line. How many kilometers has Carlos walked when he reaches the bench? Answer: 12 Solution: The total length of the trail is 16 kilometers. We need to find 3/4 of this total distance. To find a fraction of a number, we multiply the number by the fraction: 16 * (3/4).
   Full step-by-step solution

   Step 1: The total length of the trail is 16 kilometers. Step 2: We need to find 3/4 of this total distance. Step 3: To find a fraction of a number, we multiply the number by the fraction: 16 * (3/4). Step 4: First, multiply 16 by the numerator: 16 * 3 = 48. Step 5: Then, divide the result by the denominator: 48 / 4 = 12. Step 6: Carlos has walked 12 kilometers when he reaches the bench.

6. A number line from 0 to 1 is divided into 6 equal parts. A frog starts at 0 and jumps forward 4 of these equal parts. What fraction represents the frog's final position on the number line? Answer: 4/6 Solution: This means the whole line represents 1, and each part is 1/6. The frog starts at 0 and jumps forward 4 parts. This means it covers 4 of the 6 equal parts.
   Full step-by-step solution

   Step 1: The number line from 0 to 1 is divided into 6 equal parts. This means the whole line represents 1, and each part is 1/6. Step 2: The frog starts at 0 and jumps forward 4 parts. This means it covers 4 of the 6 equal parts. Step 3: To find the fraction, we put the number of parts the frog jumped (4) over the total number of parts (6). This gives us 4/6. The frog's final position is 4/6.

7. A farmer has a fence that is 96 feet long. She needs to mark the point that is 3/8 of the way from the left end. What fraction of the whole fence will be to the right of this mark? Answer: 5/8 Solution: The whole fence represents 1 whole or 8/8. The mark is placed 3/8 of the way from the left end. To find the fraction to the right of the mark, subtract 3/8 from the whole fence: 8/8 - 3/8 = 5/8.
   Full step-by-step solution

   Step 1: The whole fence represents 1 whole or 8/8. Step 2: The mark is placed 3/8 of the way from the left end. Step 3: To find the fraction to the right of the mark, subtract 3/8 from the whole fence: 8/8 - 3/8 = 5/8. Step 4: Therefore, 5/8 of the fence is to the right of the mark. The answer is 5/8.

8. Lily is baking cookies and needs to measure 3/4 cup of flour. She has a measuring cup that shows fractions from 0 to 1. If she starts at 0 and fills the cup, what fraction of the cup will be empty when she has exactly 3/4 cup of flour? Answer: 1/4 Solution: 1. The measuring cup goes from 0 (empty) to 1 (full). If she fills the cup to the 3/4 mark, that means 3/4 of the cup is full.
   Full step-by-step solution

   Let's go step by step. 1. Understand the problem: Lily wants exactly 3/4 cup of flour. The measuring cup goes from 0 (empty) to 1 (full). If she fills the cup to the 3/4 mark, that means 3/4 of the cup is full. 2. The total capacity of the cup is 1 whole. If the cup is full, the amount of flour is 1. If the cup has 3/4 flour, then the empty part is the remaining fraction. 3. To find the empty part: Empty part = Total capacity − Filled part Empty part = 1 − 3/4 4. Write 1 as a fraction: 1 = 4/4 5. Subtract: 4/4 − 3/4 = 1/4 6. Conclusion: When she has exactly 3/4 cup of flour, the fraction of the cup that is empty is 1/4. Final answer: 1/4